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Sample records for linear elastic mechanics

  1. Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

    Wang, John T.

    2010-01-01

    The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

  2. Introduction to linear elasticity

    Gould, Phillip L

    2013-01-01

    Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also:  Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...

  3. Generalized linear elastic fracture mechanics: an application to a crack touching the bimaterial interface

    Náhlík, Luboš; Šestáková, L.; Hutař, Pavel; Knésl, Zdeněk

    2011-01-01

    Roč. 452-453, - (2011), s. 445-448 ISSN 1013-9826 R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GA101/09/1821 Institutional research plan: CEZ:AV0Z20410507 Keywords : generalized stress intensity factor * bimaterial interface * composite materials * strain energy density factor * fracture criterion * generalized linear elastic fracture mechanics Subject RIV: JL - Materials Fatigue, Friction Mechanics

  4. The application of linear elastic fracture mechanics to thermally stressed welded components

    Green, D.

    1981-01-01

    Linear Elastic Fracture Mechanics techniques are applied to components constructed from brittle materials and operating at low or ambient temperatures. It is argued that these techniques can justifiably be applied to components at high temperature provided that stresses are thermally induced, self-equilibrating and cyclic. Such loading conditions occur for example in an LMFBR and a simple welded detail containing a crevice is taken as an example. Theoretical and experimental estimates of crack growth in this component are compared and good agreement is shown. (author)

  5. The region of influence of significant defects and the mechanical vibrations of linear elastic solids

    Suarez Antola, R.

    2004-12-01

    The presence of cracks, voids or fields of pores, and their growth under applied forces or environmental actions, can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in machines and structures. A quite general expression for the square of modes proper frequency as a functional of displacement field, density field and elastic moduli fields is used as a starting point. The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields, introducing the concept of region of influence of each defect. This region of influence is derived from the relation between the stress field of flawed components in machines or structures, and the elastic energy released from a suitable reference state, due to the presence of significant defects in the above mentioned mechanical components. An approximate analytical expression is obtained, which relates the relative variation in the square of mode s proper frequency with position, size, shape and orientation of defects in mode displacement field. Some simple mathematical models of machine and structural elements with cracks or fields of pores are considered as examples. The connections between the relative lowering in the square of mode s proper frequency and the stress intensity factor of a defect are discussed : the concept of region of influence of a defect is used as a bridge between (low frequency and low amplitude) vibration dynamics and linear elastic fracture mechanics. Some limitations of the present approach are discussed as well as the possibility of applying the region of influence of defects to the damping of normal modes of vibration

  6. Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations.

    Kim, Dae-Hyeong; Song, Jizhou; Choi, Won Mook; Kim, Hoon-Sik; Kim, Rak-Hwan; Liu, Zhuangjian; Huang, Yonggang Y; Hwang, Keh-Chih; Zhang, Yong-wei; Rogers, John A

    2008-12-02

    Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.

  7. The Relationships between Weight Functions, Geometric Functions,and Compliance Functions in Linear Elastic Fracture Mechanics

    Yuan, Rong [Univ. of California, Berkeley, CA (United States)

    2007-01-01

    Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight

  8. Elastic plastic fracture mechanics

    Simpson, L.A.

    1978-07-01

    The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)

  9. Non-linear elastic deformations

    Ogden, R W

    1997-01-01

    Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

  10. Uniqueness theorems in linear elasticity

    Knops, Robin John

    1971-01-01

    The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

  11. A generic approach for a linear elastic fracture mechanics analysis of components containing residual stress

    Lee, Hyeong Y.; Nikbin, Kamran M.; O'Dowd, Noel P.

    2005-01-01

    A review of through thickness transverse residual stress distribution measurements in a number of components, manufactured from a range of steels, has been carried out. Residual stresses introduced by welding and mechanical deformation have been considered. The geometries consisted of welded T-plate joints, pipe butt joints, tube-on-plate joints, tubular Y-joints and tubular T-joints as well as cold bent tubes and repair welds. In addition, the collected data cover a range of engineering steels including ferritic, austenitic, C-Mn and Cr-Mo steels. The methods used to measure the residual stresses also varied. These included neutron diffraction, X-ray diffraction and deep hole drilling techniques. Measured residual stress data, normalised by their respective yield stress have shown an inverse linear correlation versus the normalised depth of the region containing the residual stress (up to 0.5 of the component thickness). A simplified generic residual stress profile based on a linear fit to the data is proposed for the case of a transverse residual tensile stress field. Whereas the profiles in assessment procedures are case specific the proposed linear profile can be varied to produce a combination of membrane and bending stress distributions to give lower or higher levels of conservatism on stress intensity factors, depending on the amount of case specific data available or the degree of safety required

  12. Integrodifferential relations in linear elasticity

    Kostin, Georgy V

    2012-01-01

    This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.

  13. Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

    Kim, Jong Sung; Kim, Yong Woo [Sunchon National University, Suncheon (Korea, Republic of)

    2014-10-15

    Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected.

  14. Review of Acceleration Methods for Seismic Analysis of Through-Wall Cracked Piping from the Viewpoint of Linear Elastic Fracture Mechanics

    Kim, Jong Sung; Kim, Yong Woo

    2014-01-01

    Two acceleration methods, an effective force method (or inertia method) and a large mass method, have been applied for performing time history seismic analysis. The acceleration methods for uncracked structures have been verified via previous studies. However, no study has identified the validity of these acceleration methods for cracked piping. In this study, the validity of the acceleration methods for through-wall cracked piping is assessed via time history implicit dynamic elastic seismic analysis from the viewpoint of linear elastic fracture mechanics. As a result, it is identified that both acceleration methods show the same results for cracked piping if a large mass magnitude and maximum time increment are adequately selected

  15. Investigation of translaminar fracture in fibrereinforced composite laminates---applicability of linear elastic fracture mechanics and cohesive-zone model

    Hou, Fang

    With the extensive application of fiber-reinforced composite laminates in industry, research on the fracture mechanisms of this type of materials have drawn more and more attentions. A variety of fracture theories and models have been developed. Among them, the linear elastic fracture mechanics (LEFM) and cohesive-zone model (CZM) are two widely-accepted fracture models, which have already shown applicability in the fracture analysis of fiber-reinforced composite laminates. However, there remain challenges which prevent further applications of the two fracture models, such as the experimental measurement of fracture resistance. This dissertation primarily focused on the study of the applicability of LEFM and CZM for the fracture analysis of translaminar fracture in fibre-reinforced composite laminates. The research for each fracture model consisted of two sections: the analytical characterization of crack-tip fields and the experimental measurement of fracture resistance parameters. In the study of LEFM, an experimental investigation based on full-field crack-tip displacement measurements was carried out as a way to characterize the subcritical and steady-state crack advances in translaminar fracture of fiber-reinforced composite laminates. Here, the fiber-reinforced composite laminates were approximated as anisotropic solids. The experimental investigation relied on the LEFM theory with a modification with respect to the material anisotropy. Firstly, the full-field crack-tip displacement fields were measured by Digital Image Correlation (DIC). Then two methods, separately based on the stress intensity approach and the energy approach, were developed to measure the crack-tip field parameters from crack-tip displacement fields. The studied crack-tip field parameters included the stress intensity factor, energy release rate and effective crack length. Moreover, the crack-growth resistance curves (R-curves) were constructed with the measured crack-tip field parameters

  16. Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

    Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J

    2012-07-01

    Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.

  17. On the use of elastic-plastic material characteristics for linear-elastic component assessments

    Kussmaul, K.; Silcher, H.; Eisele, U.

    1995-01-01

    In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)

  18. Continuum mechanics elasticity, plasticity, viscoelasticity

    Dill, Ellis H

    2006-01-01

    FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...

  19. A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

    Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

    2017-12-01

    Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

  20. Statistical mechanics of elasticity

    Weiner, JH

    2012-01-01

    Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.

  1. Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

    Majumdar, S.; Kwasny, R.

    1985-01-01

    High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

  2. Isogeometric BDDC deluxe preconditioners for linear elasticity

    Pavarino, L. F.

    2018-03-14

    Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

  3. Isogeometric BDDC deluxe preconditioners for linear elasticity

    Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, Stefano

    2018-01-01

    Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.

  4. Non-linear theory of elasticity

    Lurie, AI

    2012-01-01

    This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

  5. Discriminative Elastic-Net Regularized Linear Regression.

    Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

    2017-03-01

    In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

  6. Mechanical behaviour of nanoparticles: Elasticity and plastic ...

    2015-06-03

    Jun 3, 2015 ... Mechanical behaviour of nanoparticles: Elasticity and plastic deformation mechanisms ... The main results in terms of elasticity and plastic deformation mechanisms are then reported ... Pramana – Journal of Physics | News.

  7. A Linear Theory for Pretwisted Elastic Beams

    Krenk, Steen

    1983-01-01

    contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...

  8. Asymptotic expansions for high-contrast linear elasticity

    Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

    2015-01-01

    We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

  9. Asymptotic expansions for high-contrast linear elasticity

    Poveda, Leonardo A.

    2015-03-01

    We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

  10. Non-linear theory of elasticity and optimal design

    Ratner, LW

    2003-01-01

    In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

  11. Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses

    Sauer, G.

    1998-01-01

    Fatigue analysis requires that the maximum strain ranges be known. These strain ranges are generally computed from linear elastic analysis. The elastic strain ranges are enhanced by a factor K e to obtain the total elastic-plastic strain range. The reliability of the fatigue analysis depends on the quality of this factor. Formulae for calculating the K e factor are proposed. A beam is introduced as a computational model for determining the elastic-plastic strains. The beam is loaded by the elastic stresses of the real structure. The elastic-plastic strains of the beam are compared with the beam's elastic strains. This comparison furnishes explicit expressions for the K e factor. The K e factor is tested by means of seven examples. (orig.)

  12. Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

    Jonas Koko

    2007-01-01

    Full Text Available A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

  13. On the hyperbolicity condition in linear elasticity

    Remigio Russo

    1991-05-01

    Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.

  14. A Lagrangian meshfree method applied to linear and nonlinear elasticity.

    Walker, Wade A

    2017-01-01

    The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

  15. Non-linear elastic thermal stress analysis with phase changes

    Amada, S.; Yang, W.H.

    1978-01-01

    The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)

  16. A Galerkin approximation for linear elastic shallow shells

    Figueiredo, I. N.; Trabucho, L.

    1992-03-01

    This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

  17. Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading

    Stepanova, Larisa; Bronnikov, Sergej

    2018-03-01

    The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. Two fracture criteria of traditional linear fracture mechanics (maximum tangential stress and minimum strain energy density criteria) are used. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.

  18. Linear elastic properties derivation from microstructures representative of transport parameters.

    Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

    2014-06-01

    It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

  19. A reexamination of some puzzling results in linearized elasticity

    University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA e-mail: jogc@mecheng.iisc.ernet.in; ..... ˆT (F) = C[ϵ] + o(∇u), where ϵ = [∇u+(∇u)T ]/2, and C = D ˆT (I) is the elasticity tensor, and one also linearizes the body force vector to get b = QT [ b∗ − ¨c. ] − ˙ × X − × ( × X) − 2 × v,. (5) where X is the position ...

  20. Extreme non-linear elasticity and transformation optics

    Gersborg, Allan Roulund; Sigmund, Ole

    2010-01-01

    realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...

  1. Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

    Mikhailov, SE

    2006-01-01

    Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

  2. Elastic-plastic fracture mechanics study of thermal shock cracking

    Hirano, K.; Kobayashi, H.; Nakazawa, H.

    1980-01-01

    This paper describes thermal shock experiments conducted on a nuclear pressure vessel steel (A533 Grade B Class 1), an AISI304 steel and a tool steel (JIS SKD62) using both a new thermal shock test facility and method. Analysis of their quasi-static thermal stress intensity factors is performed on the basis of linear-elastic fracture mechanics; and a thermal shock fracture toughness value, Ksub(tsc) is evaluated. Then elastic-plastic fracture toughness tests are carried out in the same high temperature range of the thermal shock experiment, and a relation between the stretched zone width, SZW, formed as a result of the fatigue precrack tip plastic blunting and the J-integral is clarified. An elastic-plastic thermal shock fracture toughness value, Jsub(tsc), is evaluated from a critical value of the stretched zone width, SZWsub(tsc), at the initiation of the thermal shock cracking by using the relation between SZW and J. The Jsub(tsc) value is compared with an elastic-plastic fracture toughness value, Jsub(Ic), and the difference between these Jsub(tsc) and Jsub(Ic) values is discussed on the basis of fractography. (author)

  3. Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

    Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2017-08-01

    Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

  4. Elastic-plastic fracture mechanics of compact bone

    Yan, Jiahau

    Bone is a composite composed mainly of organics, minerals and water. Most studies on the fracture toughness of bone have been conducted at room temperature. Considering that the body temperature of animals is higher than room temperature, and that bone has a high volumetric percentage of organics (generally, 35--50%), the effect of temperature on fracture toughness of bone should be studied. Single-edged V-shaped notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37 and 50°C. The fracture toughness of bovine femur and manatee rib were found to decrease from 7.0 to 4.3 MPa·m1/2 and from 5.5 to 4.1 MPa·m1/2, respectively, over a temperature range of 50°C. The decreases were attributed to inability of the organics to sustain greater stresses at higher temperatures. We studied the effects of water and organics on fracture toughness of bone using water-free and organics-free SEVN specimens at 23°C. Water-free and organics-free specimens were obtained by placing fresh bone specimen in a furnace at different temperatures. Water and organics significantly affected the fracture toughness of bone. Fracture toughness of the water-free specimens was 44.7% (bovine femur) and 32.4% (manatee rib) less than that of fresh-bone specimens. Fracture toughness of the organics-free specimens was 92.7% (bovine femur) and 91.5% (manatee rib) less than that of fresh bone specimens. Linear Elastic Fracture Mechanics (LEFM) is widely used to study bone. However, bone often has small to moderate scale yielding during testing. We used J integral, an elastic-plastic fracture-mechanics parameter, to study the fracture process of bone. The J integral of bovine femur increased from 6.3 KJ/mm2 at 23°C to 6.7 KJ/mm2 at 37°C. Although the fracture toughness of bovine bone decreases as the temperature increases, the J integral results show a contrary trend. The energy spent in advancing the crack beyond the linear-elastic

  5. Force sensing using 3D displacement measurements in linear elastic bodies

    Feng, Xinzeng; Hui, Chung-Yuen

    2016-07-01

    In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

  6. Morphology and linear-elastic moduli of random network solids.

    Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E

    2011-06-17

    The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  7. Emergence of linear elasticity from the atomistic description of matter

    Cakir, Abdullah, E-mail: acakir@ntu.edu.sg [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Pica Ciamarra, Massimo [Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University (Singapore); Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli (Italy)

    2016-08-07

    We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

  8. Emergence of linear elasticity from the atomistic description of matter

    Cakir, Abdullah; Pica Ciamarra, Massimo

    2016-01-01

    We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of the fluctuations of the local elastic constants close to the jamming transition.

  9. Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

    Donald Mark Santee

    2006-01-01

    Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

  10. Effects of elastic anisotropy on mechanical behavior of intermetallic compounds

    Yoo, M.H.

    1991-01-01

    Fundamental aspects of the deformation and fracture behavior of ordered intermetallic compounds are examined within the framework of linear anisotropic elasticity theory of dislocations and cracks. The orientation dependence and the tension/compression asymmetry of yield stress are explained in terms of the anisotropic coupling effect of non-glide stresses to the glide strain. The anomalous yield behavior is related to the disparity (edge/screw) of dislocation mobility and the critical stress required for the dislocation multiplication mechanism of Frank-Read type. The slip-twin conjugate relationship, extensive faulting, and pseudo-twinning (martensitic transformation) at a crack tip can be enhanced also by the anisotropic coupling effect, which may lead to transformation toughening of shear type

  11. Numerical investigation of elastic mechanical properties of graphene structures

    Georgantzinos, S.K.; Giannopoulos, G.I.; Anifantis, N.K.

    2010-01-01

    The computation of the elastic mechanical properties of graphene sheets, nanoribbons and graphite flakes using spring based finite element models is the aim of this paper. Interatomic bonded interactions as well as van der Waals forces between carbon atoms are simulated via the use of appropriate spring elements expressing corresponding potential energies provided by molecular theory. Each layer is idealized as a spring-like structure with carbon atoms represented by nodes while interatomic forces are simulated by translational and torsional springs with linear behavior. The non-bonded van der Waals interactions among atoms which are responsible for keeping the graphene layers together are simulated with the Lennard-Jones potential using appropriate spring elements. Numerical results concerning the Young's modulus, shear modulus and Poisson's ratio for graphene structures are derived in terms of their chilarity, width, length and number of layers. The numerical results from finite element simulations show good agreement with existing numerical values in the open literature.

  12. Non-linear waves in heterogeneous elastic rods via homogenization

    Quezada de Luna, Manuel

    2012-03-01

    We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.

  13. Non-linear elasticity of extracellular matrices enables contractile cells to communicate local position and orientation.

    Jessamine P Winer

    2009-07-01

    Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.

  14. Some remarks on elastic fracture mechanics

    Destuynder, P.; Djaoua, M.; Lescure, S.

    1981-12-01

    A thermodynamical approach of propagation law in elastic media is given in this paper. From a particular choice of an energy dissipation potential, we deduce some propagation laws corresponding to particular loading cases. Finally a new computational method of the energy release rate is suggested and discussed from a computational point of view [fr

  15. Mechanics of Fluctuating Elastic Plates and Fiber Networks

    Liang, Xiaojun

    Lipid membranes and fiber networks in biological systems perform important mechanical functions at the cellular and tissue levels. In this thesis I delve into two detailed problems--thermal fluctuation of membranes and non-linear compression response of fiber networks. Typically, membrane fluctuations are analysed by decomposing into normal modes or by molecular simulations. In the first part of my thesis, I propose a new semi-analytic method to calculate the partition function of a membrane. The membrane is viewed as a fluctuating von Karman plate and discretized into triangular elements. Its energy is expressed as a function of nodal displacements, and then the partition function and co-variance matrix are computed using Gaussian integrals. I recover well-known results for the dependence of the projected area of a lipid bilayer membrane on the applied tension, and recent simulation results on the ependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications I use this technique to study a membrane with heterogeneity and different boundary conditions. I also use this technique to study solid membranes by taking account of the non-linear coupling of in-plane strains with out-of-plane deflections using a penalty energy, and apply it to graphene, an ultra-thin two-dimensional solid. The scaling of graphene fluctuations with membrane size is recovered. I am able to capture the dependence of the thermal expansion coefficient of graphene on temperature. Next, I study curvature mediated interactions between inclusions in membranes. I assume the inclusions to be rigid, and show that the elastic and entropic forces between them can compete to yield a local maximum in the free energy if the membrane bending modulus is small. If the spacing between the inclusions is less than this local maximum then the attractive entropic forces dominate and the separation between the inclusions will be determined by short range interactions; if the

  16. A two-dimensional linear elasticity problem for anisotropic materials, solved with a parallelization code

    Mihai-Victor PRICOP

    2010-09-01

    Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code.

  17. Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

    Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

    2017-07-01

    Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

  18. Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass

    Minh Hoang Nguyen

    2016-12-01

    Full Text Available This paper introduced a kind of cart and pole system. The pole in this system is not a solid beam but an elastic beam. The paper analyzed the dynamic equation of this complex system. Then, a linear feedback controller was designed to stabilize this model in order to keep the elastic beam balanced in the up-side position. The control results were proved to work well through simulation.

  19. Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

    Pepi, John W.

    2017-08-01

    Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

  20. Linear models of income patterns in consumer demand for foods and evaluation of its elasticity

    Pavel Syrovátka

    2005-01-01

    Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.

  1. On the hyperporous non-linear elasticity model for fusion-relevant pebble beds

    Di Maio, P.A.; Giammusso, R.; Vella, G.

    2010-01-01

    Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.

  2. A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

    Diosady, Laslo T.; Murman, Scott M.

    2018-01-01

    A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

  3. The Simulation and Correction to the Brain Deformation Based on the Linear Elastic Model in IGS

    MU Xiao-lan; SONG Zhi-jian

    2004-01-01

    @@ The brain deformation is a vital factor affecting the precision of the IGS and it becomes a hotspot to simulate and correct the brain deformation recently.The research organizations, which firstly resolved the brain deformation with the physical models, have the Image Processing and Analysis department of Yale University, Biomedical Modeling Lab of Vanderbilt University and so on. The former uses the linear elastic model; the latter uses the consolidation model.The linear elastic model only needs to drive the model using the surface displacement of exposed brain cortex,which is more convenient to be measured in the clinic.

  4. Size dependence of elastic mechanical properties of nanocrystalline aluminum

    Xu, Wenwu; Dávila, Lilian P., E-mail: ldavila@ucmerced.edu

    2017-04-24

    The effect of grain size on the elastic mechanical properties of nanocrystalline pure metal Al is quantified by molecular dynamics simulation method. In this work, the largest nanocrystalline Al sample has a mean grain size of 29.6 nm and contains over 100 millions atoms in the modeling system. The simulation results show that the elastic properties including elastic modulus and ultimate tensile strength of nanocrystalline Al are relatively insensitive to the variation of mean grain size above 13 nm yet they become distinctly grain size dependent below 13 nm. Moreover, at a grain size <13 nm, the elastic modulus decreases monotonically with decreasing grain size while the ultimate tensile strength of nanocrystalline Al initially decreases with the decrease of the grain size down to 9 nm and then increases with further reduction of grain size. The increase of ultimate tensile strength below 9 nm is believed to be a result of an extended elasticity in the ultrafine grain size nanocrystalline Al. This study can facilitate the prediction of varied mechanical properties for similar nanocrystalline materials and even guide testing and fabrication schemes of such materials.

  5. Submillisecond elastic recoil reveals molecular origins of fibrin fiber mechanics.

    Hudson, Nathan E; Ding, Feng; Bucay, Igal; O'Brien, E Timothy; Gorkun, Oleg V; Superfine, Richard; Lord, Susan T; Dokholyan, Nikolay V; Falvo, Michael R

    2013-06-18

    Fibrin fibers form the structural scaffold of blood clots. Thus, their mechanical properties are of central importance to understanding hemostasis and thrombotic disease. Recent studies have revealed that fibrin fibers are elastomeric despite their high degree of molecular ordering. These results have inspired a variety of molecular models for fibrin's elasticity, ranging from reversible protein unfolding to rubber-like elasticity. An important property that has not been explored is the timescale of elastic recoil, a parameter that is critical for fibrin's mechanical function and places a temporal constraint on molecular models of fiber elasticity. Using high-frame-rate imaging and atomic force microscopy-based nanomanipulation, we measured the recoil dynamics of individual fibrin fibers and found that the recoil was orders of magnitude faster than anticipated from models involving protein refolding. We also performed steered discrete molecular-dynamics simulations to investigate the molecular origins of the observed recoil. Our results point to the unstructured αC regions of the otherwise structured fibrin molecule as being responsible for the elastic recoil of the fibers. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  6. Submillisecond Elastic Recoil Reveals Molecular Origins of Fibrin Fiber Mechanics

    Hudson, Nathan E.; Ding, Feng; Bucay, Igal; O’Brien, E. Timothy; Gorkun, Oleg V.; Superfine, Richard; Lord, Susan T.; Dokholyan, Nikolay V.; Falvo, Michael R.

    2013-01-01

    Fibrin fibers form the structural scaffold of blood clots. Thus, their mechanical properties are of central importance to understanding hemostasis and thrombotic disease. Recent studies have revealed that fibrin fibers are elastomeric despite their high degree of molecular ordering. These results have inspired a variety of molecular models for fibrin’s elasticity, ranging from reversible protein unfolding to rubber-like elasticity. An important property that has not been explored is the timescale of elastic recoil, a parameter that is critical for fibrin’s mechanical function and places a temporal constraint on molecular models of fiber elasticity. Using high-frame-rate imaging and atomic force microscopy-based nanomanipulation, we measured the recoil dynamics of individual fibrin fibers and found that the recoil was orders of magnitude faster than anticipated from models involving protein refolding. We also performed steered discrete molecular-dynamics simulations to investigate the molecular origins of the observed recoil. Our results point to the unstructured αC regions of the otherwise structured fibrin molecule as being responsible for the elastic recoil of the fibers. PMID:23790375

  7. Quantification of local and global elastic anisotropy in ultrafine grained gradient microstructures, produced by linear flow splitting

    Niehuesbernd, Jörn; Müller, Clemens; Pantleon, Wolfgang

    2013-01-01

    . Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process...

  8. Elastic and Mechanical Properties of the MAX Phases

    Barsoum, Michel W.; Radovic, Miladin

    2011-08-01

    The more than 60 ternary carbides and nitrides, with the general formula Mn+1AXn—where n = 1, 2, or 3; M is an early transition metal; A is an A-group element (a subset of groups 13-16); and X is C and/or N—represent a new class of layered solids, where Mn+1Xn layers are interleaved with pure A-group element layers. The growing interest in the Mn+1AXn phases lies in their unusual, and sometimes unique, set of properties that can be traced back to their layered nature and the fact that basal dislocations multiply and are mobile at room temperature. Because of their chemical and structural similarities, the MAX phases and their corresponding MX phases share many physical and chemical properties. In this paper we review our current understanding of the elastic and mechanical properties of bulk MAX phases where they differ significantly from their MX counterparts. Elastically the MAX phases are in general quite stiff and elastically isotropic. The MAX phases are relatively soft (2-8 GPa), are most readily machinable, and are damage tolerant. Some of them are also lightweight and resistant to thermal shock, oxidation, fatigue, and creep. In addition, they behave as nonlinear elastic solids, dissipating 25% of the mechanical energy during compressive cycling loading of up to 1 GPa at room temperature. At higher temperatures, they undergo a brittle-to-plastic transition, and their mechanical behavior is a strong function of deformation rate.

  9. A calculational round robin in elastic-plastic fracture mechanics

    Larsson, L.H.

    1983-01-01

    Eighteen organisations participated in this elastic-plastic fracture mechanics (EPFM) numerical analysis round robin which treated the same three-point bend problem as a similar round robin conducted by ASTM four years earlier. The work involved the calculation of overall deformation, J, CTOD and crack profile using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. It was found that all of the elastic solutions were accurate to within a few per cent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. No significant progress has taken place in the state of the art of numerical EPFM analysis over the four-year interval. The reasons for this scatter and tentative conclusions on the most suitable numerical analysis methods in EPFM are discussed. (author)

  10. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

    Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

    2015-10-01

    We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

  11. Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

    Wang, Wenjun; Li, Peng; Jin, Feng

    2016-09-01

    A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

  12. Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium

    Sofiyev, A.H.; Kuruoglu, N.

    2013-01-01

    In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. -- Highlights: • Nonlinear buckling of FGM conical shell surrounded by elastic medium is studied. • Pasternak foundation model is used to describe the shell–foundation interaction. • Nonlinear basic equations are derived. • Problem is solved by using Superposition and Galerkin methods. • Influences of various parameters on the nonlinear critical load are investigated

  13. Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

    Kao, B.G.

    1979-11-01

    Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

  14. Compact solitary waves in linearly elastic chains with non-smooth on-site potential

    Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milan (Italy); Gramchev, Todor [Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy); Walcher, Sebastian [Lehrstuhl A Mathematik, RWTH Aachen, 52056 Aachen (Germany)

    2007-04-27

    It was recently observed by Saccomandi and Sgura that one-dimensional chains with nonlinear elastic interaction and regular on-site potential can support compact solitary waves, i.e. travelling solitary waves with strictly compact support. In this paper, we show that the same applies to chains with linear elastic interaction and an on-site potential which is continuous but non-smooth at minima. Some different features arise; in particular, the speed of compact solitary waves is not uniquely fixed by the equation. We also discuss several generalizations of our findings.

  15. Four-dimensional Hooke's law can encompass linear elasticity and inertia

    Antoci, S.; Mihich, L.

    1999-01-01

    The question is examined whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke law is found able to account for the inertia of matter; in the flat-space, slow-motion approximation the field equations for the displacement four-vector field ξ i can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity

  16. Electronic structure, elasticity, bonding features and mechanical behaviour of zinc intermetallics: A DFT study

    Fatima, Bushra, E-mail: bushrafatima25@gmail.com; Acharya, Nikita; Sanyal, Sankar P. [Department of Physics, Barkatullah University, Bhopal, 462026 (India)

    2016-05-06

    The structural stability, electronic structure, elastic and mechanical properties of TiZn and ZrZn intermetallics have been studied using ab-initio full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation for exchange and correlation potentials. The various structural parameters, such as lattice constant (a{sub 0}), bulk modulus (B), and its pressure derivative (B’) are analysed and compared. The investigation of elastic constants affirm that both TiZn and ZrZn are elastically stable in CsCl (B{sub 2} phase) structure. The electronic structures have been analysed quantitatively from the band structure which reveals the metallic nature of these compounds. To better illustrate the nature of bonding and charge transfer, we have also studied the Fermi surfaces. The three well known criterion of ductility namely Pugh’s rule, Cauchy’s pressure and Frantsevich rule elucidate the ductile nature of these compounds.

  17. Theoretical study of elastic, mechanical and thermodynamic properties of MgRh intermetallic compound

    S. Boucetta

    2014-03-01

    Full Text Available In the last years, Magnesium alloys are known to be of great technological importance and high scientific interest. In this work, density functional theory plane-wave pseudo potential method, with local density approximation (LDA and generalized gradient approximation (GGA are used to perform first-principles quantum mechanics calculations in order to investigate the structural, elastic and mechanical properties of the intermetallic compound MgRh with a CsCl-type structure. Comparison of the calculated equilibrium lattice constant and experimental data shows good agreement. The elastic constants were determined from a linear fit of the calculated stress–strain function according to Hooke's law. From the elastic constants, the bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio σ, anisotropy factor A and the ratio B/G for MgRh compound are obtained. The sound velocities and Debye temperature are also predicted from elastic constants. Finally, the linear response method has been used to calculate the thermodynamic properties. The temperature dependence of the enthalpy H, free energy F, entropy S, and heat capacity at constant volume Cv of MgRh crystal in a quasi-harmonic approximation have been obtained from phonon density of states and discussed for the first report. This is the first quantitative theoretical prediction of these properties.

  18. Classical mechanics including an introduction to the theory of elasticity

    Hentschke, Reinhard

    2017-01-01

    This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory...

  19. Numerical modelling in non linear fracture mechanics

    Viggo Tvergaard

    2007-07-01

    Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.

  20. Microstructure, elastic deformation behavior and mechanical properties of biomedical β-type titanium alloy thin-tube used for stents.

    Tian, Yuxing; Yu, Zhentao; Ong, Chun Yee Aaron; Kent, Damon; Wang, Gui

    2015-05-01

    Cold-deformability and mechanical compatibility of the biomedical β-type titanium alloy are the foremost considerations for their application in stents, because the lower ductility restricts the cold-forming of thin-tube and unsatisfactory mechanical performance causes a failed tissue repair. In this paper, β-type titanium alloy (Ti-25Nb-3Zr-3Mo-2Sn, wt%) thin-tube fabricated by routine cold rolling is reported for the first time, and its elastic behavior and mechanical properties are discussed for the various microstructures. The as cold-rolled tube exhibits nonlinear elastic behavior with large recoverable strain of 2.3%. After annealing and aging, a nonlinear elasticity, considered as the intermediate stage between "double yielding" and normal linear elasticity, is attributable to a moderate precipitation of α phase. Quantitive relationships are established between volume fraction of α phase (Vα) and elastic modulus, strength as well as maximal recoverable strain (εmax-R), where the εmax-R of above 2.0% corresponds to the Vα range of 3-10%. It is considered that the "mechanical" stabilization of the (α+β) microstructure is a possible elastic mechanism for explaining the nonlinear elastic behavior. Copyright © 2015 Elsevier Ltd. All rights reserved.

  1. Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

    Berger, J. B.; Wadley, H. N. G.; McMeeking, R. M.

    2017-02-01

    A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple

  2. Elastic Multi-scale Mechanisms: Computation and Biological Evolution.

    Diaz Ochoa, Juan G

    2018-01-01

    Explanations based on low-level interacting elements are valuable and powerful since they contribute to identify the key mechanisms of biological functions. However, many dynamic systems based on low-level interacting elements with unambiguous, finite, and complete information of initial states generate future states that cannot be predicted, implying an increase of complexity and open-ended evolution. Such systems are like Turing machines, that overlap with dynamical systems that cannot halt. We argue that organisms find halting conditions by distorting these mechanisms, creating conditions for a constant creativity that drives evolution. We introduce a modulus of elasticity to measure the changes in these mechanisms in response to changes in the computed environment. We test this concept in a population of predators and predated cells with chemotactic mechanisms and demonstrate how the selection of a given mechanism depends on the entire population. We finally explore this concept in different frameworks and postulate that the identification of predictive mechanisms is only successful with small elasticity modulus.

  3. Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

    Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

    1996-12-31

    Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

  4. A non-linear elastic constitutive framework for replicating plastic deformation in solids.

    Roberts, Scott Alan; Schunk, Peter Randall

    2014-02-01

    Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

  5. Dynamic Modeling and Control of Electromechanical Coupling for Mechanical Elastic Energy Storage System

    Yang Yu

    2013-01-01

    Full Text Available The structural scheme of mechanical elastic energy storage (MEES system served by permanent magnet synchronous motor (PMSM and bidirectional converters is designed. The aim of the research is to model and control the complex electromechanical system. The mechanical device of the complex system is considered as a node in generalized coordinate system, the terse nonlinear dynamic model of electromechanical coupling for the electromechanical system is constructed through Lagrange-Maxwell energy method, and the detailed deduction of the mathematical model is presented in the paper. The theory of direct feedback linearization (DFL is applied to decouple the nonlinear dynamic model and convert the developed model from nonlinear to linear. The optimal control theory is utilized to accomplish speed tracking control for the linearized system. The simulation results in three different cases show that the proposed nonlinear dynamic model of MEES system is correct; the designed algorithm has a better control performance in contrast with the conventional PI control.

  6. Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach

    Akbarov, Surkay D

    2015-01-01

    This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.

  7. Identification of general linear mechanical systems

    Sirlin, S. W.; Longman, R. W.; Juang, J. N.

    1983-01-01

    Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.

  8. Dynamic analysis of aircraft impact using the linear elastic finite element codes FINEL, SAP and STARDYNE

    Lundsager, P.; Krenk, S.

    1975-08-01

    The static and dynamic response of a cylindrical/ spherical containment to a Boeing 720 impact is computed using 3 different linear elastic computer codes: FINEL, SAP and STARDYNE. Stress and displacement fields are shown together with time histories for a point in the impact zone. The main conclusions from this study are: - In this case the maximum dynamic load factors for stress and displacements were close to 1, but a static analysis alone is not fully sufficient. - More realistic load time histories should be considered. - The main effects seem to be local. The present study does not indicate general collapse from elastic stresses alone. - Further study of material properties at high rates is needed. (author)

  9. Mechanisms of elastic wave generation in solids by ion impact

    Deemer, B.; Murphy, J.; Claytor, T.

    1990-01-01

    This study is directed at understanding the mechanisms of acoustic signal generation by modulated beams of energetic ions as a function of ion energy. Interaction of ions with solids initiates a range of processes including sputtering, ion implantation, ionization, both internal and external, as well as thermal deposition in the solid. Accumulated internal stress also occurs by generation of dislocations resulting from, inelastic nuclear scattering of the incident ion beam. With respect to elastic wave generation, two potential mechanisms are thermoelastic induced stress and momentum transfer. The latter process includes contributions of momentum transfer from the incident beam and from ions ejected via sputtering. Other aspects of the generation process include the potential for shock wave generation since the mean particle velocity for a wide range of ion energies exceeds the velocity of sound in solids. This study seeks to distinguish the contribution of these mechanisms by studying the signature, angular distribution and energy dependence of the elastic wave response in the time domain and to use this information to understand technologically important processes such as implantation and sputtering

  10. New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

    Spannenberg Jescica

    2017-09-01

    Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

  11. Method of determining elastic and plastic mechanical properties of ceramic materials using spherical indenters

    Adler, Thomas A.

    1996-01-01

    The invention pertains a method of determining elastic and plastic mechanical properties of ceramics, intermetallics, metals, plastics and other hard, brittle materials which fracture prior to plastically deforming when loads are applied. Elastic and plastic mechanical properties of ceramic materials are determined using spherical indenters. The method is most useful for measuring and calculating the plastic and elastic deformation of hard, brittle materials with low values of elastic modulus to hardness.

  12. Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity

    Franca, L.P.; Stenberg, R.

    1989-06-01

    Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt

  13. On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

    Ikehata, M; Itou, H

    2011-01-01

    In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation.

  14. Evaluation of linear polymerization shrinkage, flexural strength and modulus of elasticity of dental composites

    Gabriela Queiroz de Melo Monteiro

    2010-03-01

    Full Text Available Linear polymerization shrinkage (LPS, flexural strength (FS and modulus of elasticity (ME of 7 dental composites (Filtek Z350™, Filtek Z250™/3M ESPE; Grandio™, Polofil Supra™/VOCO; TPH Spectrum™, TPH3™, Esthet-X™/Denstply were measured. For the measurement of LPS, composites were applied to a cylindrical metallic mold and polymerized (n = 8. The gap formed at the resin/mold interface was observed using scanning electron microscopy (1500×. For FS and ME, specimens were prepared according to the ISO 4049 specifications (n = 10. Statistical analysis of the data was performed with one-way ANOVA and the Tukey test. TPH Spectrum presented significantly higher LPS values (29.45 µm. Grandio had significantly higher mean values for FS (141.07 MPa and ME (13.91 GPa. The relationship between modulus of elasticity and polymerization shrinkage is the main challenge for maintenance of the adhesive interface, thus composites presenting high shrinkage values, associated with a high modulus of elasticity tend to disrupt the adhesive interface under polymerization.

  15. Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

    Sozio, Fabio; Yavari, Arash

    2017-01-01

    In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

  16. A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

    Li, Chen; Liao, Yufei

    2018-03-01

    Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

  17. Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

    DeLuca, R.

    2006-03-01

    Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.

  18. Elasticity and mechanical advantage in cables and ropes

    O'Shea, M J

    2007-01-01

    The conditions under which one can gain mechanical advantage by pulling with a force F perpendicular to a cable (or rope) that is fixed at both ends are examined. While this is a commonly discussed example in introductory physics classes, its solution in terms of fundamental properties of the cable requires one to model the elasticity of the cable. This solution has several complex and interesting features, e.g. a large increase in the tension in the cable may occur upon application of F if (i) F lies in a certain range and (ii) the initial tension T 1 in the cable (before F is applied) satisfies T 1 < 0.0340 κ. Here, κ is the spring constant of a unit length of the cable. For steel cables and cables composed of other materials such as carbon nanorods where the elasticity is low, significant increases in tension are possible. Examples involving walking a tightrope and attempting to increase the tension in a rope hauling a load are considered. Two programs to solve the equations of this work are available in the electronic version of this journal

  19. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

    Kim, Jin Kyu; Kim, Dong Keon

    2016-01-01

    A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics

  20. Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

    Harris, John G.

    2001-10-01

    Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

  1. Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

    Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)

    2016-09-15

    A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.

  2. Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots

    Bauer, Fabian; Römer, Ulrich, E-mail: ulrich.roemer@kit.edu; Fidlin, Alexander; Seemann, Wolfgang [Institute of Engineering Mechanics, Karlsruhe Institute of Technology (Germany)

    2016-11-15

    This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 80 % in a speed range from 0.3 to 2.3 m/s using elastic couplings—mechanical springs with movement speed independent parameters. The considered planar robot consists of a trunk, two two-segmented legs, two actuators in the hip joints, two actuators in the knee joints and an elastic coupling between the shanks. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled via input–output linearization. A numerical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The process of energy turnover is investigated in detail for the robot with and without elastic coupling between the shanks. Furthermore, the influences of the elastic couplings’ topology and of joint friction are analyzed. It is shown that the optimization of the robot’s motion and elastic coupling towards energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability, but a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered via numerical optimization is a linear torsion spring with transmissions between the shanks. A design proposal for this elastic coupling—which does not affect the robot’s trunk and parallel shank motion and can be used to enhance an existing robot—is given for planar as well as spatial robots.

  3. Schwinger mechanism in linear covariant gauges

    Aguilar, A. C.; Binosi, D.; Papavassiliou, J.

    2017-02-01

    In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modeled by means of certain physically motivated Ansätze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansätze are compatible with the existence of nontrivial solutions. When such Ansätze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing," while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.

  4. Old men running: mechanical work and elastic bounce.

    Cavagna, G A; Legramandi, M A; Peyré-Tartaruga, L A

    2008-02-22

    It is known that muscular force is reduced in old age. We investigate what are the effects of this phenomenon on the mechanics of running. We hypothesized that the deficit in force would result in a lower push, causing reduced amplitude of the vertical oscillation, with smaller elastic energy storage and increased step frequency. To test this hypothesis, we measured the mechanical energy of the centre of mass of the body during running in old and young subjects. The amplitude of the oscillation is indeed reduced in the old subjects, resulting in an approximately 20% smaller elastic recovery and a greater step frequency (3.7 versus 2.8 Hz, p=1.9x10(-5), at 15-17 km h(-1)). Interestingly, the greater step frequency is due to a lower aerial time, and not to a greater natural frequency of the system, which is similar in old and young subjects (3.6 versus 3.4 Hz, p=0.2). Moreover, we find that in the old subjects, the step frequency is always similar to the natural frequency, even at the highest speeds. This is at variance with young subjects who adopt a step frequency lower than the natural frequency at high speeds, to contain the aerobic energy expenditure. Finally, the external work to maintain the motion of the centre of mass is reduced in the old subjects (0.9 versus 1.2 J kg(-1) m(-1), p=5.1x10(-6)) due to the lower work done against gravity, but the higher step frequency involves a greater internal work to reset the limbs at each step. The net result is that the total work increases with speed more steeply in the old subjects than in young subjects.

  5. Fluid Mechanics of Capillary-Elastic Instabilities in Microgravity Environment

    Grotberg, James B.

    2002-01-01

    The aim of this project is to investigate the closure and reopening of lung airways due to surface tension forces, coupled with airway elasticity. Airways are liquid-lined, flexible tubes and closure of airways can occur by a Rayleigh instability of the liquid lining, or an instability of the elastic support for the airway as the surface tension of the air-liquid interface pulls the tube shut, or both. Regardless of the mechanism, the airway is closed because the liquid lining has created a plug that prevents axial gas exchange. In the microgravity environment, surface tension forces dominate lung mechanics and would lead to more prevalent, and more uniformly distributed air-way closure, thereby creating a potential for respiratory problems for astronauts. Once closed the primary option for reopening an airway is by deep inspiration. This maneuver will pull the flexible airways open and force the liquid plug to flow distally by the incoming air stream. Airway reopening depends to a large extent on this plug flow and how it may lead to plug rupture to regain the continuity of gas between the environment and the alveoli. In addition to mathematical modeling of plug flows in liquid-lined, flexible tubes, this work has involved benchtop studies of propagating liquid plugs down tube networks that mimic the human airway tree. We have extended the work to involve animal models of liquid plug propagation in rat lungs. The liquid is radio-opaque and x-ray video imaging is used to ascertain the movement and distribution of the liquid plugs so that comparisons to theory may be made. This research has other uses, such as the delivery of liquids or drugs into the lung that may be used for surfactant replacement therapy or for liquid ventilation.

  6. Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

    Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

    2017-11-01

    Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

  7. Theoretical study of phonon dispersion, elastic, mechanical and thermodynamic properties of barium chalcogenides

    Musari, A. A.; Orukombo, S. A.

    2018-03-01

    Barium chalcogenides are known for their high-technological importance and great scientific interest. Detailed studies of their elastic, mechanical, dynamical and thermodynamic properties were carried out using density functional theory and plane-wave pseudo potential method within the generalized gradient approximation. The optimized lattice constants were in good agreement when compared with experimental data. The independent elastic constants, calculated from a linear fit of the computed stress-strain function, were used to determine the Young’s modulus (E), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ) and Zener’s anisotropy factor (A). Also, the Debye temperature and sound velocities for barium chalcogenides were estimated from the three independent elastic constants. The calculations of phonon dispersion showed that there are no negative frequencies throughout the Brillouin zone. Hence barium chalcogenides have dynamically stable NaCl-type crystal structure. Finally, their thermodynamic properties were calculated in the temperature range of 0-1000 K and their constant-volume specific heat capacities at room-temperature were reported.

  8. CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

    Benzley, S.E.; Beisinger, Z.E.

    1981-01-01

    1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

  9. A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

    Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.

    2012-08-01

    We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.

  10. Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials

    American Society for Testing and Materials. Philadelphia

    2009-01-01

    1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...

  11. Linear elastic obstacles: analysis of experimental results in the case of stress dependent pre-exponentials

    Surek, T.; Kuon, L.G.; Luton, M.J.; Jones, J.J.

    1975-01-01

    For the case of linear elastic obstacles, the analysis of experimental plastic flow data is shown to have a particularly simple form when the pre-exponential factor is a single-valued function of the modulus-reduced stress. The analysis permits the separation of the stress and temperature dependence of the strain rate into those of the pre-exponential factor and the activation free energy. As a consequence, the true values of the activation enthalpy, volume and entropy also are obtained. The approach is applied to four sets of experimental data, including Zr, and the results for the pre-exponential term are examined for self-consistency in view of the assumed functional dependence

  12. First-order system least squares for the pure traction problem in planar linear elasticity

    Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.

    1996-12-31

    This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.

  13. A unified approach to elastic-plastic fracture mechanics

    Neale, B.K.; Townley, C.H.A.

    1976-01-01

    To assess the integrity of a cracked structure, using materials data obtained from simple laboratory tests, it is essential to define materials properties which are independent of the shape and the size of the specimen and of the loading system applied to it. In those situations where either the specimen or the structure fails after significant yielding has taken place, there is considerable speculation about the materials parameters which are relevant. By extending the Griffith equation for the stability of a perfectly elastic cracked body, the authors derive a fracture criterion which is applicable in the post yield regime. Comparisons are made with procedures based on the J-contour integral, equivalent energy, and crack opening displacements and with the post yield fracture mechanics of Heald, Spink and Worthington, and Dowling and Townley. For certain materials, it is shown that the factor controlling crack initiation is the fracture toughness Ksub(1c), irrespective of the amount of prior plastic damage, and hence independent of the shape and size of the specimen tested. Load carrying capacity in the post yield regime cannot, however, be derived directly from a knowledge of fracture toughness; the ultimate tensile strength of the material is also relevant

  14. EDSPA, 1-D Mechanical Displacement for Elastic, Thermoelastic, Viscoelastic Behaviour

    Schlich, M.; Elsen, R.

    1995-01-01

    1 - Description of program or function: EDSPA solves the one dimensional mechanical displacement equation in radial (sphere) axisymmetric cylindrical (infinite cylinder, slab) coordinates. The constitutive laws for the material to be considered can comprise the - elastic and/or - thermoelastic and/or - viscoplastic behaviour. The boundary conditions allow to prescribe displacement and/or stress values. The delivered version of EDSPA is especially suitable for the calculation of borehole problems in rock salt (heater boreholes or free converging boreholes or caverns) where convergence rates and/or contact pressures are of interest. 2 - Method of solution: The coarse-mesh method is used to transform the displacement differential equation (quasi-stationary case: second order ordinary differential equation as a two point boundary value problem) into a system of algebraic equations. This three-diagonal system is solved with the Thomas algorithm (direct solver). 3 - Restrictions on the complexity of the problem: Because of EDSPA's simple one-dimensional formulation there are no restrictions for storage allocation and argument ranges

  15. Shear-wave elastographic features of breast cancers: comparison with mechanical elasticity and histopathologic characteristics.

    Lee, Su Hyun; Moon, Woo Kyung; Cho, Nariya; Chang, Jung Min; Moon, Hyeong-Gon; Han, Wonshik; Noh, Dong-Young; Lee, Jung Chan; Kim, Hee Chan; Lee, Kyoung-Bun; Park, In-Ae

    2014-03-01

    The objective of this study was to compare the quantitative and qualitative shear-wave elastographic (SWE) features of breast cancers with mechanical elasticity and histopathologic characteristics. This prospective study was conducted with institutional review board approval, and written informed consent was obtained. Shear-wave elastography was performed for 30 invasive breast cancers in 30 women before surgery. The mechanical elasticity of a fresh breast tissue section, correlated with the ultrasound image, was measured using an indentation system. Quantitative (maximum, mean, minimum, and standard deviation of elasticity in kilopascals) and qualitative (color heterogeneity and presence of signal void areas in the mass) SWE features were compared with mechanical elasticity and histopathologic characteristics using the Pearson correlation coefficient and the Wilcoxon signed rank test. Maximum SWE values showed a moderate correlation with maximum mechanical elasticity (r = 0.530, P = 0.003). There were no significant differences between SWE values and mechanical elasticity in histologic grade I or II cancers (P = 0.268). However, SWE values were significantly higher than mechanical elasticity in histologic grade III cancers (P masses were present in 43% of breast cancers (13 of 30) and were correlated with dense collagen depositions (n = 11) or intratumoral necrosis (n = 2). Quantitative and qualitative SWE features reflect both the mechanical elasticity and histopathologic characteristics of breast cancers.

  16. A calculational round robin in elastic-plastic fracture mechanics

    Larsson, L.H.

    Eighteen organizations participated in this round robin which treated the same three-point bend problem as an ASTM round robin four years earlier. Overall deformation, J, CTOD and crack profile were the main results required using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. All elastic solutions were accurate to within a few percent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. Apparently no significant progress has taken place in the state of the art of numerical EPFM analysis in four years time. The paper discusses the reasons for this scatter and draws tentative conclusions on the most suitable numerical analysis methods in EPFM. (Auth.)

  17. Biodegradation mechanism of linear alkylbenzenesulfonate-14C

    Kubodera, Tadayoshi; Muto, Toshio; Yamamoto, Tatsuo

    1978-01-01

    The biodegradation of linear alkylbenzenesulfonate- 14 C (LAS- 14 C) tagged with 14 C at the linear side chain was studied on activated sludge by tracer method in addition to the methylene blue method which is widely employed in the biodegradation of LAS. It was found that there were three periods of rapid adsorption period, acclimation period, and degradation process. The radiolysis of dodecylbenzenesulfonate was studied on irradiating by 5000 Ci 60 Co source. The decomposition products were identified by GLC and GC-MS spectrometry after desulfonation. 1-Tetralone, 1-indanone, 4-methyl-1-tetralone, naphthalene et al. were found in them. (author)

  18. A new technique for generating the isotropic and linearly anisotropic components of elastic and discrete inelastic transfer matrices

    Garcia, R.D.M.

    1984-01-01

    A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt

  19. Some fundamental definitions of the elastic parameters for homogeneous isotropic linear elastic materials in pavement design and analysis

    De Beer, Morris

    2008-07-01

    Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

  20. Comparison between isotropic linear-elastic law and isotropic hyperelastic law in the finite element modeling of the brachial plexus.

    Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P

    2017-12-01

    Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS ® from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

  1. Geometrical foundations of continuum mechanics an application to first- and second-order elasticity and elasto-plasticity

    Steinmann, Paul

    2015-01-01

    This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.   After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear con...

  2. The use of the J* integral for non-linear fracture mechanics

    Hellen, T.K.

    1976-09-01

    The Griffith energy balance criterion, first postulated over 50 years ago, is still the basis of linear elastic fracture mechanics. From this, accurate numerical methods for establishing stress intensity factors and energy release rates have been developed. One such method involves path independent contour integrals about the crack tip. An improved contour integral, designated J* is discussed, and shown to have distinct advantages over others in non-linear strain situations. A number of examples are shown including fractures in thermo-plastic and creep situations. (author)

  3. An enhanced finite volume method to model 2D linear elastic structures

    Suliman, Ridhwaan

    2014-04-01

    Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...

  4. Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements

    Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François

    2014-01-01

    Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper)

  5. Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity.

    Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine

    2015-08-01

    Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved.

  6. Progress in elastic-plastic fracture mechanics and its applications

    Paris, P.C.; Zahalak, G.I.

    1980-01-01

    This paper surveys recent developments in the application of J-Integral methods to problems of elastic-plastic fracture. The analytical and experimental development of the J-Integral concept over the last ten years is reviewed briefly. Tearing instability theory is presented in general terms, and specific applications of the theory are discussed. Principles of fracture-proof design are shown to follow naturally from the tearing instability theory. These principles are illustrated first for simple structures, and then generalized to more complex configurations and loading conditions. Examples include multiple member tension structures, beams, frames, nuclear reactor pressure vessel nozzles and piping, and beams on elastic foundations. It is concluded that J-integral based methods offer the best immediate opportunity for the development of sound analytical techniques for treating important practical problems of elastic-plastic fracture

  7. Evaluation of single crystal coefficients from mechanical and x-ray elastic constants of the polycrystal

    Hauk, V.; Kockelmann, H.

    1979-01-01

    Methods of calculation are developed for determination of single crystal elastic compliance or stiffness constants of cubic and hexagonal materials from mechanical and X-ray elastic constants of polycrystals. The calculations are applied to pure, cubic iron and hexagonal WC. There are no single crystal constants in the literature for WC, because no single crystals suitable for measurement are available. (orig.) [de

  8. comparison of elastic-plastic FE method and engineering method for RPV fracture mechanics analysis

    Sun Yingxue; Zheng Bin; Zhang Fenggang

    2009-01-01

    This paper described the FE analysis of elastic-plastic fracture mechanics for a crack in RPV belt line using ABAQUS code. It calculated and evaluated the stress intensity factor and J integral of crack under PTS transients. The result is also compared with that by engineering analysis method. It shows that the results using engineering analysis method is a little larger than the results using FE analysis of 3D elastic-plastic fracture mechanics, thus the engineering analysis method is conservative than the elastic-plastic fracture mechanics method. (authors)

  9. Variational problems arising in classical mechanics and nonlinear elasticity

    Spencer, P.

    1999-01-01

    In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in

  10. Non-linear finite element analysis in structural mechanics

    Rust, Wilhelm

    2015-01-01

    This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

  11. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...

  12. Theory of elastic thin shells solid and structural mechanics

    Gol'Denveizer, A L; Dryden, H L

    1961-01-01

    Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is

  13. Application of elastic and elastic-plastic fracture mechanics methods to surface flaws

    McCabe, Donald E.; Ernst, Hugo A.; Newman, James C., Jr.

    Fuel tanks that are a part of the External Tank assembly for the Space Shuttle are made of relatively thin 2219-T87 aluminum plate. These tanks contain about 917 m of fusion weld seam, all of which is nondestructively inspected for flaws and all those found are repaired. The tanks are subsequently proof-tested to a pressure that is sufficiently severe to cause weld metal yielding in a few local regions of the weld seam. The work undertaken in the present project was to develop a capability to predict flaw growth from undetected surface flaws that are assumed to be located in the highly stressed regions. The technical challenge was to develop R-curve prediction capability for surface cracks in specimens that contain the flaws of unusual sizes and shapes deemed to be of interest. The test techniques developed and the elastic-plastic analysis concepts adopted are presented. The flaws of interest were quite small surface cracks that were narrow-deep ellipses that served to exacerbate the technical difficulties involved.

  14. Partial Linearization of Mechanical Systems with Application to Observer Design

    Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der

    2008-01-01

    We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by

  15. Contribution of elastic tissues to the mechanics and energetics of muscle function during movement.

    Roberts, Thomas J

    2016-01-01

    Muscle force production occurs within an environment of tissues that exhibit spring-like behavior, and this elasticity is a critical determinant of muscle performance during locomotion. Muscle force and power output both depend on the speed of contraction, as described by the isotonic force-velocity curve. By influencing the speed of contractile elements, elastic structures can have a profound effect on muscle force, power and work. In very rapid movements, elastic mechanisms can amplify muscle power by storing the work of muscle contraction slowly and releasing it rapidly. When energy must be dissipated rapidly, such as in landing from a jump, energy stored rapidly in elastic elements can be released more slowly to stretch muscle contractile elements, reducing the power input to muscle and possibly protecting it from damage. Elastic mechanisms identified so far rely primarily on in-series tendons, but many structures within muscles exhibit spring-like properties. Actomyosin cross-bridges, actin and myosin filaments, titin, and the connective tissue scaffolding of the extracellular matrix all have the potential to store and recover elastic energy during muscle contraction. The potential contribution of these elements can be assessed from their stiffness and estimates of the strain they undergo during muscle function. Such calculations provide boundaries for the possible roles these springs might play in locomotion, and may help to direct future studies of the uses of elastic elements in muscle. © 2016. Published by The Company of Biologists Ltd.

  16. Mechanical Properties and Elastic Constants Due to Damage Accumulation and Amorphization in SiC

    Gao, Fei; Weber, William J.

    2004-01-01

    Damage accumulation due to cascade overlap, which was simulated previously, has been used to study the changes of elastic constants, bulk and elastic moduli as a function of dose. These mechanical properties generally decrease with increasing dose, and the rapid decrease at low-dose level indicates that point defects and small clusters play an important role in the changes of elastic constants rather than topological disorder. The internal strain relaxation has no effect on the elastic constants, C11 and C12, in perfect SiC, but it has a significant influence on all elastic constants calculated in damaged SiC. The elastic constants in the cascade-amorphized (CA) SiC decrease about 19%, 29% and 46% for C11, C12 and C44, respectively. The bulk modulus decrease 23% and the elastic modulus decreases 29%, which is consistent with experimental measurements. The stability of both the perfect SiC and CA-SiC under hydrostatic tension has been also investigated. All mechanical properties in the CA-SiC exhibit behavior similar to that in perfect SiC, but the critical stress at which the CA-SiC becomes structurally unstable is one order of magnitude smaller than that for perfect SiC

  17. Spring or string: does tendon elastic action influence wing muscle mechanics in bat flight?

    Konow, Nicolai; Cheney, Jorn A; Roberts, Thomas J; Waldman, J Rhea S; Swartz, Sharon M

    2015-10-07

    Tendon springs influence locomotor movements in many terrestrial animals, but their roles in locomotion through fluids as well as in small-bodied mammals are less clear. We measured muscle, tendon and joint mechanics in an elbow extensor of a small fruit bat during ascending flight. At the end of downstroke, the tendon was stretched by elbow flexion as the wing was folded. At the end of upstroke, elastic energy was recovered via tendon recoil and extended the elbow, contributing to unfurling the wing for downstroke. Compared with a hypothetical 'string-like' system lacking series elastic compliance, the tendon spring conferred a 22.5% decrease in muscle fascicle strain magnitude. Our findings demonstrate tendon elastic action in a small flying mammal and expand our understanding of the occurrence and action of series elastic actuator mechanisms in fluid-based locomotion. © 2015 The Author(s).

  18. Fluid transportation mechanisms by a coupled system of elastic membranes and magnetic fluids

    Ido, Y.; Tanaka, K.; Sugiura, Y.

    2002-01-01

    The basic properties of the fluid transportation mechanism that is produced by the coupled waves propagating along a thin elastic membrane covering a magnetic fluid layer in a shallow and long rectangular vessel are investigated. It is shown that the progressive magnetic field induced by the rectangular pulses generates sinusoidal vibration of the displacement of elastic membrane and makes the system work more efficiently than the magnetic field induced by the pulse-width-modulation method

  19. Resettable binary latch mechanism for use with paraffin linear motors

    Maus, Daryl; Tibbitts, Scott

    1991-01-01

    A new resettable Binary Latch Mechanism was developed utilizing a paraffin actuator as the motor. This linear actuator alternately latches between extended and retracted positions, maintaining either position with zero power consumption. The design evolution and kinematics of the latch mechanism are presented, as well as the development problems and lessons that were learned.

  20. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

    Angela Mihai, L.; Goriely, Alain

    2013-01-01

    Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

  1. Embryo mechanics: balancing force production with elastic resistance during morphogenesis.

    Davidson, Lance A

    2011-01-01

    Morphogenesis requires the spatial and temporal control of embryo mechanics, including force production and mechanical resistance to those forces, to coordinate tissue deformation and large-scale movements. Thus, biomechanical processes play a key role in directly shaping the embryo. Additional roles for embryo mechanics during development may include the patterning of positional information and to provide feedback to ensure the success of morphogenetic movements in shaping the larval body and organs. To understand the multiple roles of mechanics during development requires familiarity with engineering principles of the mechanics of structures, the viscoelastic properties of biomaterials, and the integration of force and stress within embryonic structures as morphogenesis progresses. In this chapter, we review the basic engineering principles of biomechanics as they relate to morphogenesis, introduce methods for quantifying embryo mechanics and the limitations of these methods, and outline a formalism for investigating the role of embryo mechanics in birth defects. We encourage the nascent field of embryo mechanics to adopt standard engineering terms and test methods so that studies of diverse organisms can be compared and universal biomechanical principles can be revealed. Copyright © 2011 Elsevier Inc. All rights reserved.

  2. Size dependent elastic modulus and mechanical resilience of dental enamel.

    O'Brien, Simona; Shaw, Jeremy; Zhao, Xiaoli; Abbott, Paul V; Munroe, Paul; Xu, Jiang; Habibi, Daryoush; Xie, Zonghan

    2014-03-21

    Human tooth enamel exhibits a unique microstructure able to sustain repeated mechanical loading during dental function. Although notable advances have been made towards understanding the mechanical characteristics of enamel, challenges remain in the testing and interpretation of its mechanical properties. For example, enamel was often tested under dry conditions, significantly different from its native environment. In addition, constant load, rather than indentation depth, has been used when mapping the mechanical properties of enamel. In this work, tooth specimens are prepared under hydrated conditions and their stiffnesses are measured by depth control across the thickness of enamel. Crystal arrangement is postulated, among other factors, to be responsible for the size dependent indentation modulus of enamel. Supported by a simple structure model, effective crystal orientation angle is calculated and found to facilitate shear sliding in enamel under mechanical contact. In doing so, the stress build-up is eased and structural integrity is maintained. Copyright © 2014 Elsevier Ltd. All rights reserved.

  3. Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

    Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)

    2013-11-15

    Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.

  4. Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

    Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi

    2013-01-01

    Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation

  5. P-S & S-P Elastic Wave Conversions from Linear Arrays of Oriented Microcracks

    Jiang, L.; Modiriasari, A.; Bobet, A.; Pyrak-Nolte, L. J.

    2017-12-01

    Natural and induced processes can produce oriented mechanical discontinuities such as en echelon cracks, fractures and faults. Previous research has shown that compressional to shear (P-S) wave conversions occur at normal incidence to a fracture because of cross-coupling fracture compliances (Nakagawa et al., 2000). Here, experiments and computer simulation are presented to demonstrate the link among cross-coupling stiffness, microcrack orientation and energy partitioning among P, S, and P-S/S-P waves. A FormLabs 2 3D printer was used to fabricate 7 samples (50 mm x 50 mm x 100 mm) with linear arrays of microcracks oriented at 0, 15, 30, 45, 60, 75, and 900 with a print resolution of 0.025 mm. The microcracks were elliptical in cross-sections (2 mm long by 1 mm wide), through the 50 mm thickness of sample, and spaced 3 mm (center-to-center for adjacent cracks). A 25 mm length of each sample contained no microcracks to act as a reference material. Broadband transducers (0.2-1.5 MHz) were used to transmit and receive P and polarized S wave signals that were propagated at normal incidence to the linear array of microcracks. P-wave amplitude increased, while S-wave amplitude remained relatively constant, as the microcrack orientation increased from 0o to 90o. At normal incidence, P-S and S-P wave conversions emerged and increased in amplitude as the crack inclination increased from 00 to 450. From 450 to 900, the amplitude of these converted modes decreased. Between negative and positive crack angles, the P-to-S and S-to-P waves were 1800 phase reversed. The observed energy partitioning matched the computed compliances obtained from numerical simulations with ABAQUS. The cross-coupling compliance for cracks inclined at 450 was found to be the smallest magnitude. 3D printing enabled the study of microstructural effects on macro-scale wave measurements. Information on the orientation of microcracks or even en echelon fractures and faults is contained in P-S conversions

  6. Elastic stress transmission and transformation (ESTT) by confined liquid: A new mechanics for fracture in elastic lithosphere of the earth

    Xu, Xing-Wang; Peters, Stephen; Liang, Guang-He; Zhang, Bao-Lin

    2016-01-01

    We report on a new mechanical principle, which suggests that a confined liquid in the elastic lithosphere has the potential to transmit a maximum applied compressive stress. This stress can be transmitted to the internal contacts between rock and liquid and would then be transformed into a normal compressive stress with tangential tensile stress components. During this process, both effective compressive normal stress and tensile tangential stresses arise along the liquid–rock contact. The minimum effective tensile tangential stress causes the surrounding rock to rupture. Liquid-driven fracture initiates at the point along the rock–liquid boundary where the maximum compressive stress is applied and propagates along a plane that is perpendicular to the minimum effective tensile tangential stress and also is perpendicular to the minimum principal stress.

  7. DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM

    O. L. Shved

    2014-01-01

    Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.

  8. Higher order coupling between rigid-body and elastic motion in flexible mechanisms

    Esat, I.I.; Ianakiev, A.

    1995-01-01

    The paper presents an investigation of the influence of the higher order coupling terms between the rigid-body and elastic motion into flexible mechanism dynamics. The configuration of the mechanical system is obtained by using the so called hybrid coordinates. The kinematic description of the mechanism was obtained using the D-H 4 x 4 transformation matrices. The elastic deformation of each point of the mechanism is described by the finite element modeling (FEM) type interpolation scheme. The dynamic model of the flexible mechanism consists due to the hybrid coordinates of two groups of differential equations. The first group describes the manipulator transport motion and the second group describes the vibration. In this paper the authors evaluated the contribution of the coupling terms between the two groups of differential equations and selected only those with high contribution

  9. Linear modeling of possible mechanisms for parkinson tremor generation

    Lohnberg, P.

    1978-01-01

    The power of Parkinson tremor is expressed in terms of possibly changed frequency response functions between relevant variables in the neuromuscular system. The derivation starts out from a linear loopless equivalent model of mechanisms for general tremor generation. Hypothetical changes in this

  10. Multispectral linear array (MLA) focal plane mechanical and thermal design

    Mitchell, A. S.; Kaminski, E. F.

    1982-01-01

    The mechanical and thermal design of an integrated focal plane subsystem of a Multispectral Linear Array (MLA) instrument is discussed in terms of focal-plane alignment, thermoelastic performance, and thermal requirements. The modular construction and thermal control of the focal plane array are discussed.

  11. Effect of pressure variation on structural, elastic, mechanical, optoelectronic and thermodynamic properties of SrNaF3 fluoroperovskite

    Erum, Nazia; Azhar Iqbal, Muhammad

    2017-12-01

    The effect of pressure variation on structural, electronic, elastic, mechanical, optical and thermodynamic characteristics of cubic SrNaF3 fluoroperovskite have been investigated by employing first-principles method within the framework of gradient approximation (GGA). For the total energy calculations, we have used the full-potential linearized augmented plane wave (FP-LAPW) method. Thermodynamic properties are computed in terms of quasi-harmonic Debye model. The pressure effects are determined in the range of 0-25 GPa, in which mechanical stability of SrNaF3 fluoroperovskite remains valid. A prominent decrease in lattice constant and bonds length is observed with the increase in pressure from 0 to 25 GPa. The effect of increase in pressure on band structure calculations with GGA and GGA plus Tran-Blaha modified Becke-Johnson (TB-mBJ) potential reveals a predominant characteristic associated with widening of bandgap. The influence of pressure on set of isotropic elastic parameters and their related properties are numerically estimated for SrNaF3 polycrystalline aggregate. Apart of linear dependence of elastic coefficients, transition from brittle to ductile behavior is observed as pressure is increased from 0 to 25 GPa. We have successfully obtained variation of lattice constant, volume expansion, bulk modulus, Debye temperature and specific heat capacities with pressure and temperature in the range of 0-25 GPa and 0-600 K. All the calculated optical properties such as the complex dielectric function ɛ(ω), optical conductivity σ(ω), energy loss function L(ω), absorption coefficient α(w), refractive index n(ω), reflectivity R(ω), and effective number of electrons n eff, via sum rules shift towards the higher energies under the application of pressure.

  12. Geometric method for stability of non-linear elastic thin shells

    Ivanova, Jordanka

    2002-01-01

    PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...

  13. Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

    Gómez, D.; Nazarov, S. A.; Pérez, M. E.

    2018-04-01

    We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

  14. Rational design of soft mechanical metamaterials : Independent tailoring of elastic properties with randomness

    Mirzaali Mazandarani, M.J.; Hedayati, R.; Vena, P; Vergani, L.; Strano, M.; Zadpoor, A.A.

    2017-01-01

    The elastic properties of mechanical metamaterials are direct functions of their topological designs. Rational design approaches based on computational models could, therefore, be used to devise topological designs that result in the desired properties. It is of particular importance to

  15. On the mechanics of elastic lines in thin shells

    Benet, Eduard; Vernerey, Franck

    The deformation of soft shells in nature and engineering is often conditioned by the presence of lines whose mechanical properties are different from the shell. For instance, the deformation of tree leaves is conditioned by the presence of harder stems, and cell mitosis is driven by a stiffening line along its membrane. From an experimental standpoint, many groups have taken advantage of this feature to develop self-actuated shells with prescribed deformations. Examples include the polymerization of gels along certain lines, or the inclusion of stiffer lines via 3D printing. However, there is not yet a general continuum theory that accounts for this type of discontinuity within the membrane. Hence, we extend the general shell theory to account for the inclusion of a line that potentially induces jumps in stresses, couple stresses and moments, across its thickness. This is achieved via coupling the rod and the membrane deformations, and ensuring continuity of displacements. The model is then applied to three important problems: a constriction disc inside a shell of revolution, the induced twisting of a shell via the torsion of an embedded line, and the effect of an helicoidal line on the uni-axial deformation of a cylindrical shell. National Science Foundation CAREER award 1350090.

  16. Foundations of the non-linear mechanics of continua

    Sedov, L I

    1966-01-01

    International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable

  17. EVALUATION OF ELASTICITY AND MECHANICAL PROPERTIES OF BREAD DOUGH MADE WITH REPLACED FLOUR POTATO (IPOMOEA BATATA

    Ely Fernando Sacón Vera

    2016-10-01

    Full Text Available The effect of the incorporation of sweet potato flour, with 30% replacement in 1kg of wheat flour was evaluated to determine the behavior of elastic and mechanical properties during the kneading and baking stage of bread. For the evaluation the following varieties were studied: Morado Brazil, Morado Ecuador, Guayaco Morado, Ina and Toquecita, and the evaluated properties were: texture (hardness, elasticity, firmness, chewiness measured by a texture meter Bloomfield and volume was measured by INEN standard (NTE INEN 0530: 80. The design employed was completely at random, using analysis of variance at 5% significance level. The results obtained showed that elasticity attribute in texture variable presented significant differences (P <0.05. Analysis concluded that including Toquecita flour in the mixture to form the dough, had the highest elasticity of 13.32mm. However, Morado Ecuador variety flour presented a 6.24 mm elasticity value, ideal for both the malleability of the dough and the freshness of the bread, and concerning volume, the inclusion of Ecuador Morado flour and Ina in the formulation of bread, showed an increase in volume at 93.30 and 93.67cm3 respectively, close to the normed value for wheat flour bread.

  18. Elastic-plastic analysis of fracture mechanics test specimens. Part 2

    Talja, H.; Wallin, K.

    1984-12-01

    This is second part of the report of the research program 'Comparisons between computational and experimental elastic-plastic results' started at the Technical Research Centre of Finland in 1981. The first part of the research program was reported earlier and contained a two dimensional linear elastic finite element analysis of four specimen geometries (CT, RCT, ASTM-3P and Charpy-V) and testing and elastic-plastic analysis of the specimen (EGF71; 1TCT, material A 542). In this report the second part of the program containing the testing and 2-D elastic-plastic analyses of five specimens is described. The four specimen geometries mentioned above and two different materials (stainless steel AISI 304 and ferrite pressure vessel steel A533B) are considered. The following comparisons are presented in the report: load vs. load displacement curves, J-integral, crack opening displacement (COD), J vs. COD and the size of the plastic zone. The agreement between the computational and experimental results is quite good. Complete agreement can be achieved only with 3-dimensional calculation models. (author)

  19. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

    Angela Mihai, L.

    2013-03-01

    Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

  20. Mechanical properties of two-way grid shells optimized considering roundness and elastic stiffness

    Ogawa, Toshiyuki; Yuta, Nishikawa; Rie, Tateishi; Ohsaki, Makoto

    2002-01-01

    A single-layer two-way grid shell defined by Bezier surface is optimized by coordinates of the control points as design variables. The purpose of this paper is to find optimal shapes considering roundness and elastic stiffness, and to investigate their mechanical properties. The distance of the center of curvature from the specified point is used for formulating the objective function for generating a round shape. Consider next a problem of minimizing the compliance as mechanical performance measure. The compliance is defined by the external work against the static loads applied to the nodes. The mechanically optimal shape is different from the round shape. Therefore, the multi objective optimization problem is formulated for optimizing the two objectives, which are roundness and the elastic stiffness defined by using the compliance. The constraint method is used for obtaining Pareto optimal solutions between the two objectives. We optimize single-layer two-way grid shells with square and rectangle plans. Mechanical properties of the optimal shapes are investigated by compliance and the distributions of axial force and bending moment. The round shape is significantly dominated by the bending moment and its compliance is large. The bending moment of the mechanically optimal shape is not very large, and the latticed shell has large stiffness through axial deformation. A trade-off shape is round enough, and the influence of the bending moment is smaller than that of the optimal round shape and the elastic stiffness is moderately large

  1. Elastic-plastic Fracture Mechanics Assessment of nozzle corners submitted to thermal shock loading

    Chapuliot, S.; Marie, S.

    2016-01-01

    This paper focuses on the development of a simplified analytical scheme for the elastic-plastic Fracture Mechanics Assessment of large nozzle corners. Within that frame, following the specific numerical effort performed for the definition of a Stress Intensity Factor compendium, complementary elastic-plastic developments are proposed here for the consideration of the thermal shock loading in the elastic-plastic domain: this type of loading is a major loading for massive structures such as nozzle corners of large components. Thus, an important numerical was performed in order to extend the applicability domain of existing analytical schemes to those complex geometries. The final formulation is a simple one, applicable to a large variety of materials and geometrical configurations as long as the structure is large and the defect remains small in comparison to the internal radius of the nozzle. - Highlights: • Fracture Mechanics Assessment of large nozzle corners. • Elastic-plastic Stress Intensity Factor determination under thermal shock loading. • Semi-analytical schemes for J calculation.

  2. Pulsed-laser time-resolved thermal mirror technique in low-absorbance homogeneous linear elastic materials.

    Lukasievicz, Gustavo V B; Astrath, Nelson G C; Malacarne, Luis C; Herculano, Leandro S; Zanuto, Vitor S; Baesso, Mauro L; Bialkowski, Stephen E

    2013-10-01

    A theoretical model for a time-resolved photothermal mirror technique using pulsed-laser excitation was developed for low absorption samples. Analytical solutions to the temperature and thermoelastic deformation equations are found for three characteristic pulse profiles and are compared to finite element analysis methods results for finite samples. An analytical expression for the intensity of the center of a continuous probe laser at the detector plane is derived using the Fresnel diffraction theory, which allows modeling of experimental results. Experiments are performed in optical glasses, and the models are fitted to the data. The parameters of the fit are in good agreement with previous literature data for absorption, thermal diffusion, and thermal expansion of the materials tested. The combined modeling and experimental techniques are shown to be useful for quantitative determination of the physical properties of low absorption homogeneous linear elastic material samples.

  3. An anisotropic linear thermo-viscoelastic constitutive law - Elastic relaxation and thermal expansion creep in the time domain

    Pettermann, Heinz E.; DeSimone, Antonio

    2017-09-01

    A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.

  4. Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

    Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

    2014-01-01

    The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

  5. On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

    BOERTJENS, G. J.; VAN HORSSEN, W. T.

    2000-08-01

    In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

  6. Mechanical analysis of single myocyte contraction in a 3-D elastic matrix.

    John Shaw

    Full Text Available Cardiac myocytes experience mechanical stress during each heartbeat. Excessive mechanical stresses under pathological conditions cause functional and structural remodeling that lead to heart diseases, yet the precise mechanisms are still incompletely understood. To study the cellular and molecular level mechanotransduction mechanisms, we developed a new 'cell-in-gel' experimental system to exert multiaxial (3-D stresses on a single myocyte during active contraction.Isolated myocytes are embedded in an elastic hydrogel to simulate the mechanical environment in myocardium (afterload. When electrically stimulated, the in-gel myocyte contracts while the matrix resists shortening and broadening of the cell, exerting normal and shear stresses on the cell. Here we provide a mechanical analysis, based on the Eshelby inclusion problem, of the 3-D strain and stress inside and outside the single myocyte during contraction in an elastic matrix.(1 The fractional shortening of the myocyte depends on the cell's geometric dimensions and the relative stiffness of the cell to the gel. A slender or softer cell has less fractional shortening. A myocyte of typical dimensions embedded in a gel of similar elastic stiffness can contract only 20% of its load-free value. (2 The longitudinal stress inside the cell is about 15 times the transverse stress level. (3 The traction on the cell surface is highly non-uniform, with a maximum near its ends, showing 'hot spots' at the location of intercalated disks. (4 The mechanical energy expenditure of the myocyte increases with the matrix stiffness in a monotonic and nonlinear manner.Our mechanical analyses provide analytic solutions that readily lend themselves to parametric studies. The resulting 3-D mapping of the strain and stress states serve to analyze and interpret ongoing cell-in-gel experiments, and the mathematical model provides an essential tool to decipher and quantify mechanotransduction mechanisms in cardiac

  7. A linear chromatic mechanism drives the pupillary response.

    Tsujimura, S.; Wolffsohn, J. S.; Gilmartin, B.

    2001-01-01

    Previous studies have shown that a chromatic mechanism can drive pupil responses. The aim of this research was to clarify whether a linear or nonlinear chromatic mechanism drives pupillary responses by using test stimuli of various colours that are defined in cone contrast space. The pupil and accommodation responses evoked by these test stimuli were continuously and simultaneously objectively measured by photorefraction. The results with isochromatic and isoluminant stimuli showed that the accommodative level remained approximately constant (< 0.25 D change in mean level) even when the concurrent pupillary response was large (ca. 0.30 mm). The pupillary response to an isoluminant grating was sustained, delayed (by ca. 60 ms) and larger in amplitude than that for a isochromatic uniform stimulus, which supports previous work suggesting that the chromatic mechanism contributes to the pupillary response. In a second experiment, selected chromatic test gratings were used and isoresponse contours in cone contrast space were obtained. The results showed that the isoresponse contour in cone contrast space is well described (r(2) = 0.99) by a straight line with a positive slope. The results indicate that a /L - M/ linear chromatic mechanism, whereby a signal from the long wavelength cone is subtracted from that of the middle wavelength cone and vice versa, drives pupillary responses. PMID:11674867

  8. Extracellular matrix elasticity and topography: material-based cues that affect cell function via conserved mechanisms

    Janson, Isaac A.; Putnam, Andrew J.

    2014-01-01

    Chemical, mechanical, and topographic extracellular matrix (ECM) cues have been extensively studied for their influence on cell behavior. These ECM cues alter cell adhesion, cell shape, and cell migration, and activate signal transduction pathways to influence gene expression, proliferation, and differentiation. ECM elasticity and topography, in particular, have emerged as material properties of intense focus based on strong evidence these physical cue can partially dictate stem cell differentiation. Cells generate forces to pull on their adhesive contacts, and these tractional forces appear to be a common element of cells’ responses to both elasticity and topography. This review focuses on recently published work that links ECM topography and mechanics and their influence on differentiation and other cell behaviors, We also highlight signaling pathways typically implicated in mechanotransduction that are (or may be) shared by cells subjected to topographic cues. Finally, we conclude with a brief discussion of the potential implications of these commonalities for cell based therapies and biomaterial design. PMID:24910444

  9. Smartphone application for mechanical quality assurance of medical linear accelerators.

    Kim, Hwiyoung; Lee, Hyunseok; Park, Jong In; Choi, Chang Heon; Park, So-Yeon; Kim, Hee Jung; Kim, Young Suk; Ye, Sung-Joon

    2017-06-07

    Mechanical quality assurance (QA) of medical linear accelerators consists of time-consuming and human-error-prone procedures. We developed a smartphone application system for mechanical QA. The system consists of two smartphones: one attached to a gantry for obtaining real-time information on the mechanical parameters of the medical linear accelerator, and another displaying real-time information via a Bluetooth connection with the former. Motion sensors embedded in the smartphone were used to measure gantry and collimator rotations. Images taken by the smartphone's high-resolution camera were processed to evaluate accuracies of jaw-positioning, crosshair centering and source-to-surface distance (SSD). The application was developed using Android software development kit and OpenCV library. The accuracy and precision of the system was validated against an optical rotation stage and digital calipers, prior to routine QA measurements of five medical linear accelerators. The system accuracy and precision in measuring angles and lengths were determined to be 0.05  ±  0.05° and 0.25  ±  0.14 mm, respectively. The mean absolute errors (MAEs) in QA measurements of gantry and collimator rotation were 0.05  ±  0.04° and 0.05  ±  0.04°, respectively. The MAE in QA measurements of light field was 0.39  ±  0.36 mm. The MAEs in QA measurements of crosshair centering and SSD were 0.40  ±  0.35 mm and 0.41  ±  0.32 mm, respectively. In conclusion, most routine mechanical QA procedures could be performed using the smartphone application system with improved precision and within a shorter time-frame, while eliminating potential human errors.

  10. Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints.

    Salari, Autoosa; Navarro, Marco A; Milescu, Mirela; Milescu, Lorin S

    2018-02-05

    To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra-based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses. © 2018 Salari et al.

  11. Linear-scaling quantum mechanical methods for excited states.

    Yam, ChiYung; Zhang, Qing; Wang, Fan; Chen, GuanHua

    2012-05-21

    The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and

  12. Mechanically equivalent elastic-plastic deformations and the problem of plastic spin

    Steigmann David J.

    2011-01-01

    Full Text Available The problem of plastic spin is phrased in terms of a notion of mechanical equivalence among local intermediate configurations of an elastic/ plastic crystalline solid. This idea is used to show that, without further qualification, the plastic spin may be suppressed at the constitutive level. However, the spin is closely tied to an underlying undistorted crystal lattice which, once specified, eliminates the freedom afforded by mechanical equivalence. As a practical matter a constitutive specification of plastic spin is therefore required. Suppression of plastic spin thus emerges as merely one such specification among many. Restrictions on these are derived in the case of rate-independent response.

  13. Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEMin Nearly Incompressible Linear Elasticity

    Dörsek, Philipp; Melenk, Jens M.

    2017-01-01

    We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...

  14. Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

    Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco

    2017-11-01

    The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

  15. Validation of favor code linear elastic fracture solutions for finite-length flaw geometries

    Dickson, T.L.; Keeney, J.A.; Bryson, J.W.

    1995-01-01

    One of the current tasks within the US Nuclear Regulatory Commission (NRC)-funded Heavy Section Steel Technology Program (HSST) at Oak Ridge National Laboratory (ORNL) is the continuing development of the FAVOR (Fracture, analysis of Vessels: Oak Ridge) computer code. FAVOR performs structural integrity analyses of embrittled nuclear reactor pressure vessels (RPVs) with stainless steel cladding, to evaluate compliance with the applicable regulatory criteria. Since the initial release of FAVOR, the HSST program has continued to enhance the capabilities of the FAVOR code. ABAQUS, a nuclear quality assurance certified (NQA-1) general multidimensional finite element code with fracture mechanics capabilities, was used to generate a database of stress-intensity-factor influence coefficients (SIFICs) for a range of axially and circumferentially oriented semielliptical inner-surface flaw geometries applicable to RPVs with an internal radius (Ri) to wall thickness (w) ratio of 10. This database of SIRCs has been incorporated into a development version of FAVOR, providing it with the capability to perform deterministic and probabilistic fracture analyses of RPVs subjected to transients, such as pressurized thermal shock (PTS), for various flaw geometries. This paper discusses the SIFIC database, comparisons with other investigators, and some of the benchmark verification problem specifications and solutions

  16. Smartphone application for mechanical quality assurance of medical linear accelerators

    Kim, Hwiyoung; Lee, Hyunseok; In Park, Jong; Choi, Chang Heon; Park, So-Yeon; Kim, Hee Jung; Kim, Young Suk; Ye, Sung-Joon

    2017-06-01

    Mechanical quality assurance (QA) of medical linear accelerators consists of time-consuming and human-error-prone procedures. We developed a smartphone application system for mechanical QA. The system consists of two smartphones: one attached to a gantry for obtaining real-time information on the mechanical parameters of the medical linear accelerator, and another displaying real-time information via a Bluetooth connection with the former. Motion sensors embedded in the smartphone were used to measure gantry and collimator rotations. Images taken by the smartphone’s high-resolution camera were processed to evaluate accuracies of jaw-positioning, crosshair centering and source-to-surface distance (SSD). The application was developed using Android software development kit and OpenCV library. The accuracy and precision of the system was validated against an optical rotation stage and digital calipers, prior to routine QA measurements of five medical linear accelerators. The system accuracy and precision in measuring angles and lengths were determined to be 0.05  ±  0.05° and 0.25  ±  0.14 mm, respectively. The mean absolute errors (MAEs) in QA measurements of gantry and collimator rotation were 0.05  ±  0.04° and 0.05  ±  0.04°, respectively. The MAE in QA measurements of light field was 0.39  ±  0.36 mm. The MAEs in QA measurements of crosshair centering and SSD were 0.40  ±  0.35 mm and 0.41  ±  0.32 mm, respectively. In conclusion, most routine mechanical QA procedures could be performed using the smartphone application system with improved precision and within a shorter time-frame, while eliminating potential human errors.

  17. THE STRESS-STRAIN STATE OF ELASTIC HALF-SPACE FROM RUNNING LINEAR LOAD ACTING ON THE LIMITED AND UNLIMITED EXTENT OVER ITS SURFACE

    I. K. Badalakha

    2009-02-01

    Full Text Available The article shows the result of solving the problem of stress-strain state of an elastic half-space because of the load action that uniformly distributed over the line, with the use of untraditional linear dependence of deformations on stressed state that is different from the generalized Hooke’s law.

  18. Development of a computer code 'CRACK' for elastic and elastoplastic fracture mechanics analysis of 2-D structures by finite element technique

    Dutta, B.K.; Kakodkar, A.; Maiti, S.K.

    1986-01-01

    The fracture mechanics analysis of nuclear components is required to ensure prevention of sudden failure due to dynamic loadings. The linear elastic analysis near to a crack tip shows presence of stress singularity at the crack tip. The simulation of this singularity in numerical methods enhance covergence capability. In finite element technique this can be achieved by placing mid nodes of 8 noded or 6 noded isoparametric elements, at one fourth ditance from crack tip. Present report details this characteristic of finite element, implementation of this element in a code 'CRACK', implementation of J-integral to compute stress intensity factor and solution of number of cases for elastic and elastoplastic fracture mechanics analysis. 6 refs., 6 figures. (author)

  19. Computational modeling of elastic properties of carbon nanotube/polymer composites with interphase regions. Part II: Mechanical modeling

    Han, Fei; Azdoud, Yan; Lubineau, Gilles

    2014-01-01

    We present two modeling approaches for predicting the macroscopic elastic properties of carbon nanotubes/polymer composites with thick interphase regions at the nanotube/matrix frontier. The first model is based on local continuum mechanics

  20. Linear differential equations to solve nonlinear mechanical problems: A novel approach

    Nair, C. Radhakrishnan

    2004-01-01

    Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

  1. A first principle calculation of anisotropic elastic, mechanical and electronic properties of TiB

    Zhang, Junqin; Zhao, Bin; Ma, Huihui; Wei, Qun; Yang, Yintang

    2018-04-01

    The structural, mechanical and electronic properties of the NaCl-type structure TiB are theoretically calculated based on the first principles. The density of states of TiB shows obvious density peaks at -0.70eV. Furthermore, there exists a pseudogap at 0.71eV to the right of the Fermi level. The calculated structural and mechanical parameters (i.e., bulk modulus, shear modulus, Young's modulus, Poisson's ratio and universal elastic anisotropy index) were in good agreement both with the previously reported experimental values and theoretical results at zero pressure. The mechanical stability criterion proves that TiB at zero pressure is mechanistically stable and exhibits ductility. The universal anisotropic index and the 3D graphics of Young's modulus are also given in this paper, which indicates that TiB is anisotropy under zero pressure. Moreover, the effects of applied pressures on the structural, mechanical and anisotropic elastic of TiB were studied in the range from 0 to 100GPa. It was found that ductility and anisotropy of TiB were enhanced with the increase of pressure.

  2. Biaxial Stretch Improves Elastic Fiber Maturation, Collagen Arrangement, and Mechanical Properties in Engineered Arteries.

    Huang, Angela H; Balestrini, Jenna L; Udelsman, Brooks V; Zhou, Kevin C; Zhao, Liping; Ferruzzi, Jacopo; Starcher, Barry C; Levene, Michael J; Humphrey, Jay D; Niklason, Laura E

    2016-06-01

    Tissue-engineered blood vessels (TEVs) are typically produced using the pulsatile, uniaxial circumferential stretch to mechanically condition and strengthen the arterial grafts. Despite improvements in the mechanical integrity of TEVs after uniaxial conditioning, these tissues fail to achieve critical properties of native arteries such as matrix content, collagen fiber orientation, and mechanical strength. As a result, uniaxially loaded TEVs can result in mechanical failure, thrombus, or stenosis on implantation. In planar tissue equivalents such as artificial skin, biaxial loading has been shown to improve matrix production and mechanical properties. To date however, multiaxial loading has not been examined as a means to improve mechanical and biochemical properties of TEVs during culture. Therefore, we developed a novel bioreactor that utilizes both circumferential and axial stretch that more closely simulates loading conditions in native arteries, and we examined the suture strength, matrix production, fiber orientation, and cell proliferation. After 3 months of biaxial loading, TEVs developed a formation of mature elastic fibers that consisted of elastin cores and microfibril sheaths. Furthermore, the distinctive features of collagen undulation and crimp in the biaxial TEVs were absent in both uniaxial and static TEVs. Relative to the uniaxially loaded TEVs, tissues that underwent biaxial loading remodeled and realigned collagen fibers toward a more physiologic, native-like organization. The biaxial TEVs also showed increased mechanical strength (suture retention load of 303 ± 14.53 g, with a wall thickness of 0.76 ± 0.028 mm) and increased compliance. The increase in compliance was due to combinatorial effects of mature elastic fibers, undulated collagen fibers, and collagen matrix orientation. In conclusion, biaxial stretching is a potential means to regenerate TEVs with improved matrix production, collagen organization, and mechanical

  3. Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity

    Amir R. Ali

    2017-01-01

    Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.

  4. Elastic contact mechanics: percolation of the contact area and fluid squeeze-out.

    Persson, B N J; Prodanov, N; Krick, B A; Rodriguez, N; Mulakaluri, N; Sawyer, W G; Mangiagalli, P

    2012-01-01

    The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.

  5. Mechanical Design of Innovative Electromagnetic Linear Actuators for Marine Applications

    Muscia, Roberto

    2017-11-01

    We describe an engineering solution to manufacture electromagnetic linear actuators for moving rudders and fin stabilizers of military shipsItalian Ministry of Defence, General Direction of Naval Equipments (NAVARM), Projects ISO (2012-2014) and EDDA (2015-2017). . The solution defines the transition from the conceptual design of the device initially studied from an electromagnetic point of view to mechanical configurations that really work. The structural problems that have been resolved with the proposed configuration are described. In order to validate the design choices discussed we illustrate some results of the numerical simulations performed by the structural finite elements method. These results quantitatively justify the suggested mechanical solution by evaluating stresses and deformations in a virtual prototype of the structure during its functioning. The parts of the device that have been studied are the most critical because in cases of excessive deformation/stress, they can irreparably compromise the actuator operation. These parts are the pole piece-base set and the retention cages of the permanent magnets. The FEM analysis has allowed us to identify the most stressed areas of the previous elements whose shape has been appropriately designed so as to reduce the maximum stresses and deformations. Moreover, the FEM analysis helped to find the most convenient solution to join the pole pieces to the respective bases. The good results obtained by the suggested engineering solution have been experimentally confirmed by tests on a small prototype actuator purposely manufactured. Finally, a qualitative analysis of the engineering problems that have to be considered to design electromagnetic linear actuators bigger than the one already manufactured is illustrated.

  6. Mechanical Design of Innovative Electromagnetic Linear Actuators for Marine Applications

    Muscia Roberto

    2017-11-01

    Full Text Available We describe an engineering solution to manufacture electromagnetic linear actuators for moving rudders and fin stabilizers of military shipsItalian Ministry of Defence, General Direction of Naval Equipments (NAVARM, Projects ISO (2012-2014 and EDDA (2015-2017.. The solution defines the transition from the conceptual design of the device initially studied from an electromagnetic point of view to mechanical configurations that really work. The structural problems that have been resolved with the proposed configuration are described. In order to validate the design choices discussed we illustrate some results of the numerical simulations performed by the structural finite elements method. These results quantitatively justify the suggested mechanical solution by evaluating stresses and deformations in a virtual prototype of the structure during its functioning. The parts of the device that have been studied are the most critical because in cases of excessive deformation/stress, they can irreparably compromise the actuator operation. These parts are the pole piece-base set and the retention cages of the permanent magnets. The FEM analysis has allowed us to identify the most stressed areas of the previous elements whose shape has been appropriately designed so as to reduce the maximum stresses and deformations. Moreover, the FEM analysis helped to find the most convenient solution to join the pole pieces to the respective bases. The good results obtained by the suggested engineering solution have been experimentally confirmed by tests on a small prototype actuator purposely manufactured. Finally, a qualitative analysis of the engineering problems that have to be considered to design electromagnetic linear actuators bigger than the one already manufactured is illustrated.

  7. Structural, elastic, mechanical and thermodynamic properties of Terbium oxide: First-principles investigations

    Samah Al-Qaisi

    Full Text Available First-principles investigations of the Terbium oxide TbO are performed on structural, elastic, mechanical and thermodynamic properties. The investigations are accomplished by employing full potential augmented plane wave FP-LAPW method framed within density functional theory DFT as implemented in the WIEN2k package. The exchange-correlation energy functional, a part of the total energy functional, is treated through Perdew Burke Ernzerhof scheme of the Generalized Gradient Approximation PBEGGA. The calculations of the ground state structural parameters, like lattice constants a0, bulk moduli B and their pressure derivative B′ values, are done for the rock-salt RS, zinc-blende ZB, cesium chloride CsCl, wurtzite WZ and nickel arsenide NiAs polymorphs of the TbO compound. The elastic constants (C11, C12, C13, C33, and C44 and mechanical properties (Young’s modulus Y, Shear modulus S, Poisson’s ratio σ, Anisotropic ratio A and compressibility β, were also calculated to comprehend its potential for valuable applications. From our calculations, the RS phase of TbO compound was found strongest one mechanically amongst the studied cubic structures whereas from hexagonal phases, the NiAs type structure was found stronger than WZ phase of the TbO. To analyze the ductility of the different structures of the TbO, Pugh’s rule (B/SH and Cauchy pressure (C12–C44 approaches are used. It was found that ZB, CsCl and WZ type structures of the TbO were of ductile nature with the obvious dominance of the ionic bonding while RS and NiAs structures exhibited brittle nature with the covalent bonding dominance. Moreover, Debye temperature was calculated for both cubic and hexagonal structures of TbO in question by averaging the computed sound velocities. Keywords: DFT, TbO, Elastic properties, Thermodynamic properties

  8. Three-dimensional elastic--plastic stress and strain analyses for fracture mechanics: complex geometries

    Bellucci, H.J.

    1975-11-01

    The report describes the continuation of research into capability for three-dimensional elastic-plastic stress and strain analysis for fracture mechanics. A computer program, MARC-3D, has been completed and was used to analyze a cylindrical pressure vessel with a nozzle insert. A method for generating crack tip elements was developed and a model was created for a cylindrical pressure vessel with a nozzle and an imbedded flaw at the inside nozzle corner. The MARC-3D program was again used to analyze this flawed model. Documentation for the use of the MARC-3D computer program has been included as an appendix

  9. Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

    Hanks, Brantley R.; Skelton, Robert E.

    1991-01-01

    Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

  10. Mechanism of rock shattering by explosions, depending on the nature of jointing and the elastic state

    Mosinets, V N

    1966-01-01

    For proper use of explosives in shattering rock it is necessary to understand the mechanism of shattering. To a great extent this mechanism of shattering is controlled by fracturing in the rock and by the elastic properties of the rock. The processes of shattering as a result of explosion are analyzed, and the conclusion is made that, in its general interpretation, the mechanism of shattering is merely of theoretical interest. The applicability to actual media changes according to structure of the medium. Relatively massive rocks are characterized by an asymmetrical distribution function of the joints and micro-fractures and other inhomogeneities, the mode being shifted to the left of the asymmetry center. Rocks cut by an extensive network of microfractures and joints are characterized by an approximately normal distribution function; rocks cut by large joints have an asymmetrical distribution function, with the mode shifted to the right of the asymmetry center.

  11. Elastic scattering of helium ions on 9Be nuclei and exchange mechanisms

    Burtebaev, N.; Dujsebaev, B.A.

    1999-01-01

    Among nuclei of 1p-shell 9 Be is an extremely deformed nucleus with cluster structure. This considerably impedes determination of nucleus-nucleus potential of interaction. The latter relates to the fact that cross-section of 3 He ion and ?-particle elastic scattering on light nuclei is formed by not only mechanism of mere potential nature but also by other processes of heavy breakaway and displacement as well as by effects of channel relation. Final probability of 6 He+ and 3 He and 5 He+? cluster existence in 9 Be nucleus can be determined in the processes of 3 He or ?-particle ion scattering. As a result, it can cause considerable growth of cross-section under backward angles due to exchange of impinging particle with identical cluster in a nucleus. In order to study the contribution of different mechanisms into formation of cross-section of elastic scattering of helium nuclides on 9 Be nucleus we have performed series of experiments in broad angular range at energies 8-20 MeV/nucleon at derived beams of isochronous cyclotron of the Institute of Nuclear Physics of Kazakhstan national Nuclear Centre

  12. J-integral elastic plastic fracture mechanics evaluation of the stability of cracks in nuclear reactor pressure vessels

    Gomez, M.P.; McMeeking, R.M.; Parks, D.M.

    1980-06-01

    Contributions were made toward developing a new methodology to assess the stability of cracks in pressure vessels made from materials that exhibit a significant increase in toughness during the early increments of crack growth. It has a wide range of validity from linear elastic to fully plastic behavior

  13. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

    Nahed S. Hussein

    2014-01-01

    Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

  14. Linear and non-linear systems identification for adaptive control in mechanical applications vibration suppression

    Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco

    2012-04-01

    During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.

  15. Technical report on micro-mechanical versus conventional modelling in non-linear fracture mechanics

    2001-07-01

    While conventional fracture mechanics is capable of predicting crack growth behaviour if sufficient experimental observations are available, micro-mechanical modelling can both increase the accuracy of these predictions and model phenomena that are inaccessible by the conventional theory such as the ductile-cleavage temperature transition. A common argument against micro-mechanical modelling is that it is too complicated for use in routine engineering applications. This is both a computational and an educational problem. That micro-mechanical modelling is unnecessarily complicated is certainly true in many situations. The on-going development of micro-mechanical models, computational algorithms and computer speed will however most probably diminish the computational problem rather rapidly. Compare for instance the rate of development of computational methods for structural analysis. Meanwhile micro-mechanical modelling may serve as a tool by which more simplified engineering methods can be validated. The process of receiving a wide acceptance of the new methods is probably much slower. This involves many steps. First the research community must be in reasonable agreement on the methods and their use. Then the methods have to be implemented into computer software and into code procedures. The development and acceptance of conventional fracture mechanics may serve as an historical example of the time required before a new methodology has received a wide usage. The CSNI Working Group on Integrity and Ageing (IAGE) decided to carry out a report on micro-mechanical modeling to promote this promising and valuable technique. The report presents a comparison with non-linear fracture mechanics and highlights key aspects that could lead to a better knowledge and accurate predictions. Content: - 1. Introduction; - 2. Concepts of non-linear fracture mechanics with point crack tip modelling; - 3. Micro-mechanical models for cleavage fracture; - 4, Micro-mechanical modelling of

  16. A variationally coupled FE-BE method for elasticity and fracture mechanics

    Lu, Y. Y.; Belytschko, T.; Liu, W. K.

    1991-01-01

    A new method for coupling finite element and boundary element subdomains in elasticity and fracture mechanics problems is described. The essential feature of this new method is that a single variational statement is obtained for the entire domain, and in this process the terms associated with tractions on the interfaces between the subdomains are eliminated. This provides the additional advantage that the ambiguities associated with the matching of discontinuous tractions are circumvented. The method leads to a direct procedure for obtaining the discrete equations for the coupled problem without any intermediate steps. In order to evaluate this method and compare it with previous methods, a patch test for coupled procedures has been devised. Evaluation of this variationally coupled method and other methods, such as stiffness coupling and constraint traction matching coupling, shows that this method is substantially superior. Solutions for a series of fracture mechanics problems are also reported to illustrate the effectiveness of this method.

  17. Effect of elastic and plastic tensile mechanical loading on the magnetic properties of NGO electrical steel

    Leuning, N., E-mail: nora.leuning@iem.rwth-aachen.de [Institute of Electrical Machines, RWTH Aachen University, D-52062 Aachen (Germany); Steentjes, S. [Institute of Electrical Machines, RWTH Aachen University, D-52062 Aachen (Germany); Schulte, M.; Bleck, W. [Steel Institute, RWTH Aachen University, D-52072 Aachen (Germany); Hameyer, K. [Institute of Electrical Machines, RWTH Aachen University, D-52062 Aachen (Germany)

    2016-11-01

    The magnetic properties of non-grain-oriented (NGO) electrical steels are highly susceptible to mechanical stresses, i.e., residual, external or thermal ones. For rotating electrical machines, mechanical stresses are inevitable and originate from different sources, e.g., material processing, machine manufacturing and operating conditions. The efficiency and specific losses are largely altered by different mechanical stress states. In this paper the effect of tensile stresses and plastic deformations on the magnetic properties of a 2.9 wt% Si electrical steel are studied. Particular attention is paid to the effect of magnetic anisotropy, i.e., the influence of the direction of applied mechanical stress with respect to the rolling direction. Due to mechanical stress, the induced anisotropy has to be evaluated as it is related to the stress-dependent magnetostriction constant and the grain alignment. - Highlights: • A detailed look at magnetic anisotropy of FeSi NGO electrical steel. • Study of magnetic behavior under elastic as well as plastic tensile stresses. • Correlation of magnetic behavior with microscopic deformation mechanisms. • Discussion of detrimental and beneficial effects of external stresses. • Loss separation at different polarizations and frequencies under increasing stress.

  18. Effect of elastic and plastic tensile mechanical loading on the magnetic properties of NGO electrical steel

    Leuning, N.; Steentjes, S.; Schulte, M.; Bleck, W.; Hameyer, K.

    2016-01-01

    The magnetic properties of non-grain-oriented (NGO) electrical steels are highly susceptible to mechanical stresses, i.e., residual, external or thermal ones. For rotating electrical machines, mechanical stresses are inevitable and originate from different sources, e.g., material processing, machine manufacturing and operating conditions. The efficiency and specific losses are largely altered by different mechanical stress states. In this paper the effect of tensile stresses and plastic deformations on the magnetic properties of a 2.9 wt% Si electrical steel are studied. Particular attention is paid to the effect of magnetic anisotropy, i.e., the influence of the direction of applied mechanical stress with respect to the rolling direction. Due to mechanical stress, the induced anisotropy has to be evaluated as it is related to the stress-dependent magnetostriction constant and the grain alignment. - Highlights: • A detailed look at magnetic anisotropy of FeSi NGO electrical steel. • Study of magnetic behavior under elastic as well as plastic tensile stresses. • Correlation of magnetic behavior with microscopic deformation mechanisms. • Discussion of detrimental and beneficial effects of external stresses. • Loss separation at different polarizations and frequencies under increasing stress.

  19. Elastic properties

    Ledbetter, H.M.

    1983-01-01

    This chapter investigates the following five aspects of engineering-material solid-state elastic constants: general properties, interrelationships, relationships to other physical properties, changes during cooling from ambient to near-zero temperature, and near-zero-temperature behavior. Topics considered include compressibility, bulk modulus, Young's modulus, shear modulus, Poisson's ratio, Hooke's law, elastic-constant measuring methods, thermodynamic potentials, higher-order energy terms, specific heat, thermal expansivity, magnetic materials, structural phase transitions, polymers, composites, textured aggregates, and other-phenomena correlations. Some of the conclusions concerning polycrystalline elastic properties and their temperature dependence are: elastic constants are physical, not mechanical, properties which relate thermodynamically to other physical properties such as specific heat and thermal expansivity; elastic constants at low temperatures are nearly temperature independent, as required by the third law of thermodynamics; and elastic constants can be used to study directional properties of materials, such as textured aggregates and composites

  20. Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom

    Náprstek, Jiří; Pospíšil, Stanislav

    2012-01-01

    Roč. 111, č. 1 (2012), s. 1-13 ISSN 0167-6105 R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902 Institutional support: RVO:68378297 Keywords : aero-elastic system * self-excited vibration * instability * aero-elastic derivatives Subject RIV: JN - Civil Engineering Impact factor: 1.342, year: 2012

  1. Chemo-mechanical modeling of tumor growth in elastic epithelial tissue

    Bratsun, Dmitry A., E-mail: bratsun@pspu.ru [Department of Applied Physics, Perm National Research Polytechnical University, Perm, 614990 (Russian Federation); Zakharov, Andrey P. [Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, 32000 Israel (Israel); Theoretical Physics Department, Perm State Humanitarian Pedagogical University, Perm, 614990 (Russian Federation); Pismen, Len [Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, 32000 Israel (Israel)

    2016-08-02

    We propose a multiscale chemo-mechanical model of the cancer tumor development in the epithelial tissue. The epithelium is represented by an elastic 2D array of polygonal cells with its own gene regulation dynamics. The model allows the simulation of the evolution of multiple cells interacting via the chemical signaling or mechanically induced strain. The algorithm includes the division and intercalation of cells as well as the transformation of normal cells into a cancerous state triggered by a local failure of the spatial synchronization of the cellular rhythms driven by transcription/translation processes. Both deterministic and stochastic descriptions of the system are given for chemical signaling. The transformation of cells means the modification of their respective parameters responsible for chemo-mechanical interactions. The simulations reproduce a distinct behavior of invasive and localized carcinoma. Generally, the model is designed in such a way that it can be readily modified to take account of any newly understood gene regulation processes and feedback mechanisms affecting chemo-mechanical properties of cells.

  2. Chemo-mechanical modeling of tumor growth in elastic epithelial tissue

    Bratsun, Dmitry A.; Zakharov, Andrey P.; Pismen, Len

    2016-08-01

    We propose a multiscale chemo-mechanical model of the cancer tumor development in the epithelial tissue. The epithelium is represented by an elastic 2D array of polygonal cells with its own gene regulation dynamics. The model allows the simulation of the evolution of multiple cells interacting via the chemical signaling or mechanically induced strain. The algorithm includes the division and intercalation of cells as well as the transformation of normal cells into a cancerous state triggered by a local failure of the spatial synchronization of the cellular rhythms driven by transcription/translation processes. Both deterministic and stochastic descriptions of the system are given for chemical signaling. The transformation of cells means the modification of their respective parameters responsible for chemo-mechanical interactions. The simulations reproduce a distinct behavior of invasive and localized carcinoma. Generally, the model is designed in such a way that it can be readily modified to take account of any newly understood gene regulation processes and feedback mechanisms affecting chemo-mechanical properties of cells.

  3. On the mechanism of bandgap formation in locally resonant finite elastic metamaterials

    Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper

    2016-10-01

    Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.

  4. First-principles investigations on structural, elastic and mechanical properties of BNxAs1‑x ternary alloys

    Zhang, Junqin; Ma, Huihui; Zhao, Bin; Wei, Qun; Yang, Yintang

    2018-05-01

    A systematic investigation of the structural optimization, elastic and mechanical properties of the BNxAs1‑x ternary alloys are reported in the present work using the density-functional theory with the generalized gradient approximation (GGA) of the exchange-correlation functional. Some of the constants which are used to analyze the properties including elastic constants and modulus, and some parameters describing the elastic anisotropy and Debye temperature are also calculated. Our calculations were performed to evaluate the equilibrium lattice constant and band structure compared with the available theoretical works. On the one hand, our results might be expected to provide a theoretical basis for future study of BNxAs1‑x alloys towards elastic or mechanical properties. On the other hand, we draw a conclusion that BNxAs1‑x alloys show direct bandgap when x equals 0.25, 0.5 or 0.75. We obtained the elastic modulus, Poisson’s ratio and universal anisotropic index which are used to demonstrate the elastic anisotropy of these alloys which is proved according to our calculations. Also, we calculated the Debye temperature to illustrate covalent interactions and obtained the lower limit of the thermal conductivity for further research.

  5. Research on the porous flow of the mechanism of viscous-elastic fluids displacing residual oil droplets in micro pores

    Dong, Guanyu

    2018-03-01

    In order to analyze the microscopic stress field acting on residual oil droplets in micro pores, calculate its deformation, and explore the hydrodynamic mechanism of viscous-elastic fluids displacing oil droplets, the viscous-elastic fluid flow equations in micro pores are established by choosing the Upper Convected Maxwell constitutive equation; the numerical solutions of the flow field are obtained by volume control and Alternate Direction Implicit methods. From the above, the velocity field and microscopic stress field; the forces acting on residual oil droplets; the deformations of residual oil droplets by various viscous-elastic displacing fluids and at various Wiesenberg numbers are calculated and analyzed. The result demonstrated that both the normal stress and horizontal force acting on the residual oil droplets by viscous-elastic fluids are much larger compared to that of inelastic fluid; the distribution of normal stress changes abruptly; under the condition of the same pressure gradient in the system under investigation, the ratio of the horizontal forces acting on the residual oil droplets by different displacing fluids is about 1:8:20, which means that under the above conditions, the driving force on a oil droplet is 20 times higher for a viscous-elastic fluid compared to that of a Newtonian Fluid. The conclusions are supportive of the mechanism that viscous-elastic driving fluids can increase the Displacement Efficiency. This should be of help in designing new chemicals and selecting Enhanced Oil Recovery systems.

  6. Sensitivity of using blunt and sharp crack models in elastic-plastic fracture mechanics

    Pan, Y.C.; Kennedy, J.M.; Marchertas, A.H.

    1985-01-01

    J-integral values are calculated for both the blunt (smeared) crack and the sharp (discrete) crack models in elastic-plastic fracture mechanics problems involving metallic materials. A sensitivity study is performed to show the relative strengths and weaknesses of the two cracking models. It is concluded that the blunt crack model is less dependent on the orientation of the mesh. For the mesh which is in line with the crack direction, however, the sharp crack model is less sensitive to the mesh size. Both models yield reasonable results for a properly discretized finite-element mesh. A subcycling technique is used in this study in the explicit integration scheme so that large time steps can be used for the coarse elements away from the crack tip. The savings of computation time by this technique are reported. 6 refs., 9 figs

  7. Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

    Pride, Steven R.; Berryman, James G.

    2009-01-05

    An analysis is presented to show how it is possible for unconsolidated granular packings to obey overall non-Hertzian pressure dependence due to the imperfect and random spatial arrangements of the grains in these packs. With imperfect arrangement, some gaps that remain between grains can be closed by strains applied to the grain packing. As these gaps are closed, former rattler grains become jammed and new stress-bearing contacts are created that increase the elastic stiffness of the packing. By allowing for such a mechanism, detailed analytical expressions are obtained for increases in bulk modulus of a random packing of grains with increasing stress and strain. Only isotropic stress and strain are considered in this analysis. The model is shown to give a favorable fit to laboratory data on variations in bulk modulus due to variations in applied pressure for bead packs.

  8. Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

    Kaczmarczyk, S.; Mirhadizadeh, S.

    2016-05-01

    In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

  9. Thermal modal analysis of novel non-pneumatic mechanical elastic wheel based on FEM and EMA

    Zhao, Youqun; Zhu, Mingmin; Lin, Fen; Xiao, Zhen; Li, Haiqing; Deng, Yaoji

    2018-01-01

    A combination of Finite Element Method (FEM) and Experiment Modal Analysis (EMA) have been employed here to characterize the structural dynamic response of mechanical elastic wheel (ME-Wheel) operating under a specific thermal environment. The influence of high thermal condition on the structural dynamic response of ME-Wheel is investigated. The obtained results indicate that the EMA results are in accordance with those obtained using the proposed Finite Element (FE) model, indicting the high reliability of this FE model applied in analyzing the modal of ME-Wheel working under practical thermal environment. It demonstrates that the structural dynamic response of ME-Wheel operating under a specific thermal condition can be predicted and evaluated using the proposed analysis method, which is beneficial for the dynamic optimization design of the wheel structure to avoid tire temperature related vibration failure and improve safety of tire.

  10. A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

    Yamamoto, K; Fujita, T; Kanda, K; Maenaka, K; Badel, A; Formosa, F

    2014-01-01

    In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator

  11. Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

    Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

    2005-09-01

    The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

  12. Enhanced Oil Recovery Using Micron-Size Polyacrylamide Elastic Microspheres (MPEMs): Underlying Mechanisms and Displacement Experiments

    Yao, Chuanjin; Lei, Guanglun; Hou, Jian; Xu, Xiaohong; Wang, Dan; Steenhuis, Tammo S.

    2015-01-01

    Micron-size polyacrylamide elastic microsphere (MPEM) is a newly developed profile control and oil displacement agent for enhanced oil recovery in heterogeneous reservoirs. In this study, laboratory experiments were performed to characterize the viscoelastic properties of MPEMs in brine water. A transparent sandpack micromodel was used to observe the microscopic flow and displacement mechanisms, and parallel-sandpack models were used to investigate the profile control and oil displacement performance using MPEMs in heterogeneous reservoirs. The results indicate that MPEMs almost do not increase the viscosity of injection water and can be conveniently injected using the original water injection pipelines. The microscopic profile control and oil displacement mechanisms of MPEMs in porous media mainly behave as selective-plugging in large pores, fluid diversion after MPEMs plugging, oil drainage caused by MPEMs breakthrough, and the mechanism of oil droplets converging into oil flow. MPEMs have a high plugging strength, which can tolerate a long-term water flushing. MPEMs can selectively enter and plug the large pores and pore-throats in high permeability sandpack, but almost do not damage the low permeability sandpack. MPEMs can effectively divert the water flow from the high permeability sandpack to the low permeability sandpack and improve the sweep efficiency of low permeability sandpack and low permeability area in the high permeability sandpack. The results also confirm the dynamic process of profile control and oil displacement using MPEMs in heterogeneous reservoirs.

  13. Enhanced Oil Recovery Using Micron-Size Polyacrylamide Elastic Microspheres (MPEMs): Underlying Mechanisms and Displacement Experiments

    Yao, Chuanjin

    2015-10-12

    Micron-size polyacrylamide elastic microsphere (MPEM) is a newly developed profile control and oil displacement agent for enhanced oil recovery in heterogeneous reservoirs. In this study, laboratory experiments were performed to characterize the viscoelastic properties of MPEMs in brine water. A transparent sandpack micromodel was used to observe the microscopic flow and displacement mechanisms, and parallel-sandpack models were used to investigate the profile control and oil displacement performance using MPEMs in heterogeneous reservoirs. The results indicate that MPEMs almost do not increase the viscosity of injection water and can be conveniently injected using the original water injection pipelines. The microscopic profile control and oil displacement mechanisms of MPEMs in porous media mainly behave as selective-plugging in large pores, fluid diversion after MPEMs plugging, oil drainage caused by MPEMs breakthrough, and the mechanism of oil droplets converging into oil flow. MPEMs have a high plugging strength, which can tolerate a long-term water flushing. MPEMs can selectively enter and plug the large pores and pore-throats in high permeability sandpack, but almost do not damage the low permeability sandpack. MPEMs can effectively divert the water flow from the high permeability sandpack to the low permeability sandpack and improve the sweep efficiency of low permeability sandpack and low permeability area in the high permeability sandpack. The results also confirm the dynamic process of profile control and oil displacement using MPEMs in heterogeneous reservoirs.

  14. Determination of elastic mechanical characteristics of surface coatings from analysis of signals obtained by impulse excitation

    Nyaguly, E.; Craştiu, I.; Deac, S.; Gozman-Pop, C.; Drăgănescu, G.; Bereteu, L.

    2018-01-01

    Most of the surface coatings are based on the synthetic polymers, which are substances composed from very large molecules that form tough, flexible, adhesive films when applied to surfaces. The other components of surface coverings materials are pigments that provide colour, opacity, gloss and other properties. Surface coatings are two-phase composite materials: constitute a polymer matrix on the one side, and on the other side of the pigments and additives dispersed in the matrix. Their role is not only aesthetically but also to ensure anticorrosive protection or even improve some mechanical properties of coated surfaces. In this paper it will follow, starting from the mechanical properties of the substrate, the metallic sheet in general, to determine the new properties of the assembly of substrate and the two coating layers, also the determination of mechanical properties of the layers. From the analysis of vibroacoustic signals obtained by the impulse excitation of the sample, one can determine the elasticity modulus. These results come to validate the results based on finite element analysis (FEA) of the same samples.

  15. Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

    Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

    2017-11-01

    The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

  16. Non-linear elastic behaviour of carbon fibres of different structural and mechanical characteristic

    ISIDOR M. DJORDJEVIC

    2007-05-01

    Full Text Available Five types of polyacrylonitrile, PAN, based carbon fibres, differing in modulus, breaking strain and in crystallite orientation, have been studied. Non-Hookean behaviour was investigated by computing the tangent tensile and compression moduli as a function of strain, from the axial stress–strain response obtained in standard tensile, compression, as well as in modified flexural tests of unidirectional carbon/ epoxy composites. The dependences of the tensile modulus on tensile strain of the carbon fibres were extracted from data obtained in single-filament tensile tests. Analytical expressions for the tensile modulus–tensile strain and compression modulus–compression strain dependences in the performed test were deduced. The structural characterization of the carbon fibres was performed by X-ray diffraction on bundle of parallel fibres. The interlayer spacing d002 and the apparent lateral dimension of the crystallites Lc were deduced by processing the 002 diffraction profiles. The established modulus–strain dependences were correlated with the fibre characteristics (breaking strain and mean modulus values, as well as with the characteristic of the 002 diffraction profile and the d002 and Lc values.

  17. Incorporating plastic collapse into the linear elastic fracture mechanics methodology in determining crack propagation lifetimes

    Glasgow, B.B.; Wolfer, W.G.

    1986-01-01

    Crack growth can result in a breech of a pressure boundary causing coolant loss or in total structural failure. This paper discusses brittle and plastic failure in terms of a unified structural model called the Two Criteria model. The model takes into account the flow stress of the material as well as the fracture toughness. Our results indicate that for fusion reactor first wall structures, ferritic steel is better able to resist crack propagation and subsequent structural failure than 316 stainless steel under the same wall loadings and geometry

  18. A critical review on the application of elastic-plastic fracture mechanics to nuclear pressure vessel and piping systems

    Scarth, D.A.; Kim, Y.J.; Vanderglas, M.L.

    1985-10-01

    A comprehensive literature survey on the application of Elastic-Plastic Fracture Mechanics to the assessment of the structural integrity of nuclear pressure vessels and piping is presented. In particular, the J-integral/Tearing Modulus (J/T) approach and the Failure Assessment Diagram (FAD) are covered in detail because of their general suitability for use in Ontario Hydro. (25 refs.)

  19. N=4 superconformal mechanics as a non linear realization

    Anabalon, Andres; Gomis, Joaquim; Kamimura, Kiyoshi; Zanelli, Jorge

    2006-01-01

    An action for a superconformal particle is constructed using the non linear realization method for the group PSU(1,1/2), without introducing superfields. The connection between PSU(1,1/2) and black hole physics is discussed. The lagrangian contains six arbitrary constants and describes a non-BPS superconformal particle. The BPS case is obtained if a precise relation between the constants in the lagrangian is verified, which implies that the action becomes kappa-symmetric

  20. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

    Rietbergen, van B.; Odgaard, A.; Kabel, J.; Huiskes, H.W.J.

    1996-01-01

    A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric

  1. Dependence of Some Mechanical Properties of Elastic Bands on the Length and Load Time

    Triana, C. A.; Fajardo, F.

    2012-01-01

    We present a study of the maximum stress supported by elastics bands of nitrile as a function of the natural length and the load time. The maximum tension of rupture and the corresponding variation in length were found by measuring the elongation of an elastic band when a mass is suspended from its free end until it reaches the breaking point. The…

  2. Cyclone–anticyclone vortex asymmetry mechanism and linear Ekman friction

    Chefranov, S. G., E-mail: schefranov@mail.ru [Russian Academy of Sciences, Obukhov Institute of Atmospheric Physics (Russian Federation)

    2016-04-15

    Allowance for the linear Ekman friction has been found to ensure a threshold (in rotation frequency) realization of the linear dissipative–centrifugal instability and the related chiral symmetry breaking in the dynamics of Lagrangian particles, which leads to the cyclone–anticyclone vortex asymmetry. An excess of the fluid rotation rate ω{sub 0} over some threshold value determined by the fluid eigenfrequency ω (i.e., ω{sub 0} > ω) is shown to be a condition for the realization of such an instability. A new generalization of the solution of the Karman problem to determine the steady-state velocity field in a viscous incompressible fluid above a rotating solid disk of large radius, in which the linear Ekman friction was additionally taken into account, has been obtained. A correspondence of this solution and the conditions for the realization of the dissipative–centrifugal instability of a chiral-symmetric vortex state and the corresponding cyclone–anticyclone vortex asymmetry has been shown. A generalization of the well-known spiral velocity distribution in an “Ekman layer” near a solid surface has been established for the case where the fluid rotation frequency far from the disk ω differs from the disk rotation frequency ω{sub 0}.

  3. Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics

    Lucchetti, Liana; Fraccia, Tommaso P.; Ciciulla, Fabrizio; Bellini, Tommaso

    2017-01-01

    Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced bi...

  4. Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

    Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso

    2017-07-10

    Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

  5. Parametric and mechanical characterization of linear low density ...

    characterization of the material is equally important in relation to quality and relia- ... be moulded as one single part (with no weld lines or joints), eliminating high .... mechanical analysis of three powders viz. polyethylene, polypropylene and ...

  6. The use of a path independent integral in non-linear fracture mechanics

    Hellen, T.K.

    1977-01-01

    A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior

  7. A detailed analysis of adhesion mechanics between a compliant elastic coating and a spherical probe

    Sridhar, I; Zheng, Z W; Johnson, K L

    2004-01-01

    As length scales decrease, adhesive forces become increasingly important. These adhesive forces contribute to the normal load in experiments conducted on thin layered systems using micro-probe instruments such as the surface force apparatus (SFA) and the atomic force microscope (AFM). Adhesion between these thin-layer systems was analysed by Sridhar et al (1997 J. Phys. D: Appl. Phys. 30 1710) for the SFA geometry and Johnson and Sridhar (2001 J. Phys. D: Appl. Phys. 34 683) for AFM using a numerical SJF (Sridhar-Johnson-Fleck) version of the JKR (Johnson-Kendal-Roberts) theory. In this paper, adhesion mechanics between a compliant elastic coating and a spherical probe is investigated using the SJF model in detail. When the substrate is rigid, the non-dimensional pull-off force may differ from the JKR value of -0.5 by as much as 90%. Computations of the contact size at zero load and pull-off force are presented for a range of values of adhesion energy. Finally, empirical relations for the contact load and contact compliance as a function of contact radius were obtained from the numerical data for practical layer-substrate material systems

  8. Elastic-plastic fracture mechanics for nuclear pressure vessels: a preliminary appraisal

    Hahn, G.T.; Broek, D.; Marschall, C.W.; Rosenfield, A.R.; Rybicki, E.F.; Schmueser, D.W.; Stonesifer, R.B.; Kanninen, M.F.

    1978-01-01

    A research program directed at assessing the margin of safety of flawed nuclear pressure vessels near and beyond general yielding is described. The program has the general objective of developing an elastic-plastic fracture mechanics methodology. The approach is based on the use of finite element models together with experimental results to identify criteria appropriate for the onset of crack extension and for stable crack growth. A number of criteria beyond the conventional LEFM R curve are being evaluated. These include the critical values of the J-integral, its derivative, the crack tip opening angle, the average crack opening angle, a generalized energy release rate, its components and a crack tip force. The optimum fracture criterion for nuclear vessels is being determined by systematic measurements of load extension curves, strain distribution, crack opening displacement, stable crack growth and instability on 'toughness scaled' model materials. Computations have been performed for center cracked panels of a model material (2219-T87 aluminium) for full shear failure. (author)

  9. The finite element part of the LAMCAL program. Elastic-plastic fracture mechanics applications

    Lamain, L.G.; Blanckenburg, J.F.G.

    1982-01-01

    The elastic-plastic FEM code described in this report is the third part of the Lamcal program of which the two other parts for mesh generating and plotting were presented previously. Also this part uses the dynamic core storage. All variables and problem defining data are stored in one common array-SPACE. If all three parts are used together, the same common-SPACE is reused in each part. The lay-out of the complete program is given. J-integral evaluation and plotting can be done immediately in the FE run or afterwards in a post processing run. Post processing is done within the FEM part with a reduced core space. Originally developed as a general code, the use of the present version is mainly focussed on research in the field of the fracture mechanics. Several J-integral routines are available as well as crack growth modelling by node release or stiffness reduction, energy calculations, crack tip elements, etc. In this report the theory is discussed and some sample problems are given. The theory is presented in two parts, the general FEM and the more specific EPFM theory. For the sample problems, a choice has been made to show the accuracy of the program under more or less severe loading conditions

  10. The Clinical Utilisation of Respiratory Elastance Software (CURE Soft): a bedside software for real-time respiratory mechanics monitoring and mechanical ventilation management.

    Szlavecz, Akos; Chiew, Yeong Shiong; Redmond, Daniel; Beatson, Alex; Glassenbury, Daniel; Corbett, Simon; Major, Vincent; Pretty, Christopher; Shaw, Geoffrey M; Benyo, Balazs; Desaive, Thomas; Chase, J Geoffrey

    2014-09-30

    Real-time patient respiratory mechanics estimation can be used to guide mechanical ventilation settings, particularly, positive end-expiratory pressure (PEEP). This work presents a software, Clinical Utilisation of Respiratory Elastance (CURE Soft), using a time-varying respiratory elastance model to offer this ability to aid in mechanical ventilation treatment. CURE Soft is a desktop application developed in JAVA. It has two modes of operation, 1) Online real-time monitoring decision support and, 2) Offline for user education purposes, auditing, or reviewing patient care. The CURE Soft has been tested in mechanically ventilated patients with respiratory failure. The clinical protocol, software testing and use of the data were approved by the New Zealand Southern Regional Ethics Committee. Using CURE Soft, patient's respiratory mechanics response to treatment and clinical protocol were monitored. Results showed that the patient's respiratory elastance (Stiffness) changed with the use of muscle relaxants, and responded differently to ventilator settings. This information can be used to guide mechanical ventilation therapy and titrate optimal ventilator PEEP. CURE Soft enables real-time calculation of model-based respiratory mechanics for mechanically ventilated patients. Results showed that the system is able to provide detailed, previously unavailable information on patient-specific respiratory mechanics and response to therapy in real-time. The additional insight available to clinicians provides the potential for improved decision-making, and thus improved patient care and outcomes.

  11. Effect of elasticity during viscoelastic polymer flooding : a possible mechanism of increasing the sweep efficiency

    Urbissinova, T.S.; Trivedi, J.J.; Kuru, E. [Alberta Univ., Edmonton, AB (Canada). Dept. of Civil and Environmental Engineering

    2010-12-15

    This paper discussed a laboratory experiment undertaken to study how the elasticity of polymer-based fluids affects microscopic sweep efficiency, which has implications for enhanced oil recovery processes. In a series of experiments, polymer solutions with the same shear viscosity but notably different elastic characteristics were injected through a mineral-oil-saturated sandpack. The experiments involved a special core holder that was designed to simulate radial flow. The solution was injected via a perforated injection line located in the centre of the cell, and fluids were produced by way of 2 production lines located at the periphery. The shear rate used in the experiments was within the range of field applications. Using polymer solutions with similar shear viscosity behaviour and different elasticity allowed the effect of elasticity on sweep efficiency to be singled out. It was concluded that adjusting the molecular weight distribution of the solution at a constant shear viscosity and polymer concentration could improve the sweep efficiency of a polymeric fluid. The higher-elasticity polymer solution had a higher resistance to flow through porous media, resulting in better sweep efficiency and lower residual oil saturation. The objective of the study was to isolate elasticity from the other parameters that affect displacement efficiency to show the individual effect of elasticity on oil recovery. 20 refs., 5 tabs., 14 figs.

  12. Some comment on the use of J criterion in elastic plastic fracture mechanics

    Roche, R.L.

    1978-01-01

    In Post Yield Fracture Mechanics, several criteria have been proposed for the onset of crack propagation, one of the most popular being the J 1 integral criterion. This is only well established for elastic materials, where it can be shown that J 1 is not path dependent, and that J 1 is equal to the variation of potential energy with crack length. Extension is easy for material exhibiting deformation type plasticity, but there is no proof of path independence for flow-type plastic material. Experimental results are often given as a proof of J 1 criterion validity, but a critical analysis shows that important assumptions are made in the use of the test results. The main assumption is that the received work, known as strain energy, is not dependent on the loading history and is only dependent on the mechanical state. The study of the J 1 path dependence is the main point of the J 1 criteria validation. A general method to assess path dependence can be founded on the 'defect vector' (or driving force) concept. The space-density of defect is given by j = grad W - σ grad (W = strain-energy, σ stress tensor, epsilon strain tensor). It is shown that the virtual translation delta a of the defect vectors inside a volume, lead to a virtual work variation given by J 1 delta a and that J 1 is the resultant of all the defect vectors included in the volume surrounded by the integration surface. Using these results the path independence conditions are examined. Some numerical results are given for incremental processes such as plasticity or creep, and where the loading path is radial (proportional) and monotonic, no appreciable path variations found. Finally the results of direct applications of J 1 criterion to real structures are examined. (author)

  13. Capillary-Physics Mechanism of Elastic-Wave Mobilization of Residual Oil

    Beresnev, I. A.; Pennington, W. D.; Turpening, R. M.

    2003-12-01

    Much attention has been given to the possibility of vibratory mobilization of residual oil as a method of enhanced recovery. The common features of the relevant applications have nonetheless been inconsistency in the results of field tests and the lack of understanding of a physical mechanism that would explain variable experiences. Such a mechanism can be found in the physics of capillary trapping of oil ganglia, driven through the pore channels by an external pressure gradient. Entrapping of ganglia occurs due to the capillary pressure building on the downstream meniscus entering a narrow pore throat. The resulting internal-pressure imbalance acts against the external gradient, which needs to exceed a certain threshold to carry the ganglion through. The ganglion flow thus exhibits the properties of the Bingham (yield-stress) flow, not the Darcy flow. The application of vibrations is equivalent to the addition of an oscillatory forcing to the constant gradient. When this extra forcing acts along the gradient, an instant "unplugging" occurs, while, when the vibration reverses direction, the flow is plugged. This asymmetry results in an average non-zero flow over one period of vibration, which explains the mobilization effect. The minimum-amplitude and maximum-frequency thresholds apply for the mobilization to occur. When the vibration amplitude exceeds a certain "saturation" level, the flow returns to the Darcy regime. The criterion of the mobilization of a particular ganglion involves the parameters of both the medium (pore geometry, interfacial and wetting properties, fluid viscosity) and the oscillatory field (amplitude and frequency). The medium parameters vary widely under natural conditions. It follows that an elastic wave with a given amplitude and frequency will always produce a certain mobilization effect, mobilizing some ganglia and leaving others intact. The exact macroscopic effect is hard to predict, as it will represent a response of the populations

  14. Crack formation mechanisms during micro and macro indentation of diamond-like carbon coatings on elastic-plastic substrates

    Thomsen, N.B.; Fischer-Cripps, A.C.; Swain, M.V.

    1998-01-01

    of cracking and the fracture mechanisms taking place. In the study various diamond-like carbon (DLC) coatings deposited onto stainless steel and tool steel were investigated. Results primarily for one DLC system will be presented here. (C) 1998 Published by Elsevier Science S.A. All rights reserved.......In the present study crack formation is investigated on both micro and macro scale using spherical indenter tips. in particular, systems consisting of elastic coatings that are well adhered to elastic-plastic substrates are studied. Depth sensing indentation is used on the micro scale and Rockwell...... indentation on the macro scale. The predominant driving force for coating failure and crack formation during indentation is plastic deformation of the underlying substrate. The aim is to relate the mechanisms creating both delamination and cohesive cracking on both scales with fracture mechanical models...

  15. Comparison of linear-elastic-plastic, and fully plastic failure models in the assessment of piping integrity

    Streit, R.D.

    1981-01-01

    The failure evaluation of Pressurized Water Reactor (PWR) primary coolant loop pipe is often based on a plastic limit load criterion; i.e., failure occurs when the stress on the pipe section exceeds the material flow stress. However, in addition the piping system must be safe against crack propagation at stresses less than those leading to plastic instability. In this paper, elastic, elastic-plastic, and fully-plastic failure models are evaluated, and the requirements for piping integrity based on these models are compared. The model yielding the 'more' critical criteria for the given geometry and loading conditions defines the appropriate failure criterion. The pipe geometry and loading used in this study was choosen based on an evaluation of a guillotine break in a PWR primary coolant loop. It is assumed that the piping may contain cracks. Since a deep circumferential crack, can lead to a guillotine pipe break without prior leaking and thus without warning it is the focus of the failure model comparison study. The hot leg pipe, a 29 in. I.D. by 2.5 in. wall thickness stainless pipe, was modeled in this investigation. Cracks up to 90% through the wall were considered. The loads considered in this evaluation result from the internal pressure, dead weight, and seismic stresses. For the case considered, the internal pressure contributes the most to the failure loading. The maximum moment stress due to the dead weight and seismic moments are simply added to the pressure stress. Thus, with the circumferential crack geometry and uniform pressure stress, the problem is axisymmetric. It is analyzed using NIKE2D--an implicit, finite deformation, finite element code for analyzing two-dimensional elastic-plastic problems. (orig./GL)

  16. Generalized space and linear momentum operators in quantum mechanics

    Costa, Bruno G. da; Borges, Ernesto P.

    2014-01-01

    We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p ^ q , and its canonically conjugate deformed position operator x ^ q . A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed

  17. Mechanical Properties of Potato- Starch Linear Low Density ...

    The mechanical properties of potato-starch filled LLDPE such as Young's Modulus, tensile strength and elongation at break were studied. Apart from the Young's Modulus, the tensile strength and elongation at break reduced with increased starch content. This is attributed to poor adhesion between starch and the polymer ...

  18. Some fundamental definitions of the elastic parameters for homogenous isotropic linear materials in road design and analysis

    De Beer, Morris

    2008-07-01

    Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

  19. Elastic creep-fatigue evaluation for ASME [American Society of Mechanical Engineers] code

    Severud, L.K.; Winkel, B.V.

    1987-02-01

    Reassessment of past ASME N-47 creep-fatigue rules have been under way by committee members. The new proposed elastic creep-fatigue methods are easier to apply than those previously in the code case. They also provide a wider range of practical application while still providing conservative assessments. It is expected that new N-47 code rules for elastic creep-fatigue evaluation will be adopted in the near future

  20. Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity.

    Moussaoui, Ahmed; Bouziane, Touria

    2016-01-01

    The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are: •The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.•The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.•The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).

  1. Mechanical design of deformation compensated flexural pivots structured for linear nanopositioning stages

    Shu, Deming; Kearney, Steven P.; Preissner, Curt A.

    2015-02-17

    A method and deformation compensated flexural pivots structured for precision linear nanopositioning stages are provided. A deformation-compensated flexural linear guiding mechanism includes a basic parallel mechanism including a U-shaped member and a pair of parallel bars linked to respective pairs of I-link bars and each of the I-bars coupled by a respective pair of flexural pivots. The basic parallel mechanism includes substantially evenly distributed flexural pivots minimizing center shift dynamic errors.

  2. Vibration Stabilization of a Mechanical Model of a X-Band Linear Collider Final Focus Magnet

    Frisch, J; Decker, V; Hendrickson, L; Markiewicz, T W; Partridge, R; Seryi, Andrei

    2004-01-01

    The small beam sizes at the interaction point of a X-band linear collider require mechanical stabilization of the final focus magnets at the nanometer level. While passive systems provide adequate performance at many potential sites, active mechanical stabilization is useful if the natural or cultural ground vibration is higher than expected. A mechanical model of a room temperature linear collider final focus magnet has been constructed and actively stabilized with an accelerometer based system.

  3. Vibration Stabilization of a Mechanical Model of a X-Band Linear Collider Final Focus Magnet

    Frisch, Josef; Chang, Allison; Decker, Valentin; Doyle, Eric; Eriksson, Leif; Hendrickson, Linda; Himel, Thomas; Markiewicz, Thomas; Partridge, Richard; Seryi, Andrei; SLAC

    2006-01-01

    The small beam sizes at the interaction point of a X-band linear collider require mechanical stabilization of the final focus magnets at the nanometer level. While passive systems provide adequate performance at many potential sites, active mechanical stabilization is useful if the natural or cultural ground vibration is higher than expected. A mechanical model of a room temperature linear collider final focus magnet has been constructed and actively stabilized with an accelerometer based system

  4. Single-cell mechanics--An experimental-computational method for quantifying the membrane-cytoskeleton elasticity of cells.

    Tartibi, M; Liu, Y X; Liu, G-Y; Komvopoulos, K

    2015-11-01

    The membrane-cytoskeleton system plays a major role in cell adhesion, growth, migration, and differentiation. F-actin filaments, cross-linkers, binding proteins that bundle F-actin filaments to form the actin cytoskeleton, and integrins that connect the actin cytoskeleton network to the cell plasma membrane and extracellular matrix are major cytoskeleton constituents. Thus, the cell cytoskeleton is a complex composite that can assume different shapes. Atomic force microscopy (AFM)-based techniques have been used to measure cytoskeleton material properties without much attention to cell shape. A recently developed surface chemical patterning method for long-term single-cell culture was used to seed individual cells on circular patterns. A continuum-based cell model, which uses as input the force-displacement response obtained with a modified AFM setup and relates the membrane-cytoskeleton elastic behavior to the cell geometry, while treating all other subcellular components suspended in the cytoplasmic liquid (gel) as an incompressible fluid, is presented and validated by experimental results. The developed analytical-experimental methodology establishes a framework for quantifying the membrane-cytoskeleton elasticity of live cells. This capability may have immense implications in cell biology, particularly in studies seeking to establish correlations between membrane-cytoskeleton elasticity and cell disease, mortality, differentiation, and migration, and provide insight into cell infiltration through nonwoven fibrous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscoelasticity, examine the role of other subcellular components (e.g., nucleus envelope) in cell elasticity, and elucidate the effects of mechanical stimuli on cell differentiation and motility. This is the first study to decouple the membrane-cytoskeleton elasticity from cell stiffness and introduce an effective approach for measuring the elastic modulus. The

  5. Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 2; Thermal and Mechanical Loadings

    Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.

    2012-01-01

    Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.

  6. On non-linear dynamics of a coupled electro-mechanical system

    Darula, Radoslav; Sorokin, Sergey

    2012-01-01

    Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

  7. Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium

    M. Mohammadi

    Full Text Available In this study, the vibration behavior of annular and circular graphene sheet coupled with temperature change and under in-plane pre-stressed is studied. Influence of the surrounding elastic medium 011 the fundamental frequencies of the single-layered graphene sheets (SLGSs is investigated. Both Winkler-type and Pasternak- type models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. By using the nonlocal elasticity theory the governing equation is derived for SLGSs. The closed-form solution for frequency vibration of circular graphene sheets lias been obtained and nonlocal parameter, inplane pre-stressed, the parameters of elastic medium and temperature change appears into arguments of Bessel functions. The results are subsequently compared with valid result reported in the literature and the molecular dynamics (MD results. The effects of the small scale, pre-stressed, mode number, temperature change, elastic medium and boundary conditions on natural frequencies are investigated. The non-dimensional frequency decreases at high temperature case with increasing the temperature change for all boundary conditions. The effect of temperature change 011 the frequency vibration becomes the opposite at high temperature case in compression with the low temperature case. The present research work thus reveals that the nonlocal parameter, boundary conditions and temperature change have significant effects on vibration response of the circular nanoplates. The present results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the graphene.

  8. The incredible shrinking dewlap: signal size, skin elasticity, and mechanical design in the green anole lizard (Anolis carolinensis).

    Lailvaux, Simon P; Leifer, Jack; Kircher, Bonnie K; Johnson, Michele A

    2015-10-01

    The expression of male secondary sexual traits can be dynamic, changing size, shape, color, or structure over the course of different seasons. However, the factors underlying such changes are poorly understood. In male Anolis carolinensis lizards, a morphological secondary sexual signal called the dewlap changes size seasonally within individuals. Here, we test the hypothesis that seasonal changes in male dewlap size are driven by increased use and extension of the dewlap in spring and summer, when males are breeding, relative to the winter and fall. We captured male green anole lizards prior to the onset of breeding and constrained the dewlap in half of them such that it could not be extended. We then measured dewlap area in the spring, summer, and winter, and dewlap skin and belly skin elasticity in summer and winter. Dewlaps in unconstrained males increase in area from spring to summer and then shrink in the winter, whereas the dewlaps of constrained males consistently shrink from spring to winter. Dewlap skin is significantly more elastic than belly skin, and skin overall is more elastic in the summer relative to winter. These results show that seasonal changes in dewlap size are a function of skin elasticity and display frequency, and suggest that the mechanical properties of signaling structures can have important implications for signal evolution and design.

  9. Mechanical properties of concrete with SAP. Part II: Modulus of elasticity

    Hasholt, Marianne Tange; Jespersen, Morten H. Seneka; Jensen, Ole Mejlhede

    2010-01-01

    In this study, focus is on the modulus of elasticity for concrete with superabsorbent polymers (SAP). The results show that based on composite theory it is possible to establish a model, which predicts overall concrete elasticity. The model assumes a three phase material of aggregate, cement paste......, and air with volume fractions of the three phases as well as elastic properties of paste and aggregates as input parameters. Addition of SAP changes the E-modulus, because it both has an influence on properties of the cement paste and on the volume of air voids. Here, the E-modulus is an example...... a more or less empirical relation. The results show that when introducing SAP, models of a more empirical nature can be misleading (and e.g. relations stated in codes are often of this empirical nature). The reason is twofold: First, the empirical models often have a general problem with the effect...

  10. Appraisal of elastic follow-up for a generic mechanical structure through two simplified methods

    Gamboni, S.; Ravera, C.; Stretti, G.; Rebora, A.

    1989-01-01

    Elastic follow-up (EFU) is a complex phenomenon which affects the behaviour of some structural components, especially in high temperature operations. One of the major problems encountered by the designer is the quantitative evaluation of the amount of elastic follow-up that must be taken into account for the structures under examination. In the present paper a review of the guidance furnished by the ASME Code regarding EFU is presented through an application concerning a structural problem in which EFU occurs. This has been carried out with the additional purpose of comparing the percentage EFU obtained by two simplified methods: an inelastic simplified method involving relaxation analysis; the reduced elastic modulus procedure generally used for EFU problems in piping systems. The results obtained demonstrate a substantial agreement between the two methodologies when applied to a general type structure. (author)

  11. The use of a path independent integral in non-linear fracture mechanics

    Hellen, T.K.

    1977-01-01

    The use of the Rice J-intergral to assess conditions at a crack tip in an elastic or non-linear elastic body is well known. The integral equals the energy release rate and is path independent for any contour surrounding the crack tip provided no other singularities are encompassed. The path independence propertiy breaks down, however, in more general situations such as in three dimensional stress systems, plasticity unloading, thermal or creep states. Hence the required crack tip characteristics represented by the value of the integral round a contour whose radius about the tip tends to zero, is not reproduced along contours away from the tip. Consequently, an alternative integral, designated J*, has been proposed which equals J for elastic cases and in the other cases cited above remains path independent. A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. (Auth. )

  12. The Mechanical of the Small Axisymmetric Oscillations of the Liquid with the Surface Tension Forces in Elastic Tank

    D. A. Goncharov

    2015-01-01

    Full Text Available In this paper we investigate small axisymmetric oscillations of a liquid in an elastic tank. We also take into account the influence of surface tension forces. For this, we turn to the mechanical analogue of the considered mechanical system. To realize the transition to mechanical analogue we use the energy method: postulating the equality of kinetic and potential energy for the investigated mechanical system and the mechanical system analog. Due to this transition we can further investigate the oscillations of a mechanical analogue. As a mechanical analogue, we consider the oscillator in the spring. The mass of the oscillator is calculated as the weight of the fluid to make oscillations. The oscillator spring constant is calculated using the identity of equations, namely, equation of free small oscillations of the oscillator and equation of free small oscillations of the system under investigation: the fluid in the elastic tank. The identity of equations allows us to draw conclusion about the identity of the natural frequencies for the source mechanical system and the system of a mechanical analogue. Next, we take into consideration the action of the surface tension. We record the Laplace condition for excess pressure because of the forces of surface tension. Then we compile the expression for the generalized force, taking into account the phenomenon of the surface tension. Next, we write the equation of oscillations of a mechanical analogue. The surface tension, due to the introduction of the generalized force in the equation for small oscillations of the mechanical analogue will change the natural frequency of the mechanical analogue. The paper presents the appropriate dependencies. The abovementioned allows us to investigate the stability of small motions of fluid in microgravity or low gravity by studying the stability of small motions of mechanical analogue. The latter is especially important due to the design and development of advanced

  13. Quantum Mechanical Calculations Of Elastic Properties Of Doped Tetragonal Yttria-Stabilized Zirconium Dioxide

    Yuriy Natanzon

    2008-01-01

    Full Text Available We report first principles calculations of the electronic and elastic properties of yttriastabilized tetragonal zirconium dioxide doped with metal oxides like: GeO2, TiO2, SiO2,MgO and Al2O3. It is shown that addition of such dopants affects selected elastic propertiesof ZrO2, which is driven by the attraction of electron density by dopant atom and creationof stronger dopant–oxygen bonds. This effect contributes to the increase of superplasticityof doped material.

  14. Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics

    Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.; Solofoarisina, W.C.

    2015-04-01

    We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.

  15. A quantum-mechanical perspective on linear response theory within polarizable embedding

    List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob

    2017-01-01

    We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...

  16. Effect of cellulosic fiber scale on linear and non-linear mechanical performance of starch-based composites.

    Karimi, Samaneh; Abdulkhani, Ali; Tahir, Paridah Md; Dufresne, Alain

    2016-10-01

    Cellulosic nanofibers (NFs) from kenaf bast were used to reinforce glycerol plasticized thermoplastic starch (TPS) matrices with varying contents (0-10wt%). The composites were prepared by casting/evaporation method. Raw fibers (RFs) reinforced TPS films were prepared with the same contents and conditions. The aim of study was to investigate the effects of filler dimension and loading on linear and non-linear mechanical performance of fabricated materials. Obtained results clearly demonstrated that the NF-reinforced composites had significantly greater mechanical performance than the RF-reinforced counterparts. This was attributed to the high aspect ratio and nano dimension of the reinforcing agents, as well as their compatibility with the TPS matrix, resulting in strong fiber/matrix interaction. Tensile strength and Young's modulus increased by 313% and 343%, respectively, with increasing NF content from 0 to 10wt%. Dynamic mechanical analysis (DMA) revealed an elevational trend in the glass transition temperature of amylopectin-rich domains in composites. The most eminent record was +18.5°C shift in temperature position of the film reinforced with 8% NF. This finding implied efficient dispersion of nanofibers in the matrix and their ability to form a network and restrict mobility of the system. Copyright © 2016 Elsevier B.V. All rights reserved.

  17. Assembly Test of Elastic Averaging Technique to Improve Mechanical Alignment for Accelerating Structure Assemblies in CLIC

    Huopana, J

    2010-01-01

    The CLIC (Compact LInear Collider) is being studied at CERN as a potential multi-TeV e+e- collider [1]. The manufacturing and assembly tolerances for the required RF-components are important for the final efficiency and for the operation of CLIC. The proper function of an accelerating structure is very sensitive to errors in shape and location of the accelerating cavity. This causes considerable issues in the field of mechanical design and manufacturing. Currently the design of the accelerating structures is a disk design. Alternatively it is possible to create the accelerating assembly from quadrants, which favour the mass manufacturing. The functional shape inside of the accelerating structure remains the same and a single assembly uses less parts. The alignment of these quadrants has been previously made kinematic by using steel pins or spheres to align the pieces together. This method proved to be a quite tedious and time consuming method of assembly. To limit the number of different error sources, a meth...

  18. Reaction Mechanism and Structure Interplay for Proton Elastic Scattering from Halo Nuclei

    Crespo, R.; Johnson, R.C.

    1999-01-01

    The aim of this work is to clarify what properties of the projectile w.f. are relevant to describe elastic scattering of halo nuclei from stable nuclei. In particular, we examine how far elastic scattering observables probe correlation effects among projectile nucleons. Our treatment is based on a multiple scattering expansion of the proton-projectile transition amplitude in a form which is well adapted to the weakly bound cluster picture of halo nuclei. In the specific case of 11 Li scattering from protons at 800 MeV/u we show that because core recoil effects are significant, scattering cross sections can not, in general, be deduced from knowledge of the total matter density alone. We advocate that the optical potential concept for the scattering of halo nuclei on protons should be avoided and that the multiple scattering series for the full transition amplitude should be used instead

  19. Reaction mechanism and structure interplay for proton elastic scattering from halo nuclei

    Crespo, R.; Johnson, R. C.

    1999-01-01

    The aim of this work is to clarify what properties of the projectile w.f. are relevant to describe elastic scattering of halo nuclei from stable nuclei. In particular, we examine how far elastic scattering observables probe correlation effects among projectile nucleons. Our treatment is based on a multiple scattering expansion of the proton-projectile transition amplitude in a form which is well adapted to the weakly bound cluster picture of halo nuclei. In the specific case of 11 Li scattering from protons at 800 MeV/u we show that because core recoil effects are significant, scattering crosssections cannot, in general, be deduced from knowledge of the total matter density alone. We advocate that the optical potential concept for the scattering of halo nuclei on protons should be avoided and that the multiple scattering series for the full transition amplitude should be used instead

  20. Hyper-elastic modeling and mechanical behavior investigation of porous poly-D-L-lactide/nano-hydroxyapatite scaffold material.

    Han, Quan Feng; Wang, Ze Wu; Tang, Chak Yin; Chen, Ling; Tsui, Chi Pong; Law, Wing Cheung

    2017-07-01

    Poly-D-L-lactide/nano-hydroxyapatite (PDLLA/nano-HA) can be used as the biological scaffold material in bone tissue engineering as it can be readily made into a porous composite material with excellent performance. However, constitutive modeling for the mechanical response of porous PDLLA/nano-HA under various stress conditions has been very limited so far. In this work, four types of fundamental compressible hyper-elastic constitutive models were introduced for constitutive modeling and investigation of mechanical behaviors of porous PDLLA/nano-HA. Moreover, the unitary expressions of Cauchy stress tensor have been derived for the PDLLA/nano-HA under uniaxial compression (or stretch), biaxial compression (or stretch), pure shear and simple shear load by using the theory of continuum mechanics. The theoretical results determined from the approach based on the Ogden compressible hyper-elastic constitutive model were in good agreement with the experimental data from the uniaxial compression tests. Furthermore, this approach can also be used to predict the mechanical behaviors of the porous PDLLA/nano-HA material under the biaxial compression (or stretch), pure shear and simple shear. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

    Sutjahjo, Edhi; Chamis, Christos C.

    1993-01-01

    Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

  2. A simple model to estimate plantarflexor muscle-tendon mechanics and energetics during walking with elastic ankle exoskeletons

    Sawicki, Gregory S.; Khan, Nabil S.

    2016-01-01

    Goal A recent experiment demonstrated that when humans wear unpowered elastic ankle exoskeletons with intermediate spring stiffness they can reduce their metabolic energy cost to walk by ~7%. Springs that are too compliant or too stiff have little benefit. The purpose of this study was to use modeling and simulation to explore the muscle-level mechanisms for the ‘sweet-spot’ in stiffness during exoskeleton assisted walking. Methods We developed a simple lumped, uniarticular musculoskeletal model of the plantarflexors operating in parallel with an elastic ‘exo-tendon’. Using an inverse approach with constrained kinematics and kinetics, we rapidly simulated human walking over a range of exoskeleton stiffness values and examined the underlying neuromechanics and energetics of the biological plantarflexors. Results Stiffer ankle exoskeleton springs resulted in larger decreases in plantarflexor muscle forces, activations and metabolic energy consumption. However, in the process of unloading the compliant biological muscle-tendon unit (MTU), the muscle fascicles (CE) experienced larger excursions that negatively impacted series elastic element (SEE) recoil that is characteristic of a tuned ‘catapult mechanism’. Conclusion The combination of disrupted muscle-tendon dynamics and the need to produce compensatory forces/moments to maintain overall net ankle moment invariance could explain the ‘sweet spot’ in metabolic performance at intermediate ankle exoskeleton stiffness. Future work will aim to provide experimental evidence to support the model predictions presented here using ultrasound imaging of muscle-level dynamics during walking with elastic ankle exoskeletons. Significance Engineers must account for the muscle-level effects of exoskeleton designs in order to achieve maximal performance objectives. PMID:26485350

  3. Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

    Jan Valíček

    2015-11-01

    Full Text Available The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ, especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ.

  4. Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

    Valíček, Jan; Harničárová, Marta; Öchsner, Andreas; Hutyrová, Zuzana; Kušnerová, Milena; Tozan, Hakan; Michenka, Vít; Šepelák, Vladimír; Mitaľ, Dušan; Zajac, Jozef

    2015-01-01

    The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ), especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ. PMID:28793645

  5. The theory of elastic waves and waveguides

    Miklowitz, J

    1984-01-01

    The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. The studies of elastodynamic theory and its application to fundamental value problems should prepare the reader to tackle many physical problems of general interest in engineering and geophysics, and of particular interest in mechanics and seismology.

  6. Quantum mechanical study of elastic scattering and rotational excitation of CO by electrons

    Onda, K.; Truhlar, D. G.

    1980-01-01

    Coupling calculations of differential, integral, and momentum transfer cross sections for pure elastic scattering and rotational excitation of CO by electron impact are reported. The calculations are based on a static charge distribution that has correct dipole and quadrupole moments, has cusps at the nuclei, and is augmented by an SCF treatment of charge polarization and a local approximation for exchange. The rotationally summed cross sections, with no adjustable parameters in the scattering calculation, are in reasonably good agreement with the experimental cross sections but are somewhat larger at small scattering angles.

  7. Mechanical and morphological study of linear low density polyethylene (LLDPE)/cyperus odoratus (CY) biocomposites

    Faris, N. A.; Noriman, N. Z.; Haron, Adli; Sam, S. T.; Hamzah, R.; Shayfull, Z.; Ghazali, M. F.

    2017-09-01

    The potential of Cyperus Odoratus (CY) as a filler was studied. The CY, in a powder form, was mixed with Linear Low Density Polyethylene (LLDPE), prior to being fed into a twin screw extruder and subsequently into an injection moulding machine to produce LLDPY/CY biocomposites. The Scanning Electron Microscope (SEM) was utilized and tensile tests were performed on the test specimens to characterize the structure and properties of the composites. The integration of CY powder and LLDPE resulted in an increment of the modulus of elasticity, but a reduction in tensile strength and elongation at break. The morphology characterization of these composites, determined through the SEM, showed poor interfacial adhesion between the filler and the thermoplastic LLDPE matrix.

  8. Mechanical strength calculation of the disk type windings with elastic couplings by the finite element method

    Sivkova, G.N.; Spirchenko, Yu.V.; Chvartatskij, P.V.

    1981-01-01

    Stressed-deformed state of toroidal field coils of the disc type with elastic couplings of the tokamaks has been investigated with provision for the effect of the central core pliability by means of the two-dimensional version of the finite element method. Numerical solution of the finite element method is performed by means of the ES 1040 computer according to the computer code permitting taking account of boundary conditions of elastic support. The calculation has been performed using as the example the project of T-20 facility coil of the disc type. Consideration of pliability of the central core of the facility inductor is accomplished by the introduction of additional rigidities to the complete matrix of rigidity. Scheme of the structure distretization includes 141 units, 211 elements. The accuracy of solution depends on the reduction accuracy of the volume load to unit forces and on the number of finite elements. Analysis of the solution convergence is performed by the comparison of solutions obtained for three different schemes of the disk discretization without regard for the inductor pliability. The comparative analysis of the results shows that transfer epures for all the three discretization versions practically coincide and stresses differ not more than by 10%. On the whole the above investigation has demonstrated good convergence of the problem solution [ru

  9. Elasticity theory and applications

    Saada, Adel S; Hartnett, James P; Hughes, William F

    2013-01-01

    Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...

  10. Fabrication of Extrinsically Conductive Silicone Rubbers with High Elasticity and Analysis of Their Mechanical and Electrical Characteristics

    Anjum Saleem

    2010-08-01

    Full Text Available Conductive plastics are attracting more and more interest in electronics due to their light weight and inability to rust, which are common problems associated with metals. The field of conducting plastics is not new. Much work has been done to impart electrical conductivity to mechanically strong polymers such as polypropylene, polycarbonate and epoxies, etc. However there is a need to fabricate more flexible and elastic conductive polymers such as conducting silicone rubbers for use in various applications. In this work silicone rubbers reinforced with conductive fillers have been fabricated for use as sensors in textiles to detect the resistance change produced by stretching or relaxing. The variations of electrical resistance have been investigated by stretching and releasing the strands of conductive rubbers as a function of time. Two types of silicone rubbers—addition cured and condensation cured—were compounded with different electrically conductive fillers, among which carbon fibers have shown the best results. The carbon fibers improved the electrical conductance of the rubbers, even in very low weight percentages. The increasing concentration of fillers decreases the elasticity of the rubber. In order to keep the original properties of silicones, the filler concentration was kept as low as possible to produce a significantly detectable signal. The fabricated compounds were analyzed for their mechanical properties by stress strain curves. Such materials find their applications in electronics, antistatic applications, sports and the automotive industry where they can be used as deformation sensors.

  11. Computational modeling of elastic properties of carbon nanotube/polymer composites with interphase regions. Part II: Mechanical modeling

    Han, Fei

    2014-01-01

    We present two modeling approaches for predicting the macroscopic elastic properties of carbon nanotubes/polymer composites with thick interphase regions at the nanotube/matrix frontier. The first model is based on local continuum mechanics; the second one is based on hybrid local/non-local continuum mechanics. The key computational issues, including the peculiar homogenization technique and treatment of periodical boundary conditions in the non-local continuum model, are clarified. Both models are implemented through a three-dimensional geometric representation of the carbon nanotubes network, which has been detailed in Part I. Numerical results are shown and compared for both models in order to test convergence and sensitivity toward input parameters. It is found that both approaches provide similar results in terms of homogenized quantities but locally can lead to very different microscopic fields. © 2013 Elsevier B.V. All rights reserved.

  12. Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw

    Aurich, D.

    1988-04-01

    Elastic-plastic finite element analyses of a test vessel (steel 1.6310=20 MnMoNi 55) with a semi-elliptical axial outer surface crack have been performed. The variations of J and CTOD along the crack front and the stresse state in the vicinity of the crack are presented. The applicability of approaches to determine J is examined. The FE results are compared with the experimental data. The results are analyzed with respect to the validity of J-controlled crack growth. It will be shown that the local ductile crack growth and, especially, the 'canoe effect' for a semi-elliptical crack can only be described correctly if local J R -curves are used which account for the varying triaxiality of the stress state along the crack front. (orig./HP) [de

  13. An analytical approach to activating demand elasticity with a demand response mechanism

    Clastres, Cedric; Khalfallah, Haikel

    2015-01-01

    The aim of this work is to demonstrate analytically the conditions under which activating the elasticity of consumer demand could benefit social welfare. We have developed an analytical equilibrium model to quantify the effect of deploying demand response on social welfare and energy trade. The novelty of this research is that it demonstrates the existence of an optimal area for the price signal in which demand response enhances social welfare. This optimal area is negatively correlated to the degree of competitiveness of generation technologies and the market size of the system. In particular, it should be noted that the value of un-served energy or energy reduction which the producers could lose from such a demand response scheme would limit its effectiveness. This constraint is even greater if energy trade between countries is limited. Finally, we have demonstrated scope for more aggressive demand response, when only considering the impact in terms of consumer surplus. (authors)

  14. Catalytic mechanism of phenylacetone monooxygenases for non-native linear substrates.

    Carvalho, Alexandra T P; Dourado, Daniel F A R; Skvortsov, Timofey; de Abreu, Miguel; Ferguson, Lyndsey J; Quinn, Derek J; Moody, Thomas S; Huang, Meilan

    2017-10-11

    Phenylacetone monooxygenase (PAMO) is the most stable and thermo-tolerant member of the Baeyer-Villiger monooxygenase family, and therefore it is an ideal candidate for the synthesis of industrially relevant compounds. However, its limited substrate scope has largely limited its industrial applications. In the present work, we provide, for the first time, the catalytic mechanism of PAMO for the native substrate phenylacetone as well as for a linear non-native substrate 2-octanone, using molecular dynamics simulations, quantum mechanics and quantum mechanics/molecular mechanics calculations. We provide a theoretical basis for the preference of the enzyme for the native aromatic substrate over non-native linear substrates. Our study provides fundamental atomic-level insights that can be employed in the rational engineering of PAMO for wide applications in industrial biocatalysis, in particular, in the biotransformation of long-chain aliphatic oils into potential biodiesels.

  15. Evaluation of Interlaminar Stresses in Composite Laminates with a Bolt-Filled Hole Using a Linear Elastic Traction-Separation Description

    Yong Cao

    2017-01-01

    Full Text Available Determination of the local interlaminar stress distribution in a laminate with a bolt-filled hole is helpful for optimal bolted joint design, due to the three-dimensional (3D nature of the stress field near the bolt hole. A new interlaminar stress distribution phenomenon induced by the bolt-head and clamp-up load, which occurs in a filled-hole composite laminate, is investigated. In order to efficiently evaluate interlaminar stresses under the complex boundary condition, a calculation strategy that using zero-thickness cohesive interface element is presented and validated. The interface element is based on a linear elastic traction-separation description. It is found that the interlaminar stress concentrations occur at the hole edge, as well as the interior of the laminate near the periphery of the bolt head. In addition, the interlaminar stresses near the periphery of the bolt head increased with an increase in the clamp-up load, and the interlaminar normal and shear stresses are not at the same circular position. Therefore, the clamp-up load cannot improve the interlaminar stress distribution in the laminate near the periphery of the bolt head, although it can reduce the magnitude of the interlaminar shear stress at the hole edge. Thus, the interlaminar stress distribution phenomena may lead to delamination initiation in the laminate near the periphery of the bolt head, and should be considered in composite bolted joint design.

  16. Extracting real-crack properties from non-linear elastic behaviour of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson ratios

    V. Y. Zaitsev

    2017-09-01

    Full Text Available Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 % of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks. Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 % portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.

  17. A Low Mass Translation Mechanism for Planetary FTIR Spectrometry using an Ultrasonic Piezo Linear Motor

    Heverly, Matthew; Dougherty, Sean; Toon, Geoffrey; Soto, Alejandro; Blavier, Jean-Francois

    2004-01-01

    One of the key components of a Fourier Transform Infrared Spectrometer (FTIR) is the linear translation stage used to vary the optical path length between the two arms of the interferometer. This translation mechanism must produce extremely constant velocity motion across its entire range of travel to allow the instrument to attain high signal-to-noise ratio and spectral resolving power. A new spectrometer is being developed at the Jet Propulsion Laboratory under NASA s Planetary Instrument Definition and Development Program (PIDDP). The goal of this project is to build upon existing spaceborne FTIR spectrometer technology to produce a new instrument prototype that has drastically superior spectral resolution and substantially lower mass, making it feasible for planetary exploration. In order to achieve these goals, Alliance Spacesystems, Inc. (ASI) has developed a linear translation mechanism using a novel ultrasonic piezo linear motor in conjunction with a fully kinematic, fault tolerant linear rail system. The piezo motor provides extremely smooth motion, is inherently redundant, and is capable of producing unlimited travel. The kinematic rail uses spherical Vespel(R). rollers and bushings, which eliminates the need for wet lubrication, while providing a fault tolerant platform for smooth linear motion that will not bind under misalignment or structural deformation. This system can produce velocities from 10 - 100 mm/s with less than 1% velocity error over the entire 100-mm length of travel for a total mechanism mass of less than 850 grams. This system has performed over half a million strokes under vacuum without excessive wear or degradation in performance. This paper covers the design, development, and testing of this linear translation mechanism as part of the Planetary Atmosphere Occultation Spectrometer (PAOS) instrument prototype development program.

  18. Method for the mechanical axis alignment of the linear induction accelerator

    Li Hong; China Academy of Engineering Physics, Mianyang; Yao Jin; Liu Yunlong; Zhang Linwen; Deng Jianjun

    2004-01-01

    Accurate mechanical axis alignment is a basic requirement for assembling a linear induction accelerator (LIA). The total length of an LIA is usually over thirty or fifty meters, and it consists of many induction cells. By using a laser tracker a new method of mechanical axis alignment for LIA is established to achieve the high accuracy. This paper introduces the method and gives implementation step and point position measure errors of the mechanical axis alignment. During the alignment process a 55 m-long alignment control survey net is built, and the theoretic revision of the coordinate of the control survey net is presented. (authors)

  19. Elastic Property Simulation of Nano-particle Reinforced Composites

    He Jiawei

    2016-01-01

    Full Text Available A series of numerical micro-mechanical models for two kinds of particle (cylindrical and discal particle reinforced composites are developed to investigate the effect of microstructural parameters on the elastic properties of composites. The effects of both the degree of particle clustering and particle’s shape on the elastic mechanical properties of composites are investigated. In addition, single particle unit cell approximation is good enough for the analysis of the effect of averaged parameters when only linear elastic response is considered without considering the particle clustering in particle-reinforced composites.

  20. Assessment of the mechanical properties of area-elastic sport surfaces with video analysis

    de Koning, J.J.; Nigg, B.M.; Gerritsen, K.G.M.

    1997-01-01

    Mechanical properties of a surface are assumed to he of importance with respect to injuries, comfort, and performance in sport. For a better understanding of the factors that do influence the etiology of injuries as well as comfort, a method was developed to compare mechanical characteristics of

  1. Non-linear effects of initial melt temperatures on microstructures and mechanical properties during quenching process of liquid Cu{sub 46}Zr{sub 54} alloy

    Mo, Yun-Fei [School of Physics and Microelectronics Science, Hunan University, Changsha, 410082 (China); Liu, Rang-Su, E-mail: liurangsu@sina.com [School of Physics and Microelectronics Science, Hunan University, Changsha, 410082 (China); Tian, Ze-An; Liang, Yong-Chao [School of Physics and Microelectronics Science, Hunan University, Changsha, 410082 (China); Zhang, Hai-Tao [School of Physics and Microelectronics Science, Hunan University, Changsha, 410082 (China); Department of Electronic and Communication Engineering, Changsha University, Changsha 410003 (China); Hou, Zhao-Yang [Department of Applied Physics, Chang’an University, Xi’an 710064 (China); Liu, Hai-Rong [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China); Zhang, Ai-long [College of Physics and Electronics, Hunan University of Arts and Science, Changde 415000 (China); Zhou, Li-Li [Department of Information Engineering, Gannan Medical University, Ganzhou 341000 (China); Peng, Ping [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China); Xie, Zhong [School of Physics and Microelectronics Science, Hunan University, Changsha, 410082 (China)

    2015-05-15

    A MD simulation of liquid Cu{sub 46}Zr{sub 54} alloys has been performed for understanding the effects of initial melt temperatures on the microstructural evolution and mechanical properties during quenching process. By using several microstructural analyzing methods, it is found that the icosahedral and defective icosahedral clusters play a key role in the microstructure transition. All the final solidification structures obtained at different initial melt temperatures are of amorphous structures, and their structural and mechanical properties are non-linearly related to the initial melt temperatures, and fluctuated in a certain range. Especially, there exists a best initial melt temperature, from which the glass configuration possesses the highest packing density, the optimal elastic constants, and the smaller extent of structural softening under deforming.

  2. Strength of materials and theory of elasticity in 19th century Italy a brief account of the history of mechanics of solids and structures

    Capecchi, Danilo

    2015-01-01

    This book examines the theoretical foundations underpinning the field of strength of materials/theory of elasticity, beginning from the origins of the modern theory of elasticity. While the focus is on the advances made within Italy during the nineteenth century, these achievements are framed within the overall European context. The vital contributions of Italian mathematicians, mathematical physicists, and engineers in respect of the theory of elasticity, continuum mechanics, structural mechanics, the principle of least work, and graphical methods in engineering are carefully explained and discussed. The book represents a work of historical research that primarily comprises original contributions and summaries of work published in journals. It is directed at those graduates in engineering, but also in architecture, who wish to achieve a more global and critical view of the discipline and will also be invaluable for all scholars of the history of mechanics.

  3. FP-LAPW study of structural, electronic, elastic, mechanical and thermal properties of AlFe intermetallic

    Jain, Ekta, E-mail: jainekta05@gmail.com [Department of Physics, Government M. L. B. Girls P. G. Autonomous College, Bhopal-462002 (India); Pagare, Gitanjali, E-mail: gita-pagare@yahoo.co.in [Department of Physics, Sarojini Naidu Government Girls P. G. Autonomous College, Bhopal-462016 (India); Sanyal, S. P., E-mail: sps.physicsbu@gmail.com [Department of Physics, Barkatullah University, Bhopal-462026 (India)

    2016-05-06

    The structural, electronic, elastic, mechanical and thermal properties of AlFe intermetallic compound in B{sub 2}-type (CsCl) structure have been investigated using first-principles calculations. The exchange-correlation term was treated within generalized gradient approximation. Ground state properties i.e. lattice constants (a{sub 0}), bulk modulus (B) and first-order pressure derivative of bulk modulus (B’) are presented. The density of states are derived which show the metallic character of present compound. Our results for C{sub 11}, C{sub 12} and C{sub 44} agree well with previous theoretical data. Using Pugh’s criteria (B/G{sub H} < 1.75), brittle character of AlFe is satisfied. In addition shear modulus (G{sub H}), Young’s modulus (E), sound wave velocities and Debye temperature (θ{sub D}) have also been estimated.

  4. Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms

    Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)

    2014-11-03

    We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.

  5. Single-nary philosophy for non-linear study of mechanics of materials

    Tran, C.

    2005-01-01

    Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

  6. Structural phase transition in La2/3Ba1/3MnO3 perovskite: Elastic, magnetic, and lattice anomalies and microscopic mechanism

    E. Fertman

    2015-07-01

    Full Text Available The temperature dependences of the elastic and magnetic properties of polycrystalline perovskite manganite La2/3Ba1/3MnO3 were studied using ultrasonic and SQUID magnetometer techniques. The minimum of the temperature-dependent sound velocity v(T and corresponding maximum of the decrement δ(T were found in the vicinity of the structural phase transition R 3 ̄ c ↔ I m m a at Ts ∼ 200 K. Large alterations of v and δ indicate a structural phase transition of the soft mode type. A high sensitivity of dc magnetization to a low uniaxial pressure caused by the softening was found in the Ts region. A negative value of the linear thermal expansion coefficient along one of the crystallographic axis was found in the Imma phase near Ts. The proposed microscopic mechanism explains the appearance of the soft mode in the vicinity of the structural phase transition temperature associated with the displacement of the manganese atom from the center of the oxygen octahedron.

  7. Quality control methods for linear accelerator radiation and mechanical axes alignment.

    Létourneau, Daniel; Keller, Harald; Becker, Nathan; Amin, Md Nurul; Norrlinger, Bernhard; Jaffray, David A

    2018-06-01

    The delivery accuracy of highly conformal dose distributions generated using intensity modulation and collimator, gantry, and couch degrees of freedom is directly affected by the quality of the alignment between the radiation beam and the mechanical axes of a linear accelerator. For this purpose, quality control (QC) guidelines recommend a tolerance of ±1 mm for the coincidence of the radiation and mechanical isocenters. Traditional QC methods for assessment of radiation and mechanical axes alignment (based on pointer alignment) are time consuming and complex tasks that provide limited accuracy. In this work, an automated test suite based on an analytical model of the linear accelerator motions was developed to streamline the QC of radiation and mechanical axes alignment. The proposed method used the automated analysis of megavoltage images of two simple task-specific phantoms acquired at different linear accelerator settings to determine the coincidence of the radiation and mechanical isocenters. The sensitivity and accuracy of the test suite were validated by introducing actual misalignments on a linear accelerator between the radiation axis and the mechanical axes using both beam steering and mechanical adjustments of the gantry and couch. The validation demonstrated that the new QC method can detect sub-millimeter misalignment between the radiation axis and the three mechanical axes of rotation. A displacement of the radiation source of 0.2 mm using beam steering parameters was easily detectable with the proposed collimator rotation axis test. Mechanical misalignments of the gantry and couch rotation axes of the same magnitude (0.2 mm) were also detectable using the new gantry and couch rotation axis tests. For the couch rotation axis, the phantom and test design allow detection of both translational and tilt misalignments with the radiation beam axis. For the collimator rotation axis, the test can isolate the misalignment between the beam radiation axis

  8. Design of linear pulse motor for control element drive mechanism of SMART

    Kim, J. H.; Huh, H.; Kim, J. I.; Jang, M. H.; Kang, D. H.

    1999-01-01

    49 Control Rod Drive Mechanisms(CEDMs) are densely installed on the reactor central head of SMART. The structural design should ensure the space for maintenance/repair, cable routing, and heat release from the motor. In this paper, an improved design is presented to enlarge the space between CEDMs by decreasing the diameter of linear pulse motor. The reduction of motor thrust force due to the decrease of the motor diameter is compensated by resizing the other structural components

  9. A Cheap Linear Attention Mechanism with Fast Lookups and Fixed-Size Representations

    de Brébisson, Alexandre; Vincent, Pascal

    2016-01-01

    The softmax content-based attention mechanism has proven to be very beneficial in many applications of recurrent neural networks. Nevertheless it suffers from two major computational limitations. First, its computations for an attention lookup scale linearly in the size of the attended sequence. Second, it does not encode the sequence into a fixed-size representation but instead requires to memorize all the hidden states. These two limitations restrict the use of the softmax attention mechani...

  10. Research of the elastic waves generated by a pulse laser. Excitation mechanism of elastic waves and application to nondestructive testing; Pulse laser de reikishita danseiha ni kansuru kenkyu. Danseiha reiki no mechanism to hihakai kensa eno oyo

    Cho, H.; Takemoto, M. [Aoyama Gakuin University, Tokyo (Japan). College of Science and Engineering

    1994-07-20

    A bulk wave is generated when a pulse laser is irradiated to the material, and the characteristics of a Young`s modulus and Poisson`s ratio can be nondestructively estimated from the bulk wave. The generation mechanism of laser ultrasonic waves must be first clarified for such application. In this paper, fundamental research was conducted to study the generation mechanism of the elastic waves excited by a Q-switched Nd-YAG laser, and the generation method and characteristics of Rayleigh waves. The following result was obtained. A bulk wave is generated by the disk-like adiabatic expansion near the surface if the laser power is small when a spot-shape pulse laser was irradiated. A bulk wave is generated by the thin disk-like adiabatic expansion beneath the surface due to the thermal diffusion in the depth direction of a base material when the laser power becomes large. Moreover, a bulk wave is generated by the impact force due to abrasion and plasma when the power becomes still larger. The information on the bulk wave characteristics and Rayleigh wave was also obtained. 25 refs., 15 figs., 1 tab.

  11. Three-dimensional linear fracture mechanics analysis by a displacement-hybrid finite-element model

    Atluri, S.N.; Kathiresan, K.; Kobayashi, A.S.

    1975-01-01

    This paper deals with a finite-element procedures for the calculation of modes I, II and III stress intensity factors, which vary, along an arbitrarily curved three-dimensional crack front in a structural component. The finite-element model is based on a modified variational principle of potential energy with relaxed continuity requirements for displacements at the inter-element boundary. The variational principle is a three-field principle, with the arbitrary interior displacements for the element, interelement boundary displacements, and element boundary tractions as variables. The unknowns in the final algebraic system of equations, in the present displacement hybrid finite element model, are the nodal displacements and the three elastic stress intensity factors. Special elements, which contain proper square root and inverse square root crack front variations in displacements and stresses, respectively, are used in a fixed region near the crack front. Interelement displacement compatibility is satisfied by assuming an independent interelement boundary displacement field, and using a Lagrange multiplier technique to enforce such interelement compatibility. These Lagrangean multipliers, which are physically the boundary tractions, are assumed from an equilibrated stress field derived from three-dimensional Beltrami (or Maxwell-Morera) stress functions that are complete. However, considerable care should be exercised in the use of these stress functions such that the stresses produced by any of these stress function components are not linearly dependent

  12. Mechanical devices for aligning optical fibers using elastic metal-deformation techniques

    van Zantvoort, J.H.C.; Plukker, S.G.L.; Kuindersma, P.I.; Mekonnen, K.A.; de Waardt, H.

    2016-01-01

    We designed and realized two different mechanical devices for aligning standard lensed telecom fibers to indium-phosphide-based photonic integrated circuits (PICs). The first device (Device A) can align one fiber in three degrees of freedom, while the second device (Device B) can align two fiber

  13. The Effects of Shear Strain, Fabric, and Porosity Evolution on Elastic and Mechanical Properties of Clay-Rich Fault Gouge

    Kenigsberg, A.; Saffer, D. M.; Riviere, J.; Marone, C.

    2017-12-01

    Ultrasonic/seismic waves are widely used for probing fault zone elastic and mechanical properties (gouge composition, frictional strength, density) and elastic properties (Vp, Vs, bulk and shear moduli), as it can provide insight into key processes and fault properties during shearing. These include fabric and force chain formation, porosity evolution, and fault zone stiffness, which are in turn factors in fault slip, damage, and healing. We report on a suite of direct shear experiments on synthetic fault gouge composed of 50% smectite /50% quartz at a normal stress of 25 MPa, in which we use ultrasonic wave transmission to continuously monitor compressional and shear wave velocities (Vp, Vs) up to shear strains of 25, while simultaneously measuring friction and monitoring the evolution of density and porosity. We find that wavespeeds vary with shear strain, due to fabric development and the evolution of density and porosity. The coefficient of friction peaks at μ .47 at a shear strain of .5 - 1, decreases to a steady state value of μ .43 by shear strains of 4.5- 6 and then remains rather constant to shear strains of 6 - 25, consistent with previous work. Density increases rapidly from 1.78 g/cm3 to 1.83 g/cm3 at shear strains from 0-2 (porosity decreases from 33% to 25% over that range), and then more gradually increases to a density of 2.08 g/cm3 (porosity of 21%) at a shear strain of 25. Vp increases from 2400 m/s to 2900 m/s during the onset of shear until a shear strain of 3, and then decreases to 2400-2500 by shear strain of 7-9. At shear strains above 9, Vp slowly increases as the layer becomes denser and less porous. We interpret the co-evolving changes in friction, porosity, and elastic moduli/wavespeed to reflect fabric development and alignment of clay particles as a function of shearing. More specifically, the decrease in Vp at a shear strain of 3 reflects the clay particles gradually aligning. Once the particles are aligned, the gradual increase of

  14. Similarity and symmetry methods applications in elasticity and mechanics of materials

    Mladenov, Ivaïlo

    2014-01-01

    The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field...

  15. Homogenized Elastic Properties of Graphene for Small Deformations

    Jurica Sorić

    2013-09-01

    Full Text Available In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.

  16. Nonlinear elastic waves in materials

    Rushchitsky, Jeremiah J

    2014-01-01

    The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

  17. Mechanical stability of custom-made implants: Numerical study of anatomical device and low elastic Young's modulus alloy.

    Didier, P; Piotrowski, B; Fischer, M; Laheurte, P

    2017-05-01

    The advent of new manufacturing technologies such as additive manufacturing deeply impacts the approach for the design of medical devices. It is now possible to design custom-made implants based on medical imaging, with complex anatomic shape, and to manufacture them. In this study, two geometrical configurations of implant devices are studied, standard and anatomical. The comparison highlights the drawbacks of the standard configuration, which requires specific forming by plastic strain in order to be adapted to the patient's morphology and induces stress field in bones without mechanical load in the implant. The influence of low elastic modulus of the materials on stress distribution is investigated. Two biocompatible alloys having the ability to be used with SLM additive manufacturing are considered, commercial Ti-6Al-4V and Ti-26Nb. It is shown that beyond the geometrical aspect, mechanical compatibility between implants and bones can be significantly improved with the modulus of Ti-26Nb implants compared with the Ti-6Al-4V. Copyright © 2016 Elsevier B.V. All rights reserved.

  18. Linear models for assessing mechanisms of sperm competition: the trouble with transformations.

    Eggert, Anne-Katrin; Reinhardt, Klaus; Sakaluk, Scott K

    2003-01-01

    Although sperm competition is a pervasive selective force shaping the reproductive tactics of males, the mechanisms underlying different patterns of sperm precedence remain obscure. Parker et al. (1990) developed a series of linear models designed to identify two of the more basic mechanisms: sperm lotteries and sperm displacement; the models can be tested experimentally by manipulating the relative numbers of sperm transferred by rival males and determining the paternity of offspring. Here we show that tests of the model derived for sperm lotteries can result in misleading inferences about the underlying mechanism of sperm precedence because the required inverse transformations may lead to a violation of fundamental assumptions of linear regression. We show that this problem can be remedied by reformulating the model using the actual numbers of offspring sired by each male, and log-transforming both sides of the resultant equation. Reassessment of data from a previous study (Sakaluk and Eggert 1996) using the corrected version of the model revealed that we should not have excluded a simple sperm lottery as a possible mechanism of sperm competition in decorated crickets, Gryllodes sigillatus.

  19. A mechanical energy harvested magnetorheological damper with linear-rotary motion converter

    Chu, Ki Sum; Zou, Li; Liao, Wei-Hsin

    2016-04-01

    Magnetorheological (MR) dampers are promising to substitute traditional oil dampers because of adaptive properties of MR fluids. During vibration, significant energy is wasted due to the energy dissipation in the damper. Meanwhile, for conventional MR damping systems, extra power supply is needed. In this paper, a new energy harvester is designed in an MR damper that integrates controllable damping and energy harvesting functions into one device. The energy harvesting part of this MR damper has a unique mechanism converting linear motion to rotary motion that would be more stable and cost effective when compared to other mechanical transmissions. A Maxon motor is used as a power generator to convert the mechanical energy into electrical energy to supply power for the MR damping system. Compared to conventional approaches, there are several advantages in such an integrated device, including weight reduction, ease in installation with less maintenance. A mechanical energy harvested MR damper with linear-rotary motion converter and motion rectifier is designed, fabricated, and tested. Experimental studies on controllable damping force and harvested energy are performed with different transmissions. This energy harvesting MR damper would be suitable to vehicle suspensions, civil structures, and smart prostheses.

  20. Experimental and numerical investigation of a phase-only control mechanism in the linear intensity regime.

    Brühl, Elisabeth; Buckup, Tiago; Motzkus, Marcus

    2018-06-07

    Mechanisms and optimal experimental conditions in coherent control still intensely stimulate debates. In this work, a phase-only control mechanism in an open quantum system is investigated experimentally and numerically. Several parameterizations for femtosecond pulse shaping (combination of chirp and multipulses) are exploited in transient absorption of a prototype organic molecule to control population and vibrational coherence in ground and excited states. Experimental results are further numerically simulated and corroborated with a four-level density-matrix model, which reveals a phase-only control mechanism based on the interaction between the tailored phase of the excitation pulse and the induced transient absorption. In spite of performing experiment and numerical simulations in the linear regime of excitation, the control effect amplitude depends non-linearly on the excitation energy and is explained as a pump-dump control mechanism. No evidence of single-photon control is observed with the model. Moreover, our results also show that the control effect on the population and vibrational coherence is highly dependent on the spectral detuning of the excitation spectrum. Contrary to the popular belief in coherent control experiments, spectrally resonant tailored excitation will lead to the control of the excited state only for very specific conditions.

  1. Linking the mechanics and energetics of hopping with elastic ankle exoskeletons.

    Farris, Dominic James; Sawicki, Gregory S

    2012-12-15

    The springlike mechanics of the human leg during bouncing gaits has inspired the design of passive assistive devices that use springs to aid locomotion. The purpose of this study was to test whether a passive spring-loaded ankle exoskeleton could reduce the mechanical and energetic demands of bilateral hopping on the musculoskeletal system. Joint level kinematics and kinetics were collected with electromyographic and metabolic energy consumption data for seven participants hopping at four frequencies (2.2, 2.5, 2.8, and 3.2 Hz). Hopping was performed without an exoskeleton; with an springless exoskeleton; and with a spring-loaded exoskeleton. Spring-loaded ankle exoskeletons reduced plantar flexor muscle activity and the biological contribution to ankle joint moment (15-25%) and average positive power (20-40%). They also facilitated reductions in metabolic power (15-20%) across frequencies from 2.2 to 2.8 Hz compared with hopping with a springless exoskeleton. Reductions in metabolic power compared with hopping with no exoskeleton were restricted to hopping at 2.5 Hz only (12%). These results highlighted the importance of reducing the rate of muscular force production and work to achieve metabolic reductions. They also highlighted the importance of assisting muscles acting at the knee joint. Exoskeleton designs may need to be tuned to optimize exoskeleton mass, spring stiffness, and spring slack length to achieve greater metabolic reductions.

  2. Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

    Sushma Santapuri

    2016-10-01

    Full Text Available A unified thermodynamic framework for the characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The comprehensive framework combines the principles of classical equilibrium and non-equilibrium thermodynamics with electrodynamics of continua in the infinitesimal strain regime.In the first part of this paper, linear Thermo-Electro-Magneto-Mechanical (TEMM quasistatic processes are characterized. Thermodynamic stability conditions are further imposed on the linear constitutive model and restrictions on the corresponding material constants are derived. The framework is then extended to irreversible transport phenomena including thermoelectric, thermomagnetic and the state-of-the-art spintronic and spin caloritronic effects. Using Onsager's reciprocity relationships and the dissipation inequality, restrictions on the kinetic coefficients corresponding to charge, heat and spin transport processes are derived. All the constitutive models are accompanied by multiphysics interaction diagrams that highlight the various processes that can be characterized using this framework. Keywords: Applied mathematics, Materials science, Thermodynamics

  3. Elastic-plastic mechanical constitutive description for rock salt triaxial compression

    Butcher, B.M.

    1981-06-01

    A model for the time-independent part of the mechanical deformation of rock salt from the Waste Isolation Pilot Plant Site in southeastern New Mexico is presented. A recently published creep model was first used to correct conventional triaxial compression data for time-dependent deformation. The experimental data was from tests at a loading rate of approximately 11.9 N/s, 23 0 C, and confining pressures from 0 to -20.7 MPa. The corrected time-independent curves were then used to determine material constants for the model. Generalization to a three-dimensional plasticity-failure theory using a general constitutive relation proposed by Rudnicki and Rice was also performed. 7 figures, 3 tables

  4. Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

    Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith

    2017-05-01

    In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

  5. Statistical mechanical analysis of the linear vector channel in digital communication

    Takeda, Koujin; Hatabu, Atsushi; Kabashima, Yoshiyuki

    2007-01-01

    A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Takeda et al (2006 Europhys. Lett. 76 1193) and enables the analysis of the system in which the elements of the channel transfer matrix are statistically correlated with each other. The significance of the proposed scheme is demonstrated by assessing the performance of an existing model of multi-input multi-output communication systems

  6. Structural, Linear, and Nonlinear Optical and Mechanical Properties of New Organic L-Serine Crystal

    K. Rajesh

    2014-01-01

    Full Text Available Nonlinear optical single crystal of organic amino acid L-Serine (LS was grown by slow evaporation technique. Solubility study of the compound was measured and metastable zone width was found. Single crystal X-ray diffraction study was carried out for the grown crystal. The linear and nonlinear optical properties of the crystal were confirmed by UV-Vis analysis and powder SHG tester. FT-IR spectrum was recorded and functional groups were analyzed. Vickers’ microhardness studies showed the mechanical strength of the grown crystal. Laser damage threshold value of the crystal was calculated. Photoconductivity studies reveal the conductivity of the crystal.

  7. Determination of Spearman Correlation Coefficient (r to Evaluate the Linear Association of Dermal Collagen and Elastic Fibers in the Perspectives of Skin Injury

    Naveen Kumar

    2018-01-01

    Full Text Available Background. Difference in scar formation at different sites, in different directions at the same site, but with changes in the elasticity of skin with age, sex, and race or in some pathological conditions, is well known to clinicians. The inappropriate collagen syntheses and delayed or lack of epithelialization are known to induce scar formation with negligible elasticity at the site of damage. Changes in the elasticity of scars may be due to an unequal distribution of dermal collagen (C and elastic (E fibers. Materials and Methods. Spearman correlation coefficients (r of collagen and elastic fibers in horizontal (H and in vertical (V directions (variables CV, CH, EV, and EH were measured from the respective quantitative fraction data in 320 skin samples from 32 human cadavers collected at five selected sites over extremities. Results. Spearman’s correlation analysis revealed the statistically significant (p<0.01 strong positive correlation between CH and CV in all the areas, that is, shoulder joint area (r=0.66, wrist (r=0.75, forearm (r=0.75, and thigh (r=0.80, except at the ankle (r=0.26, p=0.14 region. Similarly, positive correlation between EH and EV has been observed at the forearm (r=0.65, moderate and thigh (r=0.42, low regions. However, a significant moderate negative correlation was observed between CV and EV at the forearm (r=-0.51 and between CH and EH at the thigh region (r=-0.65. Conclusion. Significant differences of correlations of collagen and elastic fibers in different directions from different areas of extremities were noted. This may be one of the possible anatomical reasons of scar behavior in different areas and different directions of the same area.

  8. Determination of Spearman Correlation Coefficient (r) to Evaluate the Linear Association of Dermal Collagen and Elastic Fibers in the Perspectives of Skin Injury.

    Kumar, Naveen; Kumar, Pramod; Badagabettu, Satheesha Nayak; Lewis, Melissa Glenda; Adiga, Murali; Padur, Ashwini Aithal

    2018-01-01

    Difference in scar formation at different sites, in different directions at the same site, but with changes in the elasticity of skin with age, sex, and race or in some pathological conditions, is well known to clinicians. The inappropriate collagen syntheses and delayed or lack of epithelialization are known to induce scar formation with negligible elasticity at the site of damage. Changes in the elasticity of scars may be due to an unequal distribution of dermal collagen (C) and elastic (E) fibers. Spearman correlation coefficients ( r ) of collagen and elastic fibers in horizontal (H) and in vertical (V) directions (variables CV, CH, EV, and EH) were measured from the respective quantitative fraction data in 320 skin samples from 32 human cadavers collected at five selected sites over extremities. Spearman's correlation analysis revealed the statistically significant ( p < 0.01) strong positive correlation between C H and C V in all the areas, that is, shoulder joint area ( r = 0.66), wrist ( r = 0.75), forearm ( r = 0.75), and thigh ( r = 0.80), except at the ankle ( r = 0.26, p = 0.14) region. Similarly, positive correlation between E H and E V has been observed at the forearm ( r = 0.65, moderate) and thigh ( r = 0.42, low) regions. However, a significant moderate negative correlation was observed between C V and E V at the forearm ( r = -0.51) and between C H and E H at the thigh region ( r = -0.65). Significant differences of correlations of collagen and elastic fibers in different directions from different areas of extremities were noted. This may be one of the possible anatomical reasons of scar behavior in different areas and different directions of the same area.

  9. The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

    Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" data-affiliation=" (Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" >Elze, Hans-Thomas

    2014-01-01

    We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schrödinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

  10. A numerical analysis on the curved bileaflet Mechanical Heart Valve (MHV) : leaflet motion and blood flow in an elastic blood vessel

    Bang, Jin Seok; Kim, Chang Nyung; Choi, Choeng Ryul

    2005-01-01

    In blood flow passing through the Mechanical Heart Valve (MHV) and elastic blood vessel, hemolysis and platelet activation causing thrombus formation can be seen owing to the shear stress in the blood. Also, fracture and deformation of leaflets can be observed depending on the shape and material properties of the leaflets which is opened and closed in a cycle. Hence, comprehensive study is needed on the hemodynamics which is associated with the motion of leaflet and elastic blood vessel in terms of fluid-structure interaction. In this paper, a numerical analysis has been performed for a three-dimensional pulsatile blood flow associated with the elastic blood vessel and curved bileaflet for multiple cycles in light of fluid-structure interaction. From this analysis fluttering phenomenon and rebound of the leaflet have been observed and recirculation and regurgitation have been found in the flow fields of the blood. Also, the pressure distribution and the radial displacement of the elastic blood vessel have been obtained. The motion of the leaflet and flow fields of the blood have shown similar tendency compared with the previous experiments carried out in other studies. The present study can contribute to the design methodology for the curved bileaflet mechanical heart valve. Furthermore, the proposed fluid-structure interaction method will be effectively used in various fields where the interaction between fluid flow and structure are involved

  11. Inertial piezoelectric linear motor driven by a single-phase harmonic wave with automatic clamping mechanism

    He, Liangguo; Chu, Yuheng; Hao, Sai; Zhao, Xiaoyong; Dong, Yuge; Wang, Yong

    2018-05-01

    A novel, single-phase, harmonic-driven, inertial piezoelectric linear motor using an automatic clamping mechanism was designed, fabricated, and tested to reduce the sliding friction and simplify the drive mechanism and power supply control of the inertial motor. A piezoelectric bimorph and a flexible hinge were connected in series to form the automatic clamping mechanism. The automatic clamping mechanism was used as the driving and clamping elements. A dynamic simulation by Simulink was performed to prove the feasibility of the motor. The finite element method software COMSOL was used to design the structure of the motor. An experimental setup was built to validate the working principle and evaluate the performance of the motor. The prototype motor outputted a no-load velocity of 3.178 mm/s at a voltage of 220 Vp-p and a maximum traction force of 4.25 N under a preload force of 8 N. The minimum resolution of 1.14 μm was achieved at a driving frequency of 74 Hz, a driving voltage of 50 Vp-p, and a preload force of 0 N.

  12. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

    Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

    1987-01-01

    The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

  13. Collusion and the elasticity of demand

    David Collie

    2004-01-01

    The analysis of collusion in infinitely repeated Cournot oligopoly games has generally assumed that demand is linear, but this note uses constant-elasticity demand functions to investigate how the elasticity of demand affects the sustainability of collusion.

  14. Elastic and nonlinear behaviour of argillaceous rocks under combined moisture and mechanical loads investigated by means of multiscale full-field strain measurement techniques

    Yang, D.S.; Nguyen Minh, D.; Chanchole, S.; Gharbi, H.; Valli, P.; Bornert, M.

    2010-01-01

    loading history of the sample seems thus to play an essential role in the evolution of the overall linear, and probably also nonlinear, properties of the rock. To further investigate this question, a new device has been designed at the Laboratoire de Mecanique des Solides, in which moisture and uniaxial stress can be imposed and controlled simultaneously and independently, and combined with real time continuous optical observations at both the scale of the sample (36 mm high, observed with one image of 4872 x 3248 pixels, 1 pixel = 7,4 μm) and the scale of the microstructure (several juxtaposed 1,5 x 1,5 mm fields observed with 2048 x 2048 pixels images, 1 pixel = 0,74 μm). Various metrological improvements with respect to the earlier setup allow us to investigate much smaller evolutions of the material (resolution better than 10 -5 at the macroscopic scale). This setup in particular allows us to impose a prescribed suction under constant uniaxial stress and thus measure the dependence of swelling properties as a function of the applied stress. The application of loading/unloading cycles with limited stress amplitude (10 MPa), at various suctions, gives access to the dependence of elastic properties with suction on the same sample, and its possible evolutions due to irreversible phenomena (damage) during a hydration/dehydration cycle. It is in addition possible to focus the analysis on the bulk material and on the motion of individual meso-cracks, to quantify their relative contribution to the overall deformation. Complex hydric/mechanical loading paths are currently explored on Bure argillite samples. The presentation will provide a synthesis of the results available at the time of the conference. In addition to these optical observations, Scanning Electron Microscope (SEM) observations of samples submitted to uniaxial compression inside the chamber of the SEM are currently underway. Thanks to the improved spatial resolution provided by a Field Emission Gun (FEG), an

  15. Performance prediction of mechanical excavators from linear cutter tests on Yucca Mountain welded tuffs

    Gertsch, R.; Ozdemir, L.

    1992-09-01

    The performances of mechanical excavators are predicted for excavations in welded tuff. Emphasis is given to tunnel boring machine evaluations based on linear cutting machine test data obtained on samples of Topopah Spring welded tuff. The tests involve measurement of forces as cutters are applied to the rock surface at certain spacing and penetrations. Two disc and two point-attack cutters representing currently available technology are thus evaluated. The performance predictions based on these direct experimental measurements are believed to be more accurate than any previous values for mechanical excavation of welded tuff. The calculations of performance are predicated on minimizing the amount of energy required to excavate the welded tuff. Specific energy decreases with increasing spacing and penetration, and reaches its lowest at the widest spacing and deepest penetration used in this test program. Using the force, spacing, and penetration data from this experimental program, the thrust, torque, power, and rate of penetration are calculated for several types of mechanical excavators. The results of this study show that the candidate excavators will require higher torque and power than heretofore estimated

  16. Linear Analytical Solutions of Mechanical Sensitivity in Large Deflection of Unsymmetrically Layered Piezoelectric Plate under Pretension

    Chun-Fu Chen

    2014-03-01

    Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.

  17. Integration of a linear accelerator into a production line of mechanically deboned separated poultry meat

    Sadat, Theo; Volle, Christophe

    2000-01-01

    Linear accelerators, commonly called Linacs, are being used for different industrial processes. This kind of machine produces high power electron beams and can treat many products with a high throughput. The main application of a Linac is the sterilization of medical disposable devices, polymerization and decontamination of food products. Salmonella commonly contaminates poultry. Thanks to E-beam treatment, it eradicates the pathogen quickly and permits the use of meat that should have been thrown away because of its infection. The world's first Linac dedicated to treat mechanically deboned poultry meat is located in Brittany at the Societe des Proteines Industrielles. It is a Thomson CSF Linac product, the CIRCE II, with an energy of 10 MeV and a power of 10 kW. This Linac has been used for more than 8 years, and its technology is fully proven. (author)

  18. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    Momani, Shaher; Odibat, Zaid

    2006-01-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

  19. A Hybrid Density Functional Theory/Molecular Mechanics Approach for Linear Response Properties in Heterogeneous Environments.

    Rinkevicius, Zilvinas; Li, Xin; Sandberg, Jaime A R; Mikkelsen, Kurt V; Ågren, Hans

    2014-03-11

    We introduce a density functional theory/molecular mechanical approach for computation of linear response properties of molecules in heterogeneous environments, such as metal surfaces or nanoparticles embedded in solvents. The heterogeneous embedding environment, consisting from metallic and nonmetallic parts, is described by combined force fields, where conventional force fields are used for the nonmetallic part and capacitance-polarization-based force fields are used for the metallic part. The presented approach enables studies of properties and spectra of systems embedded in or placed at arbitrary shaped metallic surfaces, clusters, or nanoparticles. The capability and performance of the proposed approach is illustrated by sample calculations of optical absorption spectra of thymidine absorbed on gold surfaces in an aqueous environment, where we study how different organizations of the gold surface and how the combined, nonadditive effect of the two environments is reflected in the optical absorption spectrum.

  20. Linear low density polyethylene (LLDPE) and lamellar zirconium phosphate (Zr P) composites: morphology and mechanical properties

    Silva, Daniela F.; Mandes, Luis C.; Lino, Adan S.

    2011-01-01

    Composites of linear low density polyethylene (LLDPE) and zirconium phosphate (ZrP) were prepared by extrusion in the molten state, containing 2 (w%) of the lamellar filler. The filler was previously synthesized by direct precipitation method and characterized. After processing, the composite and the pure virgin polymer were molded by compression in order to obtain films of 1 mm thick which were characterized by X-ray diffraction at high angle (WAXD), stress-strain mechanical analysis and scanning electron microscopy (SEM). The WAXD and SEM analysis showed that there was no intercalation of LLDPE in zirconium phosphate, possibly due to the fact that the layers do not have spacing enough to allow the intercalation of polymer chains in the galleries of the filler and thus allow the exfoliation. (author)

  1. Development of linear pulse motor type control element drive mechanism for smart

    Je-Yong, Yu; Jong-in, Kim; Ji-ho, Kim; Hyung, Huh; Moon-Hee, Chang

    2001-01-01

    The system-integrated modular advanced reactor (SMART) currently under development at the Korea Atomic Energy Research Institute is being designed with soluble boron free operation and the use of nuclear heating for reactor start-up. These design features require a Control Element Drive Mechanism(CEDM) for SMART to have fine-step movement capability as well as high reliability for fine reactivity control. In this paper, the design characteristics of a new concept CEDM driven by a Linear Pulse Motor (LPM) which meets the design requirements of the integral reactor SMART are introduced. The primary dimensions of the linear pulse motor are determined by electro-magnetic analysis and the results are also presented. In parallel with the electro-magnetic analysis, the conceptual design of the CEDM is visualized and checked for interferences among parts by assembling three dimensional (3D) models on computer. A prototype of the LPM with double air-gaps for the CEDM sub-assemblies to lift 100 kg is designed, analysed, manufactured and tested to confirm the validity of the CEDM design concept. A converter and test facility are manufactured to verify the dynamic performance of the LPM. The mover of the LPM is welded with ferromagnetic material and non-ferromagnetic material to get the magnetic flux path between the inner stator and outer stator. The thrust forces of LPM predicted by the analytic model have shown good agreement with experimental results from the prototype LPM. It is found that the LPM type CEDM has high force density and a simple drive mechanism to reduce volume and satisfy reactor operating circumstances with high pressure and temperature. (authors)

  2. Linear pulse motor type control element drive mechanism for the integral reactor

    Yu, J. Y.; Choi, S.; Kim, J. H.; Huh, H.; Park, K. B.

    2007-01-01

    The integral reactor SMART currently under development at Korea Atomic Energy Research Institute is designed with soluble boron free operation and use of nuclear heating for reactor startup. These design features require the Control Element Drive Mechanism (CEDM) for SMART to have fine-step movement capability as well as high reliability for the fine reactivity control. In this paper, design characteristics of a new concept CEDM driven by the Linear Pulse Motor (LPM) which meets the design requirements of the integral reactor SMART are introduced. The primary dimensions of the linear pulse motor are determined by the electro-magnetic analysis and the results are also presented. In parallel with the electro-magnetic analysis, the conceptual design of the CEDM is visualized and checked for interferences among parts by assembling three dimensional (3D) models on the computer. Prototype of LPM with double air-gaps for the CEDM sub-assemblies to lift 100 kg is designed, analysed, manufactured and tested to confirm the validity of the CEDM design concept. A converter and a test facility are manufactured to verify the dynamic performance of the LPM. The mover of the LPM is welded with ferromagnetic material and non-ferromagnetic material to get the magnetic flux path between inner stator and outer stator. The thrust forces of LPM predicted by analytic model have shown good agreement with experimental results from the prototype LPM. It is found that the LPM type CEDM has high force density and simple drive mechanism to reduce volume and satisfy the reactor operating circumstances with high pressure and temperature

  3. Using hierarchical linear growth models to evaluate protective mechanisms that mediate science achievement

    von Secker, Clare Elaine

    The study of students at risk is a major topic of science education policy and discussion. Much research has focused on describing conditions and problems associated with the statistical risk of low science achievement among individuals who are members of groups characterized by problems such as poverty and social disadvantage. But outcomes attributed to these factors do not explain the nature and extent of mechanisms that account for differences in performance among individuals at risk. There is ample theoretical and empirical evidence that demographic differences should be conceptualized as social contexts, or collections of variables, that alter the psychological significance and social demands of life events, and affect subsequent relationships between risk and resilience. The hierarchical linear growth models used in this dissertation provide greater specification of the role of social context and the protective effects of attitude, expectations, parenting practices, peer influences, and learning opportunities on science achievement. While the individual influences of these protective factors on science achievement were small, their cumulative effect was substantial. Meta-analysis conducted on the effects associated with psychological and environmental processes that mediate risk mechanisms in sixteen social contexts revealed twenty-two significant differences between groups of students. Positive attitudes, high expectations, and more intense science course-taking had positive effects on achievement of all students, although these factors were not equally protective in all social contexts. In general, effects associated with authoritative parenting and peer influences were negative, regardless of social context. An evaluation comparing the performance and stability of hierarchical linear growth models with traditional repeated measures models is included as well.

  4. Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

    Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P

    2007-01-01

    In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures

  5. Quantification of stromal vascular cell mechanics with a linear cell monolayer rheometer

    Elkins, Claire M., E-mail: cma9@stanford.edu; Fuller, Gerald G. [Department of Chemical Engineering, Stanford University, Stanford, California 94305 (United States); Shen, Wen-Jun; Khor, Victor K.; Kraemer, Fredric B. [Division of Endocrinology, Gerontology and Metabolism, Stanford University, Stanford, California 94305 and Veterans Affairs Palo Alto Health Care System, Palo Alto, California 94304 (United States)

    2015-01-15

    Over the past few decades researchers have developed a variety of methods for measuring the mechanical properties of whole cells, including traction force microscopy, atomic force microscopy (AFM), and single-cell tensile testing. Though each of these techniques provides insight into cell mechanics, most also involve some nonideal conditions for acquiring live cell data, such as probing only one portion of a cell at a time, or placing the cell in a nonrepresentative geometry during testing. In the present work, we describe the development of a linear cell monolayer rheometer (LCMR) and its application to measure the mechanics of a live, confluent monolayer of stromal vascular cells. In the LCMR, a monolayer of cells is contacted on both top and bottom by two collagen-coated plates and allowed to adhere. The top plate then shears the monolayer by stepping forward to induce a predetermined step strain, while a force transducer attached to the top plate collects stress information. The stress and strain data are then used to determine the maximum relaxation modulus recorded after step-strain, G{sub r}{sup 0}, referred to as the zero-time relaxation modulus of the cell monolayer. The present study validates the ability of the LCMR to quantify cell mechanics by measuring the change in G{sub r}{sup 0} of a confluent cell monolayer upon the selective inhibition of three major cytoskeletal components (actin microfilaments, vimentin intermediate filaments, and microtubules). The LCMR results indicate that both actin- and vimentin-deficient cells had ∼50% lower G{sub r}{sup 0} values than wild-type, whereas tubulin deficiency resulted in ∼100% higher G{sub r}{sup 0} values. These findings constitute the first use of a cell monolayer rheometer to quantitatively distinguish the roles of different cytoskeletal elements in maintaining cell stiffness and structure. Significantly, they are consistent with results obtained using single-cell mechanical testing methods

  6. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

  7. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

  8. Elastic properties of Gum Metal

    Kuramoto, Shigeru; Furuta, Tadahiko; Hwang, Junghwan; Nishino, Kazuaki; Saito, Takashi

    2006-01-01

    In situ X-ray diffraction measurements under tensile loading and dynamic mechanical analysis were performed to investigate the mechanisms of elastic deformation in Gum Metal. Tensile stress-strain curves for Gum Metal indicate that cold working substantially decreases the elastic modulus while increasing the yield strength, thereby confirming nonlinearity in the elastic range. The gradient of each curve decreased continuously to about one-third its original value near the elastic limit. As a result of this decrease in elastic modulus and nonlinearity, elastic deformability reaches 2.5% after cold working. Superelasticity is attributed to stress-induced martensitic transformations, although the large elastic deformation in Gum Metal is not accompanied by a phase transformation

  9. Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

    Moreno, A.

    1977-01-01

    A new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (author)

  10. Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

    Moreno, A.

    1977-01-01

    In this work a new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (Author) 91 refs

  11. Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

    Leibov Roman

    2017-01-01

    This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...

  12. Effects of Ni vacancy, Ni antisite, Cr and Pt on the third-order elastic constants and mechanical properties of NiAl

    Wu, Shaohua; Wu, Xiaozhi; Wang, Rui; Liu, Qing; Gan, Liyong

    2014-01-01

    Effects of Ni vacancy, Ni antisite in Al sublattice, Cr in Al sublattice, Pt in Ni sublattice on the second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of the B2 NiAl have been investigated using the first-principles methods. Lattice constant and the SOECs of NiAl are in good agreement with the previous results. The brittle/ductile transition map based on Pugh ratio G/B and Cauchy pressure Pc shows that Ni antisite, Cr, Pt and pressure can improve the ductility of NiAl, respectively. Ni vacancy and lower pressure can enhance the Vickers hardness Hv of NiAl. The density of states (DOS) and the charge density difference are also used to analysis the effects of vacancy, Ni antisite, Cr and Pt on the mechanical properties of NiAl, and the results are in consistent with the transition map. © 2014 Elsevier Ltd. All rights reserved.

  13. Effects of Ni vacancy, Ni antisite, Cr and Pt on the third-order elastic constants and mechanical properties of NiAl

    Wu, Shaohua

    2014-12-01

    Effects of Ni vacancy, Ni antisite in Al sublattice, Cr in Al sublattice, Pt in Ni sublattice on the second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of the B2 NiAl have been investigated using the first-principles methods. Lattice constant and the SOECs of NiAl are in good agreement with the previous results. The brittle/ductile transition map based on Pugh ratio G/B and Cauchy pressure Pc shows that Ni antisite, Cr, Pt and pressure can improve the ductility of NiAl, respectively. Ni vacancy and lower pressure can enhance the Vickers hardness Hv of NiAl. The density of states (DOS) and the charge density difference are also used to analysis the effects of vacancy, Ni antisite, Cr and Pt on the mechanical properties of NiAl, and the results are in consistent with the transition map. © 2014 Elsevier Ltd. All rights reserved.

  14. Modeling Pseudo-elastic Behavior of Springback

    Xia, Z. Cedric

    2005-01-01

    constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied

  15. Mechanical Behavior of UO2 at Sub-grain Length Scales: Quantification of Elastic, Plastic and Creep Properties via Microscale Testing

    Peralta, Pedro

    2018-04-16

    Techniques were developed to measure properties at sub-grain scales using depleted Uranium Oxide (d-UO2) samples heat-treated to obtain different grain sizes and oxygen stoichiometries, through three main tasks: 1) sample processing and characterization, 2) microscale and conventional testing and 3) modeling. Grain size and crystallography were characterized using Scanning Electron Microscopy (SEM), in conjunction with Electron Backscattering Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI). Grains were then carefully selected based on their crystallographic orientations to perform ex-situ micromechanical tests with samples machined via Focused Ion Beam (FIB), with emphasis on micro-cantilever bending. These experiments were performed under controlled atmospheres, to insure stoichiometry control, at temperatures up to 700 °C and allowed measurements involving elastic (effective Young’s modulus), plastic (critical resolved shear stresses) and creep (creep strain rates) behavior. Conventional compression experiments were performed simultaneously to compare with the ex-situ measurements and study potential size effects. Modeling was implemented using anisotropic elasticity and inelastic constitutive relations for plasticity and creep based on kinematics and kinetics of dislocation glide that account for the effects of crystal orientation, and stress. The models will be calibrated and validated using the experimental data. This project provided insight on correlations among stoichiometry, crystallography and mechanical behavior in advanced oxide fuels, provided valuable experimental data to validate and calibrate mesoscale fuel performance codes and also a framework to measure sub-grain scale mechanical properties that should be suitable for use with irradiated samples due to small volumes required. The goals and metrics of the ongoing study of thermo-mechanical behavior in depleted uranium dioxide (d-UO2) outlined in this project have been

  16. Elastic wave excitation in centrosymmetric strontium titanate crystals

    Yushin, N.K.; Sotnikov, A.V.

    1980-01-01

    The main experimental dependencies are measured and the excitation mechanism of elastic waves in centrosymmetric crystals is established. The surface generation of three-dimensional elastic waves of the 30 MHz frequency in strontium titanate crystals is observed and studied. Elastic wave excitation is observed in the 4 350 K temperature range. The efficiency of hysteresis excitation depends on the external electric field. The effect of light irradiation on the amplitude of excited elastic waves is observed. It is shown that escitation is connected with linearization of electrostriction by the constant electric field appearing in a near-surface crystal layer due to phenomena in the Schottky barrier and appearance of electretic near-electrode layers

  17. The Mechanism of Rh-Catalyzed Transformation of Fatty Acids to Linear Alpha olefins

    Sondre H. Hopen Eliasson

    2017-12-01

    Full Text Available Linear alpha olefins (LAOs are key commodity chemicals and petrochemical intermediates that are currently produced from fossil resources. Fatty acids are the obvious renewable starting material for LAOs, which can be obtained via transition-metal-catalyzed decarbonylative dehydration. However, even the best catalysts that have been obtained to date, which are based on palladium, are not active and stable enough for industrial use. To provide insight for design of better catalysts, we here present the first computationally derived mechanism for another attractive transition-metal for this reaction, rhodium. By comparing the calculated mechanisms and free energy profiles for the two metals, Pd and Rh, we single out important factors for a facile, low-barrier reaction and for a stable catalyst. While the olefin formation is rate limiting for both of the metals, the rate-determining intermediate for Rh is, in contrast to Pd, the starting complex, (PPh32Rh(COCl. This complex largely draws its stability from the strength of the Rh(I–CO bond. CO is a much less suitable ligand for the high-oxidation state Rh(III. However, for steric reasons, rhodium dissociates a bulkier triphenylphosphine and keeps the carbonyl during the oxidative addition, which is less favorable than for Pd. When compared to Pd, which dissociates two phosphine ligands at the start of the reaction, the catalytic activity of Rh also appears to be hampered by its preference for high coordination numbers. The remaining ancillary ligands leave less space for the metal to mediate the reaction.

  18. Elastic-Plastic Fracture Mechanics Analyses for Circumferential Part-Through Surface Cracks at the Interface Between elbows and Pipes

    Song, Tae Kwang; Oh, Chang Kyun; Kim, Yun Jae; Kim, Jong Sung; Jin, Tae Eun

    2007-01-01

    This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes

  19. Elastic-Plastic Fracture Mechanics Analyses For circumferential Part-through Surface Cracks At The Interface Between Elbows and Pipes

    Song, Tae Kwang; Kim, Yun Jae; Oh, Chang Kyun; Kim, Jong Sung; Jin, Tae Eun

    2007-01-01

    This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes

  20. Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

    Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

    2017-12-27

    In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

  1. Modelling of the Thermo-Mechanical Behavior of the Two-Beam Module for the Compact Linear Collider

    Raatikainen, Riku; Österberg, K; Lehtovaara, A; Pajunen, S

    2011-01-01

    To fulfil the mechanical requirements set by the luminosity goals of the compact linear collider, the 2-m long two-beam modules, the shortest repetitive elements in the main linear accelerator, have to be controlled at micrometer level. At the same time these modules are exposed to high power dissipation that varies while the accelerator is ramped up to nominal power and when the mode of the accelerator operation is modified. These variations will give rise to inevitable temperature transients driving mechanical distortions in and between different module components. Therefore, the thermo-mechanical behaviour of the module is of a high importance. This thesis describes a finite element method model for the two-beam compact linear collider module. The components are described in detail compared to earlier models, which should result in a realistic description of the module. Due to the complexity of the modules, the modelling is divided into several phases from geometrical simplification and modification to the...

  2. A benchtop biorobotic platform for in vitro observation of muscle-tendon dynamics with parallel mechanical assistance from an elastic exoskeleton.

    Robertson, Benjamin D; Vadakkeveedu, Siddarth; Sawicki, Gregory S

    2017-05-24

    We present a novel biorobotic framework comprised of a biological muscle-tendon unit (MTU) mechanically coupled to a feedback controlled robotic environment simulation that mimics in vivo inertial/gravitational loading and mechanical assistance from a parallel elastic exoskeleton. Using this system, we applied select combinations of biological muscle activation (modulated with rate-coded direct neural stimulation) and parallel elastic assistance (applied via closed-loop mechanical environment simulation) hypothesized to mimic human behavior based on previously published modeling studies. These conditions resulted in constant system-level force-length dynamics (i.e., stiffness), reduced biological loads, increased muscle excursion, and constant muscle average positive power output-all consistent with laboratory experiments on intact humans during exoskeleton assisted hopping. Mechanical assistance led to reduced estimated metabolic cost and MTU apparent efficiency, but increased apparent efficiency for the MTU+Exo system as a whole. Findings from this study suggest that the increased natural resonant frequency of the artificially stiffened MTU+Exo system, along with invariant movement frequencies, may underlie observed limits on the benefits of exoskeleton assistance. Our novel approach demonstrates that it is possible to capture the salient features of human locomotion with exoskeleton assistance in an isolated muscle-tendon preparation, and introduces a powerful new tool for detailed, direct examination of how assistive devices affect muscle-level neuromechanics and energetics. Copyright © 2017 Elsevier Ltd. All rights reserved.

  3. How mechanical behavior of glassy polymers enables us to characterize melt deformation: elastic yielding in glassy state after melt stretching?

    Wang, Shi-Qing; Zhao, Zhichen; Tsige, Mesfin; Zheng, Yexin

    Fast melt deformation well above the glass transition temperature Tg is known to produce elastic stress in an entangled polymer due to the chain entropy loss at the length scale of the network mesh size. Here chains of high molecular weight are assumed to form an entanglement network so that such a polymer behaves transiently like vulcanized rubber capable of affine deformation. We consider quenching a melt-deformed glassy polymer to well below Tg to preserve the elastic stress. Upon heating such a sample to Tg, the sample can return to the shape it took before melt deformation. This is the basic principle behind the design of all polymer-based shape-memory materials. This work presents intriguing evidence based on both experiment and computer simulation that the chain network, deformed well above Tg, can drive the glassy polymer to undergo elastic yielding. Our experimental systems include polystyrene, poly(methyl methacrylate) and polycarbonate; the molecular dynamics simulation is based on Kremer-Grest bead-spring model. National Science Foundation (DMR-1444859 and DMR-1609977).

  4. Polarized electron beams elastically scattered by atoms as a tool for testing fundamental predictions of quantum mechanics.

    Dapor, Maurizio

    2018-03-29

    Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.

  5. Highly porous layers of silica nanospheres sintered by drying: scaling up of the elastic properties of the beads to the macroscopic mechanical properties.

    Lesaine, Arnaud; Bonamy, Daniel; Gauthier, Georges; Rountree, Cindy L; Lazarus, Véronique

    2018-05-16

    Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitly considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand, homogenization approaches (e.g. rule of mixtures, and Eshelby, Mori-Tanaka and self-consistent schemes), based on continuum mechanics and asymptotic analysis, provide the stiffness tensor from the knowledge of the porosity and the elastic constants of the beads. Herein, the self-consistent scheme accurately predicts both bulk and shear moduli, with no adjustable parameter, provided the porosity is less than 35%, for layers composed of particles as small as 15 nm in diameter. Conversely, Kendall's approach is found to predict the Young's modulus over the full porosity range. Moreover, the adhesion energy in Kendall's model has to be adjusted to a value of the order of the fracture energy of the particle material. This suggests that sintering during drying leads to the formation of covalent siloxane bonds between the particles.

  6. Illustrated instructions for mechanical quality assurance of a medical linear accelerator.

    Court, Laurence; Wang, He; Aten, David; Brown, Derek; MacGregor, Hannelie; du Toit, Monique; Chi, Melinda; Gao, Song; Yock, Adam; Aristophanous, Michalis; Balter, Peter

    2018-03-03

    The purpose of this study was to develop and test a set of illustrated instructions for effective training for mechanical quality assurance (QA) of medical linear accelerators (linac). Illustrated instructions were created for mechanical QA and underwent several steps of review, testing, and refinement. Eleven testers with no recent QA experience were then recruited from our radiotherapy department (one student, two computational scientists, and eight dosimetrists). This group was selected because they have experience of radiation therapy but no preconceived ideas about how to do QA. The following parameters were progressively decalibrated on a Varian C-series linac: Group A = gantry angle, ceiling laser position, X1 jaw position, couch longitudinal position, physical graticule position (five testers); Group B = Group A + wall laser position, couch lateral and vertical position, collimator angle (three testers); Group C = Group B + couch angle, wall laser angle, and optical distance indicator (three testers). Testers were taught how to use the linac and then used the instructions to try to identify these errors. An experienced physicist observed each session, giving support on machine operation as necessary. Testers were able to follow the instructions. They determined gantry, collimator, and couch angle errors within 0.4°, 0.3°, and 0.9° of the actual changed values, respectively. Laser positions were determined within 1 mm and jaw positions within 2 mm. Couch position errors were determined within 2 mm and 3 mm for lateral/longitudinal and vertical errors, respectively. Accessory-positioning errors were determined within 1 mm. Optical distance indicator errors were determined within 2 mm when comparing with distance sticks and 6 mm when using blocks, indicating that distance sticks should be the preferred approach for inexperienced staff. Inexperienced users were able to follow these instructions and catch errors within the criteria suggested

  7. Fracture mechanics analysis of reactor pressure vessel under pressurized thermal shock - The effect of elastic-plastic behavior and stainless steel cladding -

    Joo, Jae Hwang; Kang, Ki Ju; Jhung, Myung Jo

    2002-01-01

    Performed here is an assessment study for deterministic fracture mechanics analysis of a pressurized thermal shock (PTS). The PTS event means an event or transient in pressurized water reactors (PWRs) causing severe overcooling (thermal shock) concurrent with or followed by significant pressure in the reactor vessel. The problems consisting of two transients and 10 cracks are solved and maximum stress intensity factors and maximum allowable nil-ductility reference temperatures are calculated. Their results are compared each other to address the general characteristics between transients, crack types and analysis methods. The effects of elastic-plastic material behavior and clad coating on the inner surface are explored

  8. A design concept of parallel elasticity extracted from biological muscles for engineered actuators.

    Chen, Jie; Jin, Hongzhe; Iida, Fumiya; Zhao, Jie

    2016-08-23

    Series elastic actuation that takes inspiration from biological muscle-tendon units has been extensively studied and used to address the challenges (e.g. energy efficiency, robustness) existing in purely stiff robots. However, there also exists another form of passive property in biological actuation, parallel elasticity within muscles themselves, and our knowledge of it is limited: for example, there is still no general design strategy for the elasticity profile. When we look at nature, on the other hand, there seems a universal agreement in biological systems: experimental evidence has suggested that a concave-upward elasticity behaviour is exhibited within the muscles of animals. Seeking to draw possible design clues for elasticity in parallel with actuators, we use a simplified joint model to investigate the mechanisms behind this biologically universal preference of muscles. Actuation of the model is identified from general biological joints and further reduced with a specific focus on muscle elasticity aspects, for the sake of easy implementation. By examining various elasticity scenarios, one without elasticity and three with elasticity of different profiles, we find that parallel elasticity generally exerts contradictory influences on energy efficiency and disturbance rejection, due to the mechanical impedance shift thus caused. The trade-off analysis between them also reveals that concave parallel elasticity is able to achieve a more advantageous balance than linear and convex ones. It is expected that the results could contribute to our further understanding of muscle elasticity and provide a theoretical guideline on how to properly design parallel elasticity behaviours for engineering systems such as artificial actuators and robotic joints.

  9. Introduction of non-linear elasticity models for characterization of shape and deformation statistics: application to contractility assessment of isolated adult cardiocytes.

    Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul

    2011-08-22

    We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.

  10. Introduction of a priori information in the elastic linearized inversion of seismic data before stacking; Introduction d'informations a priori dans l'inversion linearisee elastique de donnees sismiques de surface avant sommation

    Tonellot, Th.L.

    2000-03-24

    In this thesis, we propose a method which takes into account a priori information (geological, diagraphic and stratigraphic knowledge) in linearized pre-stack seismic data inversion. The approach is based on a formalism in which the a priori information is incorporated in an a priori model of elastic parameters - density, P and S impedances - and a model covariance operator which describes the uncertainties in the model. The first part of the thesis is dedicated to the study of this covariance operator and to the norm associated to its inverse. We have generalized the exponential covariance operator in order to describe the uncertainties in the a priori model elastic parameters and their correlations at each location. We give the analytical expression of the covariance operator inverse in 1-D, 2-D, and 3-D, and we discretized the associated norm with a finite element method. The second part is dedicated to synthetic and real examples. In a preliminary step, we have developed a pre-stack data well calibration method which allows the estimation of the source signal. The impact of different a priori information is then demonstrated on synthetic and real data. (author)

  11. Understanding the elastic relaxation mechanisms of strain in Ge islands on pit-patterned Si(001) substrates

    Vastola, G; Montalenti, F; Miglio, Leo

    2008-01-01

    Substrate pre-patterning is a new and effective route for growing ordered arrays of heteroepitaxial nanoislands. Here, by exploiting elasticity theory solved by using finite element methods, we show why islands growing inside pits are better relaxed with respect to the flat-substrate case. Pit pre-patterning is demonstrated to be more important than previously realized, allowing for further degrees of freedom in controlling not only positioning but also shape, strain, and coherence of the growing islands. Our results offer a solid interpretation for the recent experimental results obtained by the group of Professor Guenther Bauer.

  12. Shear-induced formation of vesicles in membrane phases: Kinetics and size selection mechanisms, elasticity versus surface tension

    Courbin, L.; Panizza, P.

    2004-02-01

    Multilamellar vesicles can be formed upon shearing lamellar phases (Lα) and phase-separated lamellar-sponge (Lα/L3) mixtures. In the first case, the vesicle volume fraction is always 100% and the vesicle size is monitored by elasticity (“onion textures”). In the second system the vesicle volume fraction can be tuned from 0 to 100% and the mean size results from a balance between capillary and viscous forces (“Taylor droplets”). However, despite these differences, in both systems we show that the formation of vesicles is a strain-controlled process monitored by a universal primary buckling instability of the lamellae.

  13. Design guidance for elastic followup

    Naugle, F.V.

    1983-01-01

    The basic mechanism of elastic followup is discussed in relation to piping design. It is shown how mechanistic insight gained from solutions for a two-bar problem can be used to identify dominant design parameters and to determine appropriate modifications where elastic followup is a potential problem. It is generally recognized that quantitative criteria are needed for elastic followup in the creep range where badly unbalanced lines can pose potential problems. Approaches for criteria development are discussed

  14. THE EFFECT OF DIAMETER ON THE MECHANICAL-PROPERTIES OF AMORPHOUS-CARBON FIBERS FROM LINEAR LOW-DENSITY POLYETHYLENE

    PENNING, JP; LAGCHER, R; PENNINGS, AJ

    The mechanical properties of amorphous carbon fibers, derived from linear low density polyethylene strongly depend on the fibre diameter, which may be attributed to the presence of a skin/core structure in these fibres. High strength carbon fibres could thus be prepared by using thin precursor

  15. Some Differential Geometric Relations in the Elastic Shell

    Xiaoqin Shen

    2016-01-01

    Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.

  16. Elasticity in Elastics-An in-vitro study.

    Kamisetty, Supradeep Kumar; Nimagadda, Chakrapani; Begam, Madhoom Ponnachi; Nalamotu, Raghuveer; Srivastav, Trilok; Gs, Shwetha

    2014-04-01

    analyzed with student independent - t test, analysis of variance and the Tukey - HSD test at p elastics had greater cross sectional area than latex elastics in all types of elastics. Forestadent heavy elastics had grater cross sectional area than GAC and Glenroe. There was no statistically significant difference in the internal diameter in between all type of elastics. Forestadent non latex elastics had greater breaking force compared to GAC and Glenroe elastics. Forces generated by the elastics decreased over 48 hours to an average load approximating 65-75% of the manufacturer's values. Force degradation was greater in non latex elastics compared to latex elastics. The results of the study demonstrated that the clinical choice of elastics should be based on the patient's medical history and the specific mechanical properties of the type of elastic. How to cite the article: Kamisetty SK, Nimagadda C, Begam MP, Nalamotu R, Srivastav T, Shwetha GS. Elasticity in Elastics-An in-vitro study. J Int Oral Health 2014;6(2):96-105.

  17. Zirconium elasticity modules

    Vavra, G.

    1978-01-01

    Considered are the limit and the intermediate values of the Young modulus E, modulus of shear G and of linear modulus of compression K obtainable at various temperatures (4.2 to 1133 K) for single crystals of α-zirconium. Determined and presented are the corrected isotropic elasticity characteristics of E, G, K over the above range of temperatures of textured and non-textured α-Zr

  18. The oscillatory behavior of heated channels: an analysis of the density effect. Part I. The mechanism (non linear analysis). Part II. The oscillations thresholds (linearized analysis)

    Boure, J.

    1967-01-01

    The problem of the oscillatory behavior of heated channels is presented in terms of delay-times and a density effect model is proposed to explain the behavior. The density effect is the consequence of the physical relationship between enthalpy and density of the fluid. In the first part non-linear equations are derived from the model in a dimensionless form. A description of the mechanism of oscillations is given, based on the analysis of the equations. An inventory of the governing parameters is established. At this point of the study, some facts in agreement with the experiments can be pointed out. In the second part the start of the oscillatory behavior of heated channels is studied in terms of the density effect. The threshold equations are derived, after linearization of the equations obtained in Part I. They can be solved rigorously by numerical methods to yield: -1) a relation between the describing parameters at the onset of oscillations, and -2) the frequency of the oscillations. By comparing the results predicted by the model to the experimental behavior of actual systems, the density effect is very often shown to be the actual cause of oscillatory behaviors. (author) [fr

  19. An elastic-plastic fracture mechanics based methodology to characterize cracking behavior and its application to environmental assisted processes

    Alvarez, J.A.; Gutierrez-Solana, F.

    1999-01-01

    Cracking processes suffered by new structural and piping steels when used in petroleum or other energy installations have demonstrated the need for a cracking resistance characterization methodology. This methodology, valid for both elastic and elastoplastic regimes, should be able to define crack propagation kinetics as a function of their controlling local parameters. This work summarizes an experimental and analytical methodology that has been shown to be suitable for characterizing cracking processes using compact tensile specimens, especially subcritical environmentally assisted ones, such as those induced by hydrogen in microalloyed steels. The applied and validated methodology has been shown to offer quantitative results of cracking behavior and to correlate these with the existing fracture micromechanisms. (orig.)

  20. Elastic Beanstalk

    Vliet, Jurg; Wel, Steven; Dowd, Dara

    2011-01-01

    While it's always been possible to run Java applications on Amazon EC2, Amazon's Elastic Beanstalk makes the process easier-especially if you understand how it works beneath the surface. This concise, hands-on book not only walks you through Beanstalk for deploying and managing web applications in the cloud, you'll also learn how to use this AWS tool in other phases of development. Ideal if you're a developer familiar with Java applications or AWS, Elastic Beanstalk provides step-by-step instructions and numerous code samples for building cloud applications on Beanstalk that can handle lots

  1. Mathematical methods in elasticity imaging

    Ammari, Habib; Garnier, Josselin; Kang, Hyeonbae; Lee, Hyundae; Wahab, Abdul

    2015-01-01

    This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic...

  2. Blocky inversion of multichannel elastic impedance for elastic parameters

    Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

    2018-04-01

    Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

  3. Linear Look-ahead in Conjunctive Cells: An Entorhinal Mechanism for Vector-Based Navigation

    John L Kubie

    2012-04-01

    Full Text Available The crisp organization of the firing bumps of entorhinal grid cells and conjunctive cells leads to the notion that the entorhinal cortex may compute linear navigation routes. Specifically, we propose a process, termed linear look-ahead, by which a stationary animal could compute a series of locations in the direction it is facing. We speculate that this computation could be achieved through learned patterns of connection strengths among entorhinal neurons. This paper has three sections. First, we describe the minimal grid cell properties that will be built into our network. Specifically, the network relies of rigid modules of neurons, where all members have identical grid scale and orientation, but differ in spatial phase. Additionally, these neurons must be densely interconnected with synapses that are modifiable early in the animal’s life. Second, we investigate whether plasticity during short bouts of locomotion could induce patterns of connections amongst grid cells or conjunctive cells. Finally, we run a simulation to test whether the learned connection patterns can exhibit linear look-ahead. Our results are straightforward. A simulated 30-minute walk produces weak strengthening of synapses between grid cells that do not support linear look-ahead. Similar training in a conjunctive-cell module produces a small subset of very strong connections between cells. These strong pairs have three properties: The pre- and post-synaptic cells have similar heading direction. The cell pairs have neighboring grid bumps. Finally, the spatial offset of firing bumps of the cell pair is in the direction of the common heading preference. Such a module can produce strong and accurate linear look ahead starting in any location and extending in any direction. We speculate that this process may: 1. compute linear paths to goals; 2. update grid cell firing during navigation; and 3. stabilize the rigid modules of grid cells and conjunctive cells.

  4. Features of the non-collinear one-phonon anomalous light scattering controlled by elastic waves with elevated linear losses: potentials for multi-frequency parallel spectrum analysis of radio-wave signals.

    Shcherbakov, Alexandre S; Arellanes, Adan Omar

    2017-12-01

    During subsequent development of the recently proposed multi-frequency parallel spectrometer for precise spectrum analysis of wideband radio-wave signals, we study potentials of new acousto-optical cells exploiting selected crystalline materials at the limits of their capabilities. Characterizing these wide-aperture cells is non-trivial due to new features inherent in the chosen regime of an advanced non-collinear one-phonon anomalous light scattering by elastic waves with significantly elevated acoustic losses. These features can be observed simpler in uniaxial, tetragonal, and trigonal crystals possessing linear acoustic attenuation. We demonstrate that formerly studied additional degree of freedom, revealed initially for multi-phonon regimes of acousto-optical interaction, can be identified within the one-phonon geometry as well and exploited for designing new cells. We clarify the role of varying the central acoustic frequency and acoustic attenuation using the identified degree of freedom. Therewith, we are strongly restricted by a linear regime of acousto-optical interaction to avoid the origin of multi-phonon processes within carrying out a multi-frequency parallel spectrum analysis of radio-wave signals. Proof-of-principle experiments confirm the developed approaches and illustrate their applicability to innovative technique for an advanced spectrum analysis of wideband radio-wave signals with the improved resolution in an extended frequency range.

  5. Linear and nonlinear analogues of the Schroedinger equation in the contextual approach in quantum mechanics

    Khrennikov, A.Yu.

    2005-01-01

    One derived the general evolutionary differential equation within the Hilbert space describing dynamics of the wave function. The derived contextual model is more comprehensive in contrast to a quantum one. The contextual equation may be a nonlinear one. Paper presents the conditions ensuring linearity of the evolution and derivation of the Schroedinger equation [ru

  6. First-principles calculation of the elastic constants, the electronic density of states and the ductility mechanism of the intermetallic compounds: YAg, YCu and YRh

    Wu Yurong [College of Electromechanical Engineering, Hunan University of Science and Technology, Xiantang 411201 (China); Hu Wangyu [Department of Applied Physics, Hunan University, Changsha 410082 (China)], E-mail: wangyuhu2001cn@yahoo.com.cn; Han Shaochang [Department of Applied Physics, Hunan University, Changsha 410082 (China)

    2008-10-01

    First-principles calculations have been used to study the elastic and electronic properties of ductility rare-earth alloy YM (M=Ag, Cu, Rh) systems. The ductility mechanism for these alloys is studied from microscopic aspect, via electronic density of states (DOS). The Fermi energy lies near a local minimum, and the hybridization is stronger than that of the common NiAl alloy, demonstrating that the ductility of these alloys is much better than that of NiAl alloy. Elastic modulus, namely, shear modulus C'=(C{sub 11}-C{sub 12})/2, bulk modulus B and C{sub 44} are calculated by volume-conserving orthorhombic, hydrostatic pressure and tri-axial shear strain, respectively. Moreover, lattice parameters, antiphase boundary (APB) energies and unstable stacking fault energies of these alloys are also studied. The APB energies are greater than the unstable stacking fault energies for these alloy systems, and this is a characteristic of the ductility rare-earth alloy. The APB energies of YRh are the highest ones in these three YM alloys, which make dislocation dissociation difficult. The DOS and APB energy results show that the ductility of YRh may be worst in these three YM systems.

  7. Study of pressure variation effect on structural, opto-electronic, elastic, mechanical, and thermodynamic properties of SrLiF3

    Erum, Nazia; Iqbal, Muhammad Azhar

    2017-11-01

    The structural, electronic, elastic, optical and thermodynamic properties of cubic fluoroperovskite SrLiF3 at ambient and high-pressure are investigated by using first-principles total energy calculations within the framework of Generalized Gradient Approximation (GGA), combined with Quasi-harmonic Debye model in which the phonon effects are considered. The pressure effects are determined in the range of 0-50 GPa, in which cubic stability of SrLiF3 fluoroperovskite remains valid. The computed lattice parameters agree well with experimental and previous theoretical results. Decrease in lattice constant and bonds length is observed with the increase in pressure from 0 to 50 GPa. The effect of increase in pressure on electronic band structure calculations with GGA and GGA plus Tran-Blaha modified Becke-Johnson (TB-mBJ) potential reveals a predominant characteristic associated with widening of bandgap. The influence of pressure on elastic constants and their related mechanical parameters have been discussed in detail. All the calculated optical properties such as the complex dielectric function Ԑ(ω), optical conductivity σ(ω), energy loss function L(ω), absorption coefficient α(w), refractive index n (ω), reflectivity R (ω), and effective number of electrons neff, via sum rules shift towards the higher energies under the application of pressure. Moreover, important thermodynamic properties heat capacities (Cp and Cv), volume expansion coefficient (α), and Debye temperature (θD) are predicted successfully in the wide temperature and pressure ranges.

  8. Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing.

    Mitri, F G; Fellah, Z E A

    2014-01-01

    The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.

  9. First-principles calculation of the elastic constants, the electronic density of states and the ductility mechanism of the intermetallic compounds: YAg, YCu and YRh

    Wu Yurong; Hu Wangyu; Han Shaochang

    2008-01-01

    First-principles calculations have been used to study the elastic and electronic properties of ductility rare-earth alloy YM (M=Ag, Cu, Rh) systems. The ductility mechanism for these alloys is studied from microscopic aspect, via electronic density of states (DOS). The Fermi energy lies near a local minimum, and the hybridization is stronger than that of the common NiAl alloy, demonstrating that the ductility of these alloys is much better than that of NiAl alloy. Elastic modulus, namely, shear modulus C'=(C 11 -C 12 )/2, bulk modulus B and C 44 are calculated by volume-conserving orthorhombic, hydrostatic pressure and tri-axial shear strain, respectively. Moreover, lattice parameters, antiphase boundary (APB) energies and unstable stacking fault energies of these alloys are also studied. The APB energies are greater than the unstable stacking fault energies for these alloy systems, and this is a characteristic of the ductility rare-earth alloy. The APB energies of YRh are the highest ones in these three YM alloys, which make dislocation dissociation difficult. The DOS and APB energy results show that the ductility of YRh may be worst in these three YM systems

  10. Cell Elasticity Determines Macrophage Function

    Patel, Naimish R.; Bole, Medhavi; Chen, Cheng; Hardin, Charles C.; Kho, Alvin T.; Mih, Justin; Deng, Linhong; Butler, James; Tschumperlin, Daniel; Fredberg, Jeffrey J.; Krishnan, Ramaswamy; Koziel, Henry

    2012-01-01

    Macrophages serve to maintain organ homeostasis in response to challenges from injury, inflammation, malignancy, particulate exposure, or infection. Until now, receptor ligation has been understood as being the central mechanism that regulates macrophage function. Using macrophages of different origins and species, we report that macrophage elasticity is a major determinant of innate macrophage function. Macrophage elasticity is modulated not only by classical biologic activators such as LPS and IFN-γ, but to an equal extent by substrate rigidity and substrate stretch. Macrophage elasticity is dependent upon actin polymerization and small rhoGTPase activation, but functional effects of elasticity are not predicted by examination of gene expression profiles alone. Taken together, these data demonstrate an unanticipated role for cell elasticity as a common pathway by which mechanical and biologic factors determine macrophage function. PMID:23028423

  11. Cell elasticity determines macrophage function.

    Naimish R Patel

    Full Text Available Macrophages serve to maintain organ homeostasis in response to challenges from injury, inflammation, malignancy, particulate exposure, or infection. Until now, receptor ligation has been understood as being the central mechanism that regulates macrophage function. Using macrophages of different origins and species, we report that macrophage elasticity is a major determinant of innate macrophage function. Macrophage elasticity is modulated not only by classical biologic activators such as LPS and IFN-γ, but to an equal extent by substrate rigidity and substrate stretch. Macrophage elasticity is dependent upon actin polymerization and small rhoGTPase activation, but functional effects of elasticity are not predicted by examination of gene expression profiles alone. Taken together, these data demonstrate an unanticipated role for cell elasticity as a common pathway by which mechanical and biologic factors determine macrophage function.

  12. Structure and dynamics of ion clusters in linear octupole traps: Phase diagrams, chirality, and melting mechanisms

    Yurtsever, E.; Onal, E. D.; Calvo, F.

    2011-01-01

    The stable structures and melting dynamics of clusters of identical ions bound by linear octupole radiofrequency traps are theoretically investigated by global optimization methods and molecular dynamics simulations. By varying the cluster sizes in the range of 10-1000 ions and the extent of trap anisotropy by more than one order of magnitude, we find a broad variety of stable structures based on multiple rings at small sizes evolving into tubular geometries at large sizes. The binding energy of these clusters is well represented by two contributions arising from isotropic linear and octupolar traps. The structures generally exhibit strong size effects, and chiral arrangements spontaneously emerge in many crystals. Sufficiently large clusters form nested, coaxial tubes with different thermal stabilities. As in isotropic octupolar clusters, the inner tubes melt at temperatures that are lower than the overall melting point.

  13. Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw. Pt. 2

    Brocks, W.; Kuenecke, G.

    1989-06-01

    Continuing preceding investigations, a further elastic-plastic finite element analysis of a test vessel with a semi-elliptical axial outer surface crack has been performed. The variations of J and CTOD along the crack front and the stress state in the vicinity of the crack are presented. The applicability of analytical approaches to determine J is examined. The FE results are used to analyze the experimental data with respect to the validity of J-controlled crack growth. Local J R -curves of the surface flaw are compared with J R -curves of various specimens of different geometries. Again, it became evident that the local ductile crack growth and, especially, the developing 'canoe shape' of the surface crack cannot be described by a single resistance curve which is assumed to be a material property. A method described in a previous report to predict the ductile crack growth by using local J R -curves which depend on the triaxiality of the stress state did not result in a satisfactory outcome, in the present case. The presumed reasons will be discussed. (orig.) [de

  14. Identification of Multiple-Mode Linear Models Based on Particle Swarm Optimizer with Cyclic Network Mechanism

    Tae-Hyoung Kim

    2017-01-01

    Full Text Available This paper studies the metaheuristic optimizer-based direct identification of a multiple-mode system consisting of a finite set of linear regression representations of subsystems. To this end, the concept of a multiple-mode linear regression model is first introduced, and its identification issues are established. A method for reducing the identification problem for multiple-mode models to an optimization problem is also described in detail. Then, to overcome the difficulties that arise because the formulated optimization problem is inherently ill-conditioned and nonconvex, the cyclic-network-topology-based constrained particle swarm optimizer (CNT-CPSO is introduced, and a concrete procedure for the CNT-CPSO-based identification methodology is developed. This scheme requires no prior knowledge of the mode transitions between subsystems and, unlike some conventional methods, can handle a large amount of data without difficulty during the identification process. This is one of the distinguishing features of the proposed method. The paper also considers an extension of the CNT-CPSO-based identification scheme that makes it possible to simultaneously obtain both the optimal parameters of the multiple submodels and a certain decision parameter involved in the mode transition criteria. Finally, an experimental setup using a DC motor system is established to demonstrate the practical usability of the proposed metaheuristic optimizer-based identification scheme for developing a multiple-mode linear regression model.

  15. Component Energy Efficiencies in a Novel Linear to Rotary Motion Inter-conversion Hydro-mechanism Running a Solar Tracker

    Kant Eliab Kanyarusoke

    2018-01-01

    Full Text Available A new mechanism interconverting linear and rotary motion was investigated for energy transfers among its components. It employed a gear-rack set, a Hooke coupling and a specially designed bladder-valve system that regulated the motion. The purpose was to estimate individual component mechanical efficiencies as they existed in the prototype so that future reengineering of the mechanism could be properly targeted. Theoretical modelling of the mechanism was first done to obtain equations for efficiencies of the key components. Two-stage experimentation followed when running a solar tracker. The first stage produced data for inputting into the model to determine the efficiencies’ theoretical variation with the Hooke coupling shaft angle. The second one verified results of the Engineering Equation Solver (EES software solutions of the model. It was found that the energy transfer to focus on was that between the Hooke coupling and the output shaft because its efficiency was below 4%

  16. Non-linear behaviour of multi-phase MOX fuels: a micro-mechanical approach

    Rousette, S.; Gatt, J.M.; Michel, J.C.

    2005-01-01

    The modelling of mechanical pellet-clad interaction requires knowledge of the thermo-mechanical behaviour of nuclear fuels. Some nuclear fuels such as MOX are composed of several phases. The mechanical properties of these phases, which are elasto-visco-plastic in-pile, are changing in-pile. The objective is to formulate a mechanical behaviour law taking all the physical phenomena into account in the different phases, which can easily be introduced into a fuel rod modelling code. Consequently, Non-uniform Transformation Field Analysis (NTFA) is used on the one hand, to correctly capture the heterogeneity of the anelastic strain in the different phases and, on the other hand, to provide a simple overall constitutive law for computational codes. This method is a good way to describe the behaviour of MOX fuel. Transformation Field Analysis (TFA), which corresponds to piecewise uniform transformation fields, is used to perform a sensitivity study. (authors)

  17. A little elastic for a better performance: kinesiotaping of the motor effector modulates neural mechanisms for rhythmic movements.

    Bravi, Riccardo; Quarta, Eros; Cohen, Erez J; Gottard, Anna; Minciacchi, Diego

    2014-01-01

    A rhythmic motor performance is brought about by an integration of timing information with movements. Investigations on the millisecond time scale distinguish two forms of time control, event-based timing and emergent timing. While event-based timing asserts the existence of a central internal timekeeper for the control of repetitive movements, the emergent timing perspective claims that timing emerges from dynamic control of nontemporal movements parameters. We have recently demonstrated that the precision of an isochronous performance, defined as performance of repeated movements having a uniform duration, was insensible to auditory stimuli of various characteristics (Bravi et al., 2014). Such finding has led us to investigate whether the application of an elastic therapeutic tape (Kinesio® Tex taping; KTT) used for treating athletic injuries and a variety of physical disorders, is able to reduce the timing variability of repetitive rhythmic movement. Young healthy subjects, tested with and without KTT, have participated in sessions in which sets of repeated isochronous wrist's flexion-extensions (IWFEs) were performed under various auditory conditions and during their recall. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that the application of KTT decreases the variability of rhythmic movements by a 2-fold effect: on the one hand KTT provides extra proprioceptive information activating cutaneous mechanoreceptors, on the other KTT biases toward the emergent timing thus modulating the processes for rhythmic movements. Therefore, KTT appears able to render movements less audio dependent by relieving, at least partially, the central structures from time control and making available more resources for an augmented performance.

  18. A little elastic for a better performance: kinesiotaping of the motor effector modulates neural mechanisms for rhythmic movements

    Riccardo eBravi

    2014-09-01

    Full Text Available A rhythmic motor performance is brought about by an integration of timing information with movements. Investigations on the millisecond time scale distinguish two forms of time control, event-based timing and emergent timing. While event-based timing asserts the existence of a central internal timekeeper for the control of repetitive movements, the emergent timing perspective claims that timing emerges from dynamic control of nontemporal movements parameters. We have recently demonstrated that the precision of an isochronous performance, defined as performance of repeated movements having a uniform duration, was insensible to auditory stimuli of various characteristics (Bravi et al., 2014. Such finding has led us to investigate whether the application of an elastic therapeutic tape (Kinesio® Tex taping; KTT used for treating athletic injuries and a variety of physical disorders, is able to reduce the timing variability of repetitive rhythmic movement. Young healthy subjects, tested with and without KTT, have participated in sessions in which sets of repeated isochronous wrist's flexion-extensions (IWFEs were performed under various auditory conditions and during their recall. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that the application of KTT decreases the variability of rhythmic movements by a twofold effect: on the one hand KTT provides extra proprioceptive information activating cutaneous mechanoreceptors, on the other KTT biases toward the emergent timing thus modulating the processes for rhythmic movements. Therefore, KTT appears able to render movements less audio dependent by relieving, at least partially, the central structures from time control and making available more resources for an augmented performance.

  19. Elastic scattering

    Leader, Elliot

    1991-01-01

    With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees

  20. A comparative study of iterative solutions to linear systems arising in quantum mechanics

    Jing Yanfei; Huang Tingzhu; Duan Yong; Carpentieri, Bruno

    2010-01-01

    This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

  1. High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

    Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

    2016-01-01

    Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier

  2. High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

    Dumbser, Michael, E-mail: michael.dumbser@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Peshkov, Ilya, E-mail: peshkov@math.nsc.ru [Open and Experimental Center for Heavy Oil, Université de Pau et des Pays de l' Adour, Avenue de l' Université, 64012 Pau (France); Romenski, Evgeniy, E-mail: evrom@math.nsc.ru [Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk (Russian Federation); Zanotti, Olindo, E-mail: olindo.zanotti@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy)

    2016-06-01

    Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier

  3. Geometrically non linear analysis of functionally graded material ...

    user

    when compared to the other engineering materials (Akhavan and Hamed, 2010). However, FGM plates under mechanical loading may undergo elastic instability. Hence, the non-linear behavior of functionally graded plates has to be understood for their optimum design. Reddy (2000) proposed the theoretical formulation ...

  4. Effect of intra-membrane C60 fullerenes on the modulus of elasticity and the mechanical resistance of gel and fluid lipid bilayers

    Zhou, Jihan; Liang, Dehai; Contera, Sonia

    2015-10-01

    Penetration and partition of C60 to the lipid bilayer core are both relevant to C60 toxicity, and useful to realise C60 biomedical potential. A key aspect is the effect of C60 on bilayer mechanical properties. Here, we present an experimental study on the mechanical effect of the incorporation of C60 into the hydrophobic core of fluid and gel phase zwitterionic phosphatidylcholine (PC) lipid bilayers. We demonstrate its incorporation inside the hydrophobic lipid core and the effect on the packing of the lipids and the vesicle size using a combination of infrared (IR) spectroscopy, atomic force microscopy (AFM) and laser light scattering. Using AFM we measured the Young's modulus of elasticity (E) of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) in the absence (presence) of intra-membranous C60 at 24.5 °C. E of fluid phase supported bilayers is not altered by C60, but E increases with incorporation of C60 in gel phase bilayers. The increase is higher for longer hydrocarbon chains: 1.6 times for DPPC and 2 times for DSPC. However the mechanical resistance of gel phase bilayers of curved bilayered structures decreases with the incorporation of C60. Our combined results indicate that C60 causes a decrease in gel phase lipid mobility, i.e. an increase in membrane viscosity.

  5. Stacking Faults and Mechanical Behavior beyond the Elastic Limit of an Imidazole-Based Metal Organic Framework: ZIF-8.

    Hegde, Vinay I; Tan, Jin-Chong; Waghmare, Umesh V; Cheetham, Anthony K

    2013-10-17

    We determine the nonlinear mechanical behavior of a prototypical zeolitic imidazolate framework (ZIF-8) along two modes of mechanical failure in response to tensile and shear forces using first-principles simulations. Our generalized stacking fault energy surface reveals an intrinsic stacking fault of surprisingly low energy comparable to that in copper, though the energy barrier associated with its formation is much higher. The lack of vibrational spectroscopic evidence for such faults in experiments can be explained with the structural instability of the barrier state to form a denser and disordered state of ZIF-8 seen in our analysis, that is, large shear leads to its amorphization rather than formation of faults.

  6. Thermal analysis of linear pulse motor for SMART control element drive mechanism

    Hur, H.; Kim, J. H.; Kim, J. I.; Jang, K. C.; Kang, D. H.

    1999-01-01

    It is important that the temperature of the motor windings be maintained within the allowable limit of the insulation, since the linear pulse motor of CEDM is always supplied with current during the reactor operation. In this study three motor windings were fabricated with three different diameters of coil wires, and the temperatures inside the windings were measured with different current values. As the insulation of the windings is composed of teflon, glass fiber, and air, it is not an easy task to determine experimentally the thermal properties of the complex insulation. In this study, the thermal properties of the insulation were obtained by comparing the results of finite element thermal analyses and those of experiment. The thermal properties obtained here will be used as input for the optimization analysis of the motor

  7. Conductance mechanism in a linear non-conjugated trimethylsilyl-acetylene molecule: tunneling through localized states

    Petrov, E.G.; Marchenko, A.; Kapitanchuk, O.; Katsonis, Nathalie Hélène; Fichou, D.

    2014-01-01

    The conductance properties of 1,3-(trimethylsilyl)-1-tridecene-6,12-diyne, a non-conjugated trimethylsil-acetylene molecule have been investigated both experimentally and theoretically. Based on scanning tunnelling spectroscopy experiments, a discussion on the mechanisms controlling the charge

  8. A variational integrators approach to second order modeling and identification of linear mechanical systems

    Bruschetta, M.; Saccon, A.; Picci, G.

    2014-01-01

    The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in

  9. SIMPLIFIED LAPAROSCOPIC GASTRIC BYPASS WITH GASTROJEJUNAL LINEAR MECHANICAL ANASTOMOSIS: TECHNICAL ASPECTS.

    Palermo, Mariano; Serra, Edgardo

    Gastric bypass is a restrictive and malabsorptive surgery. The restrictive part consists in the creation of a small gastric pouch. The gastrointestinal bypass serves as the malabsorptive element. To describe a simplified gastric bypass approach for morbid obese patients, showing our results, and also remarking the importance of this technique for reducing the learning curve. The patient is positioned in a split legs position and carefully strapped to the operating room table, with the surgeon between the patient's legs. Five trocars are inserted after pneumoperitoneum at the umbilicus. Dissection of the esophagogastric angle and lesser curvature is mandatory before the gastric pouch manufacturing. This pouch is done with two blue load staplers. Using a blue load linear stapler inserted only half way into the hole in the pouch is used to perform the gastrojejunal anastomosis and in order to create an anastomosis that is about 2 cm in length. A side-to-side jejunojejunostomy is done with a white load linear stapler. The last step of the gastric bypass consists in the cut of the jejunum between the two anastomosis with a white load linear stapler. Blue test is performed in order to detect leaks. From January 2012 to December 2015, 415 simplified RYGB were performed. Gender: 67% female and 33 % males. Average of BMI 44.7. Mean age was 42 years old. Mean operative time 79 min. 39 % of this sample had T2 diabetes. Regarding complications were observed, one fistula, one gastrojejunal stenosis and one obstruction due to a bezoar. The described technique is a simplified approach in which all the anastomosis are performed in the upper part of the abdomen, allowing the surgeons to be more systematized and avoiding them to make mistakes in the confection of the Roux-en-Y anastomosis. This simplified gastric bypass is a safe and reproducible technique. Bypass gástrico é cirurgia restritiva e malabsortiva. A parte restritiva consiste na criação de uma pequena bolsa g

  10. Mechanical evaluation of linear friction welds in titanium alloys through indentation experiments

    Corzo, M.; Casals, O.; Alcala, J.; Mateo, A.; Anglada, M.

    2005-01-01

    This article shows the results of a project that focuses on the characterization of the weld interface region of dissimilar joints between titanium alloys for aeronautical applications, specifically Ti-6Al-2Sn-4Zr-6Mo with Ti-6Al-4V, and Ti-6Al-2Sn-4Zr-6Mo with Ti-6Al-2Sn-4Zr-2Mo. The uniaxial flow stress and hardening response of the material containing the weld were analyzed following the finite elements simulations and mathematical formulations to correlate hardness and the amount of pile-up and sinking-in phenomena around sharp indenters with uniaxial mechanical properties. This allows to accurately stablishing the influence that welding process has on the mechanical response of the parts. Tests performed on these friction-welded specimens showed that the fine grained microstructures in the welds exhibited better properties than the base materials. (Author) 12 refs

  11. Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer

    Blavier, Jean-Francois L.; Heverly, Matthew C.; Key, Richard W.; Sander, Stanley P.

    2011-01-01

    A document discusses a mechanism that uses flex-pivots in a parallelogram arrangement to provide frictionless motion with an unlimited lifetime. A voicecoil actuator drives the parallelogram over the required 5-cm travel. An optical position sensor provides feedback for a servo loop that keeps the velocity within 1 percent of expected value. Residual tip/tilt error is compensated for by a piezo actuator that drives the interferometer mirror. This mechanism builds on previous work that targeted ground-based measurements. The main novelty aspects include cryogenic and vacuum operation, high reliability for spaceflight, compactness of the design, optical layout compatible with the needs of an imaging FTS (i.e. wide overall field-of-view), and mirror optical coatings to cover very broad wavelength range (i.e., 0.26 to 15 m).

  12. Elasticity theory of ultrathin nanofilms

    Li, Jiangang; Yun, Guohong; Narsu, B; Yao, Haiyan

    2015-01-01

    A self-consistent theoretical scheme for describing the elastic behavior of ultrathin nanofilms (UTNFs) was proposed. Taking into account the lower symmetry of an UTNF compared to its bulk counterpart, additional elastic and magnetoelastic parameters were introduced to model the elasticity rigorously. The applications of current theory to several elastic and magnetoelastic systems gave excellent agreement with experiments. More importantly, the surface elastic and magnetoelastic parameters used to fit the experimental results are physically reasonable and in close agreement with those obtained from experiment and simulation. This fact suggests that the additional elastic (magnetoelastic) constants due to symmetry breaking are of great importance in theoretical description of the mechanical properties of UTNFs. And we proved that the elasticity of UTNFs should be described by a three-dimensional model just including the intrinsic surface and bulk parameters, but not the effective surface parameters. It is believed that the theory reported here is a universal strategy for elasticity and magnetoelasticity of ultrathin films. (paper)

  13. Mechanisms of force production during linear accelerations in bluegill sunfish Lepomis macrochirus

    Tytell, Eric D.; Wise, Tyler N.; Boden, Alexandra L.; Sanders, Erin K.; Schwalbe, Margot A. B.

    2016-11-01

    In nature, fish rarely swim steadily. Although unsteady behaviors are common, we know little about how fish change their swimming kinematics for routine accelerations, and how these changes affect the fluid dynamic forces and the wake produced. To study force production during acceleration, particle image velocimetry was used to quantify the wake of bluegill sunfish Lepomis macrochirus and to estimate the pressure field during linear accelerations and steady swimming. We separated "steady" and "unsteady" trials and quantified the forward acceleration using inertial measurement units. Compared to steady sequences, unsteady sequences had larger accelerations and higher body amplitudes. The wake consisted of single vortices shed during each tail movement (a '2S' wake). The structure did not change during acceleration, but the circulation of the vortices increased, resulting in larger forces. A fish swimming unsteadily produced significantly more force than the same fish swimming steadily, even when the accelerations were the same. This increase is likely due to increased added mass during unsteady swimming, as a result of the larger body amplitude. Pressure estimates suggest that the increase in force is correlated with more low pressure regions on the anterior body. This work was supported by ARO W911NF-14-1-0494 and NSF RCN-PLS 1062052.

  14. Mechanism of linear and nonlinear optical properties of bis-thiourea cadmium chloride single crystal

    Yang, J.T.; Luo, S.J.; Yi, L.; Laref, A.

    2013-01-01

    Within the generalized gradient approximation (GGA), a calculation of the electronic structure of a semiorganic crystal named bis-thiourea cadmium chloride (BTCC) was performed, then the linear and nonlinear optical responses were obtained over a wide energy range, using a scissor energy of 1.30 eV, and our results are in good agreement with the experiments. The accurate full-potential projected augmented wave (FP-PAW) method was used. The prominent spectrum of the second harmonic generation (SHG) was successfully correlated with the dielectric function in terms of single- and double-photon resonances. Both the virtual electron (VE) and virtual hole (VH) processes make contributions to the SHG of BTCC crystal, and the VH process is enhanced by the Cd-centered tetrahedron. The SHG effect of the semiorganic material is attributed to the charge transfer (CT). The CT model for the semiorganic crystal is named as “M-Π O ⋯X”. “M” is a metal atom providing electrons, “Π O ” is a π-conjugated covalent of an organic molecule, and “X” is a high electronegativity atom. The CT across the BTCC molecule is along a π-electron conjugation covalence bond, and the delocalized electrons of sulfur provide an excellent bridge. The strong “pull” effect for the CT is due to the intramolecular hydrogen bonds provided by the chlorine with the high electron affinity.

  15. Maintenance of working capacity of movement mechanism of load trolley with linear traction electric drive of bridge type crane.

    Goncharov, K. A.; Denisov, I. A.

    2017-10-01

    The article considers the influence of the air gap size between the linear motor elements on the stability of the traction drive of the movement mechanism of the trolley of the bridge type crane. The main factors affecting the air gap size and the causes of their occurrence are described. The technique of calculating the magnitude of air gap variation is described in relation to the general deformation of the crane metal structure. Recommendations on the need for installation of additional equipment for load trolleys of various designs are given. The optimal values of the length of the trolley base are proposed. Observance of these values ensures normal operation of the traction drive.

  16. Proximity-interference wake-induced vibration at subcritical Re: Mechanism analysis using a linear dynamic model

    Li, Xintao; Zhang, Weiwei; Gao, Chuanqiang

    2018-03-01

    Wake-induced vibration (WIV) contains rich and complex phenomena due to the flow interference between cylinders. The aim of the present study is to gain physical insight into the intrinsic dynamics of WIV via linear stability analysis (LSA) of the fluid-structure interaction (FSI) system. A reduced-order-model-based linear dynamic model, combined with the direct computational fluid dynamics/computational structural dynamics simulation method, is adopted to investigate WIV in two identical tandem cylinders at low Re. The spacing ratio L/D, with L as the center-to-center distance and D as the diameter of cylinders, is selected as 2.0 to consider the effect of proximity flow interference. Results show that extensive WIV along with the vortex shedding could occur at subcritical Re conditions due to the instability of one coupled mode (i.e., coupled mode I, CM-I) of the FSI system. The eigenfrequency of CM-I transfers smoothly from close to the reduced natural frequency of structure to the eigenfrequency of uncoupled wake mode as the reduced velocity U* increases. Thus, CM-I characterizes as the structure mode (SM) at low U*, while it characterizes as the wake mode (WM) at large U*. Mode conversion of CM-I is the primary cause of the "frequency transition" phenomenon observed in WIV responses. Furthermore, LSA indicates that there exists a critical mass ratio mcr*, below which no upper instability boundary of CM-I exists (Uup p e r *→∞ ). The unbounded instability of CM-I ultimately leads to the "infinite WIV" phenomenon. The neutral stability boundaries for WIV in the (Re, U*) plane are determined through LSA. It is shown that the lowest Re possible for WIV regarding the present configuration is R el o w e s t≈34 . LSA accurately captures the dynamics of WIV at subcritical Re and reveals that it is essentially a fluid-elastic instability problem. This work lays a good foundation for the investigation of WIV at supercritical high Re and gives enlightenment to the

  17. In vivo areal modulus of elasticity estimation of the human tympanic membrane system: modelling of middle ear mechanical function in normal young and aged ears

    Gaihede, Michael Lyhne; Donghua, Liao; Gregersen, H.

    2007-01-01

    The quasi-static elastic properties of the tympanic membrane system can be described by the areal modulus of elasticity determined by a middle ear model. The response of the tympanic membrane to quasi-static pressure changes is determined by its elastic properties. Several clinical problems are r...... finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2-3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus....

  18. Prediction of high airway pressure using a non-linear autoregressive model of pulmonary mechanics.

    Langdon, Ruby; Docherty, Paul D; Schranz, Christoph; Chase, J Geoffrey

    2017-11-02

    For mechanically ventilated patients with acute respiratory distress syndrome (ARDS), suboptimal PEEP levels can cause ventilator induced lung injury (VILI). In particular, high PEEP and high peak inspiratory pressures (PIP) can cause over distension of alveoli that is associated with VILI. However, PEEP must also be sufficient to maintain recruitment in ARDS lungs. A lung model that accurately and precisely predicts the outcome of an increase in PEEP may allow dangerous high PIP to be avoided, and reduce the incidence of VILI. Sixteen pressure-flow data sets were collected from nine mechanically ventilated ARDs patients that underwent one or more recruitment manoeuvres. A nonlinear autoregressive (NARX) model was identified on one or more adjacent PEEP steps, and extrapolated to predict PIP at 2, 4, and 6 cmH 2 O PEEP horizons. The analysis considered whether the predicted and measured PIP exceeded a threshold of 40 cmH 2 O. A direct comparison of the method was made using the first order model of pulmonary mechanics (FOM(I)). Additionally, a further, more clinically appropriate method for the FOM was tested, in which the FOM was trained on a single PEEP prior to prediction (FOM(II)). The NARX model exhibited very high sensitivity (> 0.96) in all cases, and a high specificity (> 0.88). While both FOM methods had a high specificity (> 0.96), the sensitivity was much lower, with a mean of 0.68 for FOM(I), and 0.82 for FOM(II). Clinically, false negatives are more harmful than false positives, as a high PIP may result in distension and VILI. Thus, the NARX model may be more effective than the FOM in allowing clinicians to reduce the risk of applying a PEEP that results in dangerously high airway pressures.

  19. Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

    Czachor, M.

    1996-01-01

    Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

  20. Phason elasticity and surface roughening

    Tang Leihan; Jaric, M.V.

    1990-01-01

    The phason elasticity of two-dimensional (2D) equilibrium quasicrystals is discussed in analogy with surface roughening phenomena. Taking a Penrose tiling model as an example, we show that the phason elastic energy is linear in the phason strain at zero temperature (T = 0), but becomes quadratic at any T > 0 and sufficiently small strain. Heuristic and real-space renormalization group arguments are given for the thermal roughening of the hyper-surface which represents quasicrystal tiling. Monte Carlo method is applied to illustrate the logarithmically diverging phason fluctuations and power-law diffraction intensities at T > 0. For three-dimensional systems, we present arguments which suggest a finite temperature transition between two quasicrystal phases, characterized by linear and quadratic phason elastic energy, respectively. (author). 17 refs, 12 figs

  1. Nanostructured Ti-Zr-Pd-Si-(Nb) bulk metallic composites: Novel biocompatible materials with superior mechanical strength and elastic recovery.

    Hynowska, A; Blanquer, A; Pellicer, E; Fornell, J; Suriñach, S; Baró, M D; Gebert, A; Calin, M; Eckert, J; Nogués, C; Ibáñez, E; Barrios, L; Sort, J

    2015-11-01

    The microstructure, mechanical behaviour, and biocompatibility (cell culture, morphology, and cell adhesion) of nanostructured Ti45 Zr15 Pd35- x Si5 Nbx with x = 0, 5 (at. %) alloys, synthesized by arc melting and subsequent Cu mould suction casting, in the form of rods with 3 mm in diameter, are investigated. Both Ti-Zr-Pd-Si-(Nb) materials show a multi-phase (composite-like) microstructure. The main phase is cubic β-Ti phase (Im3m) but hexagonal α-Ti (P63/mmc), cubic TiPd (Pm3m), cubic PdZr (Fm3m), and hexagonal (Ti, Zr)5 Si3 (P63/mmc) phases are also present. Nanoindentation experiments show that the Ti45 Zr15 Pd30 Si5 Nb5 sample exhibits lower Young's modulus than Ti45 Zr15 Pd35 Si5 . Conversely, Ti45 Zr15 Pd35 Si5 is mechanically harder. Actually, both alloys exhibit larger values of hardness when compared with commercial Ti-40Nb, (HTi-Zr-Pd-Si ≈ 14 GPa, HTi-Zr-Pd-Si-Nb ≈ 10 GPa and HTi-40Nb ≈ 2.7 GPa). Concerning the biological behaviour, preliminary results of cell viability performed on several Ti-Zr-Pd-Si-(Nb) discs indicate that the number of live cells is superior to 94% in both cases. The studied Ti-Zr-Pd-Si-(Nb) bulk metallic system is thus interesting for biomedical applications because of the outstanding mechanical properties (relatively low Young's modulus combined with large hardness), together with the excellent biocompatibility. © 2014 Wiley Periodicals, Inc.

  2. The visco-elastic multilayer program VEROAD

    Hopman, P.C.

    1996-01-01

    The mathematical principles and derivation of a linear visco-elastic multilayer computer program are described. The mathematical derivation is based on Fourier Transformation. The program is called VEROAD, which is an acronym for Visco-Elastic ROad Analysis Delft. The program allows calculation of

  3. A Formalism for the Consistent Description of Non-Linear Elasticity of Anisotropic Media Formalisme pour une description cohérente de l'élasticité non linéaire des milieux anisotropes

    Helbig K.

    2006-12-01

    Full Text Available The propagation of elastic waves is generally treated under four assumptions: - that the medium is isotropic,- that the medium is homogeneous, - that there is a one-to-one relationship between stress and strain, - that stresses are linearly related to strains (equivalently, that strains are linearly related to stresses. Real media generally violate at least some-and often all-of these assumptions. A valid theoretical description of wave propagation in real media thus depends on the qualitative and quantitative description of the relevant inhomogeneity, anisotropy, and non-linearity: one either has to assume (or show that the deviation from the assumption can - for the problem at hand - be neglected, or develop a theoretical description that is valid even under the deviation. While the effect of a single deviation from the ideal state is rather well understood, difficulties arise in the combination of several such deviations. Non-linear elasticity of anisotropic (triclinic rock samples has been reported, e. g. by P. Rasolofosaon and H. Yin at the 6th IWSA in Trondheim (Rasolofosaon and Yin, 1996. Non-linear anisotropic elasticity matters only for non-infinitesimalamplitudes, i. e. , at least in the vicinity of the source. How large this vicinity is depends on the accuracy of observation and interpretation one tries to maintain, on the source intensity, and on the level of non-linearity. This paper is concerned with the last aspect, i. e. , with the meaning of the numbers beyond the fact that they are the results of measurements. As a measure of the non-linearity of the material, one can use the strain level at which the effective stiffness tensor deviates significantly from the zero-strain stiffness tensor. Particularly useful for this evaluation is the eigensystem (six eigenstiffnesses and six eigenstrains of the stiffness tensor : the eigenstrains provide suitable strain typesfor the calculation of the effective stiffness tensor, and the

  4. Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

    Gelebart, Lionel; Mondon-Cancel, Romain

    2013-01-01

    FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)

  5. Statistical Mechanics of the Human Placenta: A Stationary State of a Near-Equilibrium System in a Linear Regime.

    Lecarpentier, Yves; Claes, Victor; Hébert, Jean-Louis; Krokidis, Xénophon; Blanc, François-Xavier; Michel, Francine; Timbely, Oumar

    2015-01-01

    All near-equilibrium systems under linear regime evolve to stationary states in which there is constant entropy production rate. In an open chemical system that exchanges matter and energy with the exterior, we can identify both the energy and entropy flows associated with the exchange of matter and energy. This can be achieved by applying statistical mechanics (SM), which links the microscopic properties of a system to its bulk properties. In the case of contractile tissues such as human placenta, Huxley's equations offer a phenomenological formalism for applying SM. SM was investigated in human placental stem villi (PSV) (n = 40). PSV were stimulated by means of KCl exposure (n = 20) and tetanic electrical stimulation (n = 20). This made it possible to determine statistical entropy (S), internal energy (E), affinity (A), thermodynamic force (A / T) (T: temperature), thermodynamic flow (v) and entropy production rate (A / T x v). We found that PSV operated near equilibrium, i.e., A ≺≺ 2500 J/mol and in a stationary linear regime, i.e., (A / T) varied linearly with v. As v was dramatically low, entropy production rate which quantified irreversibility of chemical processes appeared to be the lowest ever observed in any contractile system.

  6. Two-Sided Estimates of Thermo-elastic Characteristics of Dispersed Inclusion Composites

    V. S. Zarubin

    2015-01-01

    Full Text Available The composites, dispersion-reinforced with inclusions from high-strength and high-modulus materials are widely used in technology. Nanostructure elements can perform the role of such inclusions as well. Possible applications of such composites in heat-stressed structures under heavy mechanical and thermal influences significantly depend on a complex of thermo-mechanical characteristics including the values of the moduli of elasticity and coefficient of linear thermal expansion. There are different approaches to construction of mathematical models that allow calculating dependences to estimate elastic characteristics of composites. Relation between thermoelastic properties of matrix and inclusions of the composite with its temperature coefficient of linear expansion is studied in less detail. Thus, attention has been insufficient in estimating a degree of reliability and a possible error of derived dependencies.A dual variation formulation of the problem of thermo-elasticity in a non-uniform solids simulating the properties and structure of the composite with dispersed inclusions, makes it possible to define two-sided limits of possible values of the volume elasticity modulus, shear modulus, and coefficient of linear thermal expansion of such composite. These limits allow us to estimate the maximum possible error, if to take a half-sum of the limit values of these parameters as the thermoelastic characteristics of the composite. Implementing this approach to find possible errors, arising when using one or another calculating dependency, improves reliability of predicted thermo-elastic characteristics as applied to existing and promising composites.

  7. The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

    der, R.

    1987-01-01

    The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transformwidetilde{C}(z)) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z=∞ and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover,widetilde{C}(z) may be expressed by a Laurent series expansion in positive and negative powers of z, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions ofwidetilde{C}(z) as obtained from the application of conventional many-body techniques to the calculation

  8. Extended Kalman filtering for the detection of damage in linear mechanical structures

    Liu, X.; Escamilla-Ambrosio, P. J.; Lieven, N. A. J.

    2009-09-01

    This paper addresses the problem of assessing the location and extent of damage in a vibrating structure by means of vibration measurements. Frequency domain identification methods (e.g. finite element model updating) have been widely used in this area while time domain methods such as the extended Kalman filter (EKF) method, are more sparsely represented. The difficulty of applying EKF in mechanical system damage identification and localisation lies in: the high computational cost, the dependence of estimation results on the initial estimation error covariance matrix P(0), the initial value of parameters to be estimated, and on the statistics of measurement noise R and process noise Q. To resolve these problems in the EKF, a multiple model adaptive estimator consisting of a bank of EKF in modal domain was designed, each filter in the bank is based on different P(0). The algorithm was iterated by using the weighted global iteration method. A fuzzy logic model was incorporated in each filter to estimate the variance of the measurement noise R. The application of the method is illustrated by simulated and real examples.

  9. Compact very low temperature scanning tunneling microscope with mechanically driven horizontal linear positioning stage.

    Suderow, H; Guillamon, I; Vieira, S

    2011-03-01

    We describe a scanning tunneling microscope for operation in a dilution refrigerator with a sample stage which can be moved macroscopically in a range up to a cm and with an accuracy down to the tens of nm. The position of the tip over the sample as set at room temperature does not change more than a few micrometers when cooling down. This feature is particularly interesting for work on micrometer sized samples. Nanostructures can be also localized and studied, provided they are repeated over micrometer sized areas. The same stage can be used to approach a hard single crystalline sample to a knife and cleave it, or break it, in situ. In situ positioning is demonstrated with measurements at 0.1 K in nanofabricated samples. Atomic resolution down to 0.1 K and in magnetic fields of 8 T is demonstrated in NbSe(2). No heat dissipation nor an increase in mechanical noise has been observed at 0.1 K when operating the slider.

  10. Non-linear finite element analyses of wide plate fracture mechanics experiments

    Harrop, L.P.; Gibson, S.

    1988-06-01

    A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)

  11. Nonlinear Elasticity

    Fu, Y. B.; Ogden, R. W.

    2001-05-01

    This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

  12. Influence of Coherent Tunneling and Incoherent Hopping on the Charge Transfer Mechanism in Linear Donor-Bridge-Acceptor Systems.

    Li, Guangqi; Govind, Niranjan; Ratner, Mark A; Cramer, Christopher J; Gagliardi, Laura

    2015-12-17

    The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.

  13. CASTEM: a system of finite element computer programs for elastic and inelastic analysis of mechanical structures of reactors

    Hoffmann, A.; Livolant, M.; Roche, R.

    1978-01-01

    The nuclear research center at Saclay has developed the system of computer program CASTEM for the analysis of mechanical structures of reactors. This finite element system is designed specially to deal with nonlinear problems concerning both the material (plasticity, thermoplasticity, creep) and the geometry (nonlinear relationships between displacement and strain, buckling). Furthermore, a special effort has been devoted to the processing of dynamic problems (vibrations, natural modes, earthquakes, shock phenomena, etc..). The CASTEM system includes a large number of elementary modules corresponding to a total of over 80,000 Fortran instructions. Allowing the calculation of various structural geometries, including: axisymmetrical shells and liquids (with non axisymmetrical loading); pipes and frames; two-dimensional massive structures; three-dimensional shells; three-dimensional massive structures. Complex dynamic analysis can be made by combination of substructures natural mode shapes. Pre and post processors: automatic meshing, plotting of results, direct comparison of stresses to ASME limits make the use of the system easy and time saving

  14. Biaxial analysis of synthetic scaffolds for hernia repair demonstrates variability in mechanical anisotropy, non-linearity and hysteresis.

    Deeken, Corey R; Thompson, Dominic M; Castile, Ryan M; Lake, Spencer P

    2014-10-01

    Over the past 60 years, the soft tissue repair market has grown to include over 50 types of hernia repair materials. Surgeons typically implant these materials in the orientation that provides maximum overlap of the mesh over the defect, with little regard for mechanical properties of the mesh material. If the characteristics of the meshes were better understood, an appropriate material could be identified for each patient, and meshes could be placed to optimize integration with neighboring tissue and avoid the mechanical mis-match that can lead to impaired graft fixation. The purpose of this study was to fully characterize and compare the mechanical properties of thirteen types of hernia repair materials via planar biaxial tensile testing. Equibiaxial (i.e., equal simultaneous loading in both directions) and strip biaxial (i.e., loading in one direction with the other direction held fixed) tests were utilized as physiologically relevant loading regimes. After applying a 0.1N pre-load on each arm, samples were subjected to equibiaxial cyclic loading using a triangular waveform to 2.5mm displacement on each arm at 0.1Hz for 10 cycles. Samples were then subjected to two strip biaxial tests (using the same cyclic loading protocol), where extension was applied along a single axis with the other axis held fixed. The thirteen evaluated mesh types exhibited a wide range of mechanical properties. Some were nearly isotropic (C-QUR™, DUALMESH(®), PHYSIOMESH™, and PROCEED(®)), while others were highly anisotropic (Ventralight™ ST, Bard™ Mesh, and Bard™ Soft Mesh). Some displayed nearly linear behavior (Bard™ Mesh), while others were non-linear with a long toe region followed by a sharp rise in tension (INFINIT(®)). These materials are currently utilized in clinical settings as if they are uniform and interchangeable, and clearly this is not the case. The mechanical properties most advantageous for successful hernia repairs are currently only vaguely described

  15. Inverse problemfor an inhomogeneous elastic beam at a combined strength

    Andreev Vladimir Igorevich

    2014-01-01

    Full Text Available In the article the authors describe a method of optimizing the stress state of an elastic beam, subject to the simultaneous action of the central concentrated force and bending moment. The optimization method is based on solving the inverse problem of the strength of materials, consisting in defining the law of changing in elasticity modulus with beam cross-section altitude. With this changing the stress state will be preset. Most problems of the elasticity theory of inhomogeneous bodies are solved in direct formulation, the essence of which is to determine the stress-strain state of a body at the known dependences of the material elastic characteristics from the coordinates. There are also some solutions of the inverse problems of the elasticity theory, in which the dependences of the mechanical characteristics from the coordinates, at which the stress state of a body is preset, are determined. In the paper the authors solve the problem of finding a dependence modulus of elasticity, where the stresses will be constant over the beam’s cross section. We will solve the problem of combined strength (in the case of the central stretching and bending. We will use an iterative method. As the initial solution, we take the solution for a homogeneous material. As the first approximation, we consider the stress state of a beam, when the modulus of elasticity varies linearly. According to the results, it can be stated that three approximations are sufficient in the considered problem. The obtained results allow us to use them in assessing the strength of a beam and its optimization.

  16. Structural–mechanical and antibacterial properties of a soft elastic polyurethane surface after plasma immersion N{sub 2}{sup +} implantation

    Morozov, Ilya A., E-mail: ilya.morozov@gmail.com [Institute of Continuous Media Mechanics UB RAS, Academika Koroleva st. 1, 614013 Perm (Russian Federation); Perm State University, Bukireva st. 15, 614990 Perm (Russian Federation); Mamaev, Alexander S. [Institute of Electrophysics UD RAS, Amundsen st. 106, 620016 Ekaterinburg (Russian Federation); Osorgina, Irina V. [Perm State University, Bukireva st. 15, 614990 Perm (Russian Federation); Lemkina, Larisa M. [Institute of Ecology and Genetics of Microorganisms UB RAS, Golev st. 13, 614081 Perm (Russian Federation); Korobov, Vladimir P. [Institute of Ecology and Genetics of Microorganisms UB RAS, Golev st. 13, 614081 Perm (Russian Federation); Perm National Research Polytechnic University, Komsomolsky av. 29, 614990 Perm (Russian Federation); Belyaev, Anton Yu [Institute of Continuous Media Mechanics UB RAS, Academika Koroleva st. 1, 614013 Perm (Russian Federation); Porozova, Svetlana E. [Perm National Research Polytechnic University, Komsomolsky av. 29, 614990 Perm (Russian Federation); Sherban, Marina G. [Perm State University, Bukireva st. 15, 614990 Perm (Russian Federation)

    2016-05-01

    The surface of elastic polyurethane treated by plasma immersion N{sub 2}{sup +} ion implantation at different fluences has been investigated. A folded surface structure is observed in all cases. Analysis has been performed to study the structural (roughness, steepness and fraction of folds, fractal characteristics), mechanical (stiffness, adhesion force between the AFM probe and the material) and wetting properties of surfaces. Under uniaxial stretching the cracks orthogonal to the axis of deformation and longitudinal folds are formed on the examined surfaces. After unloading the initial structure of the surface of deformed materials exposed to low fluences becomes smoother and does not recover, i.e. it has plastic properties. By contrast, the structure of the surfaces of materials subjected to high-fluence treatment recovers without visible changes and the cracks are fully closed. The study of Staphylococcus colonies grown on these materials has demonstrated significant reduction (from 3 to 5 times) in the vitality of bacteria on treated surfaces. This result was repeated on samples after 11 months of storage. Such antibacterial properties are primarily related to the structural changes of the surfaces accompanied by the increased hydrophilicity. - Highlights: • Surface of soft polyurethane after plasma immersion ion implantation was studied. • Treated surfaces have fluence dependent plicated fractal structure. • Surface properties were investigated both in undeformed and stretched states. • Vitality of bacteria on treated surfaces demonstrated significant reduction.

  17. Nanoindentation Analysis of Elastic/Mechanical Behaviour of Surface of Transparent Glass Ceramics with Fresnoite Ba2TiSi2O8 Nanocrystals

    Shinozaki, K; Honma, T; Komatsu, T

    2011-01-01

    Transparent glass-ceramics containing Ba 2 TiSi 2 O 8 (BTS) nanocrystals with sizes of ∼200 nm were obtained by heat treatment of 40BaO-20TiO 2 -40SiO 2 glass. Their elastic/mechanical properties were evaluated using the cube-resonance method and the Berkovich nanoindentation technique under standard and 'continuous stiffness measurement' (CSM) modes, and the relation between these properties and the volume fraction (f) of BTS nanocrystals was clarified. The glass-ceramics were obtained by 1-h heat treatments at 760-790 deg. C of the precursor glass, resulting in the formation of BTS nanocrystals with f=2.7-54.5%, with a corresponding Young's modulus of 84-107 GPa. The CSM nanoindentation measurements gave an indentation modulus of 90 GPa for the glass and 110 GPa for the glass-ceramic heat-treated at 790 deg. C, for indentation depths of 200-1500 nm. The results suggest that the BTS nanocrystals confer a high resistance to deformation during indenter loading.

  18. A proposal for evaluation method of crack growth due to cyclic overload for piping materials based on an elastic-plastic fracture mechanics parameter

    Yamaguchi, Yoshihito; Katsuyama, Jinya; Onizawa, Kunio; Li, Yinsheng; Sugino, Hideharu

    2011-01-01

    The magnitude of Niigata-ken Chuetsu-Oki earthquake in 2007 was beyond the assumed one provided in seismic design. Therefore it becomes an important issue to evaluate the crack growth behaviors due to the cyclic overload like large earthquake. Fatigue crack growth is usually evaluated by Paris's law using the range of stress intensity factor (ΔK). However, ΔK is inappropriate in a loading condition beyond small scale yielding. In this study, the crack growth behaviors for piping materials were investigated based on an elastic-plastic fracture mechanics parameter, J-integral. It was indicated that the crack growth due to the cyclic overload beyond small scale yielding could be the sum of fatigue and ductile crack growth. The retardation effect of excessive loading on the crack growth was observed after the loading. The modified Wheeler model using J-integral has been proposed for the prediction of retardation effect. Finally, an evaluation method for crack growth behaviors due to the cyclic overload is suggested. (author)

  19. How tall can gelatin towers be? An introduction to elasticity and buckling

    Taberlet, Nicolas; Ferrand, Jérémy; Camus, Élise; Lachaud, Léa; Plihon, Nicolas

    2017-12-01

    The stability of elastic towers is studied through simple hands-on experiments. Using gelatin-based stackable bricks, one can investigate the maximum height a simple structure can reach before collapsing. We show through experiments and by using the classical linear elastic theory that the main limitation to the height of such towers is the buckling of the elastic structures under their own weight. Moreover, the design and architecture of the towers can be optimized to greatly improve their resistance to self-buckling. To this aim, the maximum height of hollow and tapered towers is investigated. The experimental and theoretical developments presented in this paper can help students grasp the fundamental concepts in elasticity and mechanical stability.

  20. Elastic properties of spherically anisotropic piezoelectric composites

    En-Bo, Wei; Guo-Qing, Gu; Ying-Ming, Poon

    2010-01-01

    Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed. (condensed matter: structure, thermal and mechanical properties)

  1. Computational Elastic Knots

    Zhao, Xin

    2013-01-01

    Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects

  2. Enhanced mechanical properties of linear segmented shape memory poly(urethane-urea) by incorporating flexible PEG400 and rigid piperazine

    Zhang, Xiao-Yan; Ma, Yu-Fei; Li, Yong-Gang; Wang, Pin-Pin; Wang, Yuan-Liang; Luo, Yan-Feng

    2012-12-01

    The goal of this study is to design and synthesize a linear segmented shape memory poly(urethane-urea) (SMPUU) that possesses near-body-temperature shape memory temperature ( T tran) and enhanced mechanical properties by incorporating flexible poly(ethylene glycol) 400 (PEG400) to form poly(D,L-lactic acid)-based macrodiols (PDLLA-PEG400-PDLLA) and then rigid piperazine (PPZ) as a chain extender to form the desired SMPUUs (PEG400-PUU-PPZ). PEG400 increased M n while maintaining a lower T g of PDLLA-PEG400-PDLLA, which together with PPZ improved the mechanical properties of PEG400-PUU-PPZ. The obtained optimum SMPUU with enhanced mechanical properties ( σ y = 24.28 MPa; ɛ f = 698%; U f = 181.5 MJ/m3) and a T g of 40.62°C exhibited sound shape memory properties as well, suggesting a promising SMPUU for in vivo biomedical applications.

  3. Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating.

    Zhou, Yu; Pearson, John E; Auerbach, Anthony

    2005-12-01

    We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.

  4. Thermodynamic analysis of mechanical behaviour in the elastic region of blends of recycled poly (ethylene terephthalate) and recycled polyolefins; Analise termodinamica do comportamento mecanico na regiao elastica de blendas de poli (tereftalato de etileno) reciclado e poliolefinas recicladas

    Marconcini, Jose M. [Universidade Federal do Parana Univ. (UFPR), Curitiba, PR (Brazil). Inst. de Tecnologia para o Desenvolvimento; Ruvolo Filho, Adhemar [Universidade Federal de Sao Carlos (UFSCar), SP (Brazil). Dept. de Quimica]. E-mail: adhemar@power.ufscar.br

    2006-10-15

    This work describes the study using mechanical tests with the blend of recycled poly(ethylene terephthalate) (PET) and recycled polyolefin with and without the addition of polypropylene grafted with maleic anhydride and poly(ethylene-co-octene-1). A thermodynamic approach based on the Helmholtz work function was applied in the analysis of mechanical tests, correlating the effects of energy storage and from the compatibilizer on the elastic region of the materials. For the system studied, the polyolefin-rich region shows higher storage of elastic energy corroborating the morphology images obtained from SEM analysis. The thermodynamic analysis seems a useful tool to evaluate the compatibilizer effect in polymeric immiscible blends. In this work, more specifically, this method was used to analyze the mechanical behavior of different compositions of recycled polymeric commodity materials. (author)

  5. Study of the electronics architecture for the mechanical stabilisation of the quadrupoles of the CLIC linear accelerator

    Artoos, K; Fernandez Carmona, P; Guinchard, M; Hauviller, C; Janssens, S; Kuzmin, A; Slaathaug, A

    2010-01-01

    To reach a sufficient luminosity, the transverse beam sizes and emittances in future linear particle accelerators should be reduced to the nanometer level. Mechanical stabilisation of the quadrupole magnets is of the utmost importance for this. The piezo actuators used for this purpose can also be used to make fast incremental orientation adjustments with a nanometer resolution. The main requirements for the CLIC stabilisation electronics is a robust, low noise, low delay, high accuracy and resolution, low band and radiation resistant feedback control loop. Due to the high number of controllers (about 4000) a cost optimization should also be made. Different architectures are evaluated for a magnet stabilisation prototype, including the sensors type and configuration, partition between software and hardware for control algorithms, and optimization of the ADC/DAC converters. The controllers will be distributed along the 50 km long accelerator and a communication bus should allow external control. Furthermore, o...

  6. Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

    Hanks, Brantley R.; Skelton, Robert E.

    1991-01-01

    This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

  7. In Situ elastic property sensors

    Olness, D.; Hirschfeld, T.; Kishiyama, K.; Steinhaus, R.

    1987-01-01

    Elasticity is an important property of many materials. Loss of elasticity can have serious consequences, such as when a gasket deteriorates and permits leakage of an expensive or hazardous material, or when a damping system begins to go awry. Loss of elasticity can also provide information related to an ancillary activity such as degradation of electrical insulation, loss of plasticizer in a plastic, or changes in permeability of a thin film. In fact, the mechanical properties of most organic compounds are altered when the compound degrades. Thus, a sensor for the mechanical properties can be used to monitor associated characteristics as well. A piezoelectric material in contact with an elastomer forms an oscillating system that can provide real-time elasticity monitoring. This combination constitutes a forced harmonic oscillator with damping provided by the elastomer. A ceramic oscillator with a total volume of a few mm 3 was used as an elasticity sensor. It was placed in intimate contact with an elastomer and then monitored remotely with a simple oscillator circuit and standard frequency counting electronics. Resonant frequency shifts and changes in Q value were observed corresponding to changes in ambient temperature and/or changes in pressure applied to the sample. Elastomer samples pretreated with ozone (to simulate aging) showed changes in Q value and frequency response, even though there were no visible changes in the elastic samples

  8. The stability of mechanical calibration for a kV cone beam computed tomography system integrated with linear accelerator

    Sharpe, Michael B.; Moseley, Douglas J.; Purdie, Thomas G.

    2006-01-01

    The geometric accuracy and precision of an image-guided treatment system were assessed. Image guidance is performed using an x-ray volume imaging (XVI) system integrated with a linear accelerator and treatment planning system. Using an amorphous silicon detector and x-ray tube, volumetric computed tomography images are reconstructed from kilovoltage radiographs by filtered backprojection. Image fusion and assessment of geometric targeting are supported by the treatment planning system. To assess the limiting accuracy and precision of image-guided treatment delivery, a rigid spherical target embedded in an opaque phantom was subjected to 21 treatment sessions over a three-month period. For each session, a volumetric data set was acquired and loaded directly into an active treatment planning session. Image fusion was used to ascertain the couch correction required to position the target at the prescribed iso-center. Corrections were validated independently using megavoltage electronic portal imaging to record the target position with respect to symmetric treatment beam apertures. An initial calibration cycle followed by repeated image-guidance sessions demonstrated the XVI system could be used to relocate an unambiguous object to within less than 1 mm of the prescribed location. Treatment could then proceed within the mechanical accuracy and precision of the delivery system. The calibration procedure maintained excellent spatial resolution and delivery precision over the duration of this study, while the linear accelerator was in routine clinical use. Based on these results, the mechanical accuracy and precision of the system are ideal for supporting high-precision localization and treatment of soft-tissue targets

  9. Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

    Namani, R.; Feng, Y.; Okamoto, R. J.; Jesuraj, N.; Sakiyama-Elbert, S. E.; Genin, G. M.; Bayly, P. V.

    2012-01-01

    The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isot...

  10. Fracture mechanics model of fragmentation

    Glenn, L.A.; Gommerstadt, B.Y.; Chudnovsky, A.

    1986-01-01

    A model of the fragmentation process is developed, based on the theory of linear elastic fracture mechanics, which predicts the average fragment size as a function of strain rate and material properties. This approach permits a unification of previous results, yielding Griffith's solution in the low-strain-rate limit and Grady's solution at high strain rates

  11. Theoretical study of the elasticity, mechanical behavior, electronic structure, interatomic bonding, and dielectric function of an intergranular glassy film model in prismatic β-Si3N4

    Ching, W. Y.; Rulis, Paul; Aryal, Sitaram; Ouyang, Lizhi; Misra, Anil

    2010-01-01

    Microstructures such as intergranular glassy films (IGFs) are ubiquitous in many structural ceramics. They control many of the important physical properties of polycrystalline ceramics and can be influenced during processing to modify the performance of devices that contain them. In recent years, there has been intense research, both experimentally and computationally, on the structure and properties of IGFs. Unlike grain boundaries or dislocations with well-defined crystalline planes, the atomic scale structure of IGFs, their fundamental electronic interactions, and their bonding characteristics are far more complicated and not well known. In this paper, we present the results of theoretical simulations using ab initio methods on an IGF model in β-Si 3 N 4 with prismatic crystalline planes. The 907-atom model has a dimension of 14.533 A x 15.225 A x 47.420 A . The IGF layer is perpendicular to the z axis, 16.4 A wide, and contains 72 Si, 32 N, and 124 O atoms. Based on this model, the mechanical and elastic properties, the electronic structure, the interatomic bonding, the localization of defective states, the distribution of electrostatic potential, and the optical dielectric function are evaluated and compared with crystalline β-Si 3 N 4 . We have also performed a theoretical tensile experiment on this model by incrementally extending the structure in the direction perpendicular to the IGF plane until the model fully separated. It is shown that fracture occurs at a strain of 9.42% with a maximum stress of 13.9 GPa. The fractured segments show plastic behavior and the formation of surfacial films on the β-Si 3 N 4 . These results are very different from those of a previously studied basal plane model [J. Chen et al., Phys. Rev. Lett. 95, 256103 (2005)] and add insights to the structure and behavior of IGFs in polycrystalline ceramics. The implications of these results and the need for further investigations are discussed.

  12. Elastic and viscoplastic properties

    Lebensohn, R.A.

    2015-01-01

    In this chapter, we review crystal elasticity and plasticity-based self-consistent theories and apply them to the determination of the effective response of polycrystalline aggregates. These mean-field formulations, which enable the prediction of the mechanical behaviour of polycrystalline aggregates based on the heterogeneous and/or directional properties of their constituent single crystal grains and phases, are ideal tools to establish relationships between microstructure and properties of these materials, ubiquitous among fuels and structural materials for nuclear systems. (author)

  13. Computational Elastic Knots

    Zhao, Xin

    2013-05-01

    Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.

  14. Elastic metamaterial beam with remotely tunable stiffness

    Qian, Wei [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Yu, Zhengyue [School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Wang, Xiaole [School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Lai, Yun [College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Yellen, Benjamin B., E-mail: yellen@duke.edu [University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Mechanical Engineering and Materials Science, Duke University, P.O. Box 90300, Hudson Hall, Durham, North Carolina 27708 (United States)

    2016-02-07

    We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ∼30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

  15. Elastic metamaterial beam with remotely tunable stiffness

    Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.

    2016-02-01

    We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

  16. Elastic-plastic transition: A universal law

    Chen Zhong

    2016-01-01

    Full Text Available Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following: 1.There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2.Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3.Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.

  17. Wave chaos in acoustics and elasticity

    Tanner, Gregor; Soendergaard, Niels

    2007-01-01

    Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics-both experimentally and from a theoretical/numerical point of view. (topical review)

  18. A Membrane Model from Implicit Elasticity Theory

    Freed, A. D.; Liao, J.; Einstein, D. R.

    2014-01-01

    A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079

  19. In vivo areal modulus of elasticity estimation of the human tympanic membrane system: modelling of middle ear mechanical function in normal young and aged ears

    Gaihede, Michael; Liao Donghua; Gregersen, Hans

    2007-01-01

    The quasi-static elastic properties of the tympanic membrane system can be described by the areal modulus of elasticity determined by a middle ear model. The response of the tympanic membrane to quasi-static pressure changes is determined by its elastic properties. Several clinical problems are related to these, but studies are few and mostly not comparable. The elastic properties of membranes can be described by the areal modulus, and these may also be susceptible to age-related changes reflected by changes in the areal modulus. The areal modulus is determined by the relationship between membrane tension and change of the surface area relative to the undeformed surface area. A middle ear model determined the tension-strain relationship in vivo based on data from experimental pressure-volume deformations of the human tympanic membrane system. The areal modulus was determined in both a younger (n = 10) and an older (n = 10) group of normal subjects. The areal modulus for lateral and medial displacement of the tympanic membrane system was smaller in the older group (mean = 0.686 and 0.828 kN m -1 , respectively) compared to the younger group (mean = 1.066 and 1.206 kN m -1 , respectively), though not significantly (2p = 0.10 and 0.11, respectively). Based on the model the areal modulus was established describing the summated elastic properties of the tympanic membrane system. Future model improvements include exact determination of the tympanic membrane area accounting for its shape via 3D finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2-3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus

  20. In vivo areal modulus of elasticity estimation of the human tympanic membrane system: modelling of middle ear mechanical function in normal young and aged ears

    Gaihede, Michael [Department of Otolaryngology, Head and Neck Surgery, Aalborg Hospital, Aarhus University Hospital, Aalborg (Denmark); Liao Donghua [Centre of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, Aarhus University Hospital, Aalborg (Denmark); Gregersen, Hans [Centre of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, Aarhus University Hospital, Aalborg (Denmark)

    2007-02-07

    The quasi-static elastic properties of the tympanic membrane system can be described by the areal modulus of elasticity determined by a middle ear model. The response of the tympanic membrane to quasi-static pressure changes is determined by its elastic properties. Several clinical problems are related to these, but studies are few and mostly not comparable. The elastic properties of membranes can be described by the areal modulus, and these may also be susceptible to age-related changes reflected by changes in the areal modulus. The areal modulus is determined by the relationship between membrane tension and change of the surface area relative to the undeformed surface area. A middle ear model determined the tension-strain relationship in vivo based on data from experimental pressure-volume deformations of the human tympanic membrane system. The areal modulus was determined in both a younger (n = 10) and an older (n = 10) group of normal subjects. The areal modulus for lateral and medial displacement of the tympanic membrane system was smaller in the older group (mean = 0.686 and 0.828 kN m{sup -1}, respectively) compared to the younger group (mean = 1.066 and 1.206 kN m{sup -1}, respectively), though not significantly (2p = 0.10 and 0.11, respectively). Based on the model the areal modulus was established describing the summated elastic properties of the tympanic membrane system. Future model improvements include exact determination of the tympanic membrane area accounting for its shape via 3D finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2-3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus.

  1. Morphological and mechanical properties of polyamide 6/linear low density polyethylene blend compatibilized by electron-beam initiated mediation process

    Shin, Boo Young; Han, Do Hung

    2014-01-01

    The aim of this study was to compatibilize immiscible polyamide 6 (PA6)/linear low density polyethylene (LLDPE) blend by using electron-beam initiated mediation process. Glycidyl methacrylate (GMA) was chosen as a mediator for cross-copolymerization at the interface between PA6 and LLDPE. The exposure process was carried out to initiate cross-copolymerization by the medium of GMA at the interface between PA and LLDPE. The mixture of the PA6/LLDPE/GMA was prepared by using a twin-screw extruder, and then the mixture was exposed to electron-beam radiation at various doses at room temperature. To investigate the results of this compatibilization strategy, the morphological and mechanical properties of the blend were analyzed. Morphology study revealed that the diameters of the dispersion particles decreased and the interfacial adhesion increased with respect to irradiation doses. The elongation at break of the blends increases significantly with increasing irradiation dose up to 100 kGy while the tensile strength and the modulus increased nonlinearly with increasing irradiation dose. The reaction mechanisms of the mediation process with the GMA mediator at the interface between PA6 and LLDPE were estimated. - Highlights: • PA6/LLDPE blend was compatibilized by the electron-beam initiated mediation process. • Interfacial adhesion was significantly enhanced by the radiation initiated cross-copolymerization. • The elongation at break of blend irradiated at 100 kGy was 4 times higher than PA6. • The GMA as a mediator played a key role in the electron-beam initiated mediation process

  2. Mechanical and thermal properties of biocomposites from nonwoven industrial Fique fiber mats with Epoxy Resin and Linear Low Density Polyethylene

    Miguel A. Hidalgo-Salazar

    2018-03-01

    Full Text Available In this work Linear Low Density Polyethylene-nonwoven industrial Fique fiber mat (LLDPE-Fique and Epoxy Resin-nonwoven industrial Fique fiber mat (EP-Fique biocomposites were prepared using thermocompression and resin film infusion processes. Neat polymeric matrices and its biocomposites were tested following ASTM standards in order to evaluate tensile and flexural mechanical properties. Also, thermal behavior of these materials has been studied by differential scanning calorimetry (DSC and thermogravimetric analysis (TGA. Tensile and flexural test revealed that nonwoven Fique reinforced composites exhibited higher modulus and strength but lower deformation capability as compared with LLDPE and EP neat matrices. TG thermograms showed that nonwoven Fique fibers incorporation has an effect on the thermal stability of the composites. On the other hand, Fique fibers did not change the crystallization and melting processes of the LLDPE matrix but restricts the motion of EP macromolecules chains thus increases the Tg of the EP-Fique composite. Finally, this work opens the possibility of considering non-woven Fique fibers as a reinforcement material with a high potential for the manufacture of biocomposites for automotive applications. In addition to the processing test specimens, it was also possible to manufacture a part of LLDPE-Fique, and one part of EP-Fique. Keywords: Biocomposites, Natural materials, Nonwoven Fique fiber mat, LLDPE, Epoxy Resin

  3. Mechanical and thermal properties of biocomposites from nonwoven industrial Fique fiber mats with Epoxy Resin and Linear Low Density Polyethylene

    Hidalgo-Salazar, Miguel A.; Correa, Juan P.

    2018-03-01

    In this work Linear Low Density Polyethylene-nonwoven industrial Fique fiber mat (LLDPE-Fique) and Epoxy Resin-nonwoven industrial Fique fiber mat (EP-Fique) biocomposites were prepared using thermocompression and resin film infusion processes. Neat polymeric matrices and its biocomposites were tested following ASTM standards in order to evaluate tensile and flexural mechanical properties. Also, thermal behavior of these materials has been studied by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Tensile and flexural test revealed that nonwoven Fique reinforced composites exhibited higher modulus and strength but lower deformation capability as compared with LLDPE and EP neat matrices. TG thermograms showed that nonwoven Fique fibers incorporation has an effect on the thermal stability of the composites. On the other hand, Fique fibers did not change the crystallization and melting processes of the LLDPE matrix but restricts the motion of EP macromolecules chains thus increases the Tg of the EP-Fique composite. Finally, this work opens the possibility of considering non-woven Fique fibers as a reinforcement material with a high potential for the manufacture of biocomposites for automotive applications. In addition to the processing test specimens, it was also possible to manufacture a part of LLDPE-Fique, and one part of EP-Fique.

  4. Extracting drug mechanism and pharmacodynamic information from clinical electroencephalographic data using generalised semi-linear canonical correlation analysis

    Brain, P; Strimenopoulou, F; Ivarsson, M; Wilson, F J; Diukova, A; Wise, R G; Berry, E; Jolly, A; Hall, J E

    2014-01-01

    Conventional analysis of clinical resting electroencephalography (EEG) recordings typically involves assessment of spectral power in pre-defined frequency bands at specific electrodes. EEG is a potentially useful technique in drug development for measuring the pharmacodynamic (PD) effects of a centrally acting compound and hence to assess the likelihood of success of a novel drug based on pharmacokinetic–pharmacodynamic (PK–PD) principles. However, the need to define the electrodes and spectral bands to be analysed a priori is limiting where the nature of the drug-induced EEG effects is initially not known. We describe the extension to human EEG data of a generalised semi-linear canonical correlation analysis (GSLCCA), developed for small animal data. GSLCCA uses data from the whole spectrum, the entire recording duration and multiple electrodes. It provides interpretable information on the mechanism of drug action and a PD measure suitable for use in PK–PD modelling. Data from a study with low (analgesic) doses of the μ-opioid agonist, remifentanil, in 12 healthy subjects were analysed using conventional spectral edge analysis and GSLCCA. At this low dose, the conventional analysis was unsuccessful but plausible results consistent with previous observations were obtained using GSLCCA, confirming that GSLCCA can be successfully applied to clinical EEG data. (paper)

  5. Faraday wave lattice as an elastic metamaterial.

    Domino, L; Tarpin, M; Patinet, S; Eddi, A

    2016-05-01

    Metamaterials enable the emergence of novel physical properties due to the existence of an underlying subwavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial.

  6. Effective elastic properties of damaged isotropic solids

    Lee, U Sik

    1998-01-01

    In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two-and three-dimensional isotropic solids

  7. Fully coupled heat conduction and deformation analyses of visco-elastic solids

    Khan, Kamran

    2012-04-21

    Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a viscoelastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly viscoelastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969,Mech. Time-Depend. Mater. 1:209-240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209-240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored. © Springer Science+Business Media, B. V. 2012.

  8. Determining the Elasticity of Materials Employing Quantum-mechanical Approaches:From the Electronic Ground State to the Limits of Materials Stability

    Friák, Martin; Hickel, T.; Kormann, F.; Udyansky, A.; Dick, A.; Šob, Mojmír

    2011-01-01

    Roč. 82, č. 2 (2011), s. 86-100 ISSN 1611-3683 R&D Projects: GA AV ČR IAA100100920; GA MŠk OC10008 Institutional research plan: CEZ:AV0Z20410507 Keywords : electronic structure * elasticity * theoretical strength Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.733, year: 2011

  9. Impact of probing volume from different mechanical measurement methods on elastic properties of thermally sprayed Ni-based coatings on a mesoscopic scale

    Margadant, N.; Neuenschwander, J.; Stauss, S.; Kaps, H.; Kulkarni, A.; Matějíček, Jiří; Rössler, G.

    2006-01-01

    Roč. 200, č. 8 (2006), s. 2805-2820 ISSN 0257-8972 Grant - others:Evropská unie Eureka 1973 “Thermetcoat” (EU) Institutional research plan: CEZ:AV0Z20430508 Keywords : Elastic Pro perties * Defects * Thermal spraying * Nickel alloy Subject RIV: JG - Metallurgy Impact factor: 1.559, year: 2006

  10. Extremal Overall Elastic Response of Polycrystalline Materials

    Bendsøe, Martin P; Lipton, Robert

    1996-01-01

    Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...... values.We show that the extremal overall elastic response is alwaysachieved by a configuration consisting of a single properlyoriented crystal. This result is compared to results for isotropicpolycrystals....

  11. Fracture mechanics

    Perez, Nestor

    2017-01-01

    The second edition of this textbook includes a refined presentation of concepts in each chapter, additional examples; new problems and sections, such as conformal mapping and mechanical behavior of wood; while retaining all the features of the original book. The material included in this book is based upon the development of analytical and numerical procedures pertinent to particular fields of linear elastic fracture mechanics (LEFM) and plastic fracture mechanics (PFM), including mixed-mode-loading interaction. The mathematical approach undertaken herein is coupled with a brief review of several fracture theories available in cited references, along with many color images and figures. Dynamic fracture mechanics is included through the field of fatigue and Charpy impact testing. Explains computational and engineering approaches for solving crack-related problems using straightforward mathematics that facilitate comprehension of the physical meaning of crack growth processes; Expands computational understandin...

  12. Free microparticles—An inducing mechanism of pre-firing in high pressure gas switches for fast linear transformer drivers

    Li, Xiaoang; Pei, Zhehao; Wu, Zhicheng; Zhang, Yuzhao; Liu, Xuandong; Li, Yongdong; Zhang, Qiaogen

    2018-03-01

    Microparticle initiated pre-firing of high pressure gas switches for fast linear transformer drivers (FLTDs) is experimentally and theoretically verified. First, a dual-electrode gas switch equipped with poly-methyl methacrylate baffles is used to capture and collect the microparticles. By analyzing the electrode surfaces and the collecting baffles by a laser scanning confocal microscope, microparticles ranging in size from tens of micrometers to over 100 μm are observed under the typical working conditions of FLTDs. The charging and movement of free microparticles in switch cavity are studied, and the strong DC electric field drives the microparticles to bounce off the electrode. Three different modes of free microparticle motion appear to be responsible for switch pre-firing. (i) Microparticles adhere to the electrode surface and act as a fixed protrusion which distorts the local electric field and initiates the breakdown in the gap. (ii) One particle escapes toward the opposite electrode and causes a near-electrode microdischarge, inducing the breakdown of the residual gap. (iii) Multiple moving microparticles are occasionally in cascade, leading to pre-firing. Finally, as experimental verification, repetitive discharges at ±90 kV are conducted in a three-electrode field-distortion gas switch, with two 8 mm gaps and pressurized with nitrogen. An ultrasonic probe is employed to monitor the bounce signals. In pre-firing incidents, the bounce is detected shortly before the collapse of the voltage waveform, which demonstrates that free microparticles contribute significantly to the mechanism that induces pre-firing in FLTD gas switches.

  13. Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

    McAneney, H; O'Rourke, S F C

    2007-01-01

    The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

  14. Free microparticles-An inducing mechanism of pre-firing in high pressure gas switches for fast linear transformer drivers.

    Li, Xiaoang; Pei, Zhehao; Wu, Zhicheng; Zhang, Yuzhao; Liu, Xuandong; Li, Yongdong; Zhang, Qiaogen

    2018-03-01

    Microparticle initiated pre-firing of high pressure gas switches for fast linear transformer drivers (FLTDs) is experimentally and theoretically verified. First, a dual-electrode gas switch equipped with poly-methyl methacrylate baffles is used to capture and collect the microparticles. By analyzing the electrode surfaces and the collecting baffles by a laser scanning confocal microscope, microparticles ranging in size from tens of micrometers to over 100 μm are observed under the typical working conditions of FLTDs. The charging and movement of free microparticles in switch cavity are studied, and the strong DC electric field drives the microparticles to bounce off the electrode. Three different modes of free microparticle motion appear to be responsible for switch pre-firing. (i) Microparticles adhere to the electrode surface and act as a fixed protrusion which distorts the local electric field and initiates the breakdown in the gap. (ii) One particle escapes toward the opposite electrode and causes a near-electrode microdischarge, inducing the breakdown of the residual gap. (iii) Multiple moving microparticles are occasionally in cascade, leading to pre-firing. Finally, as experimental verification, repetitive discharges at ±90 kV are conducted in a three-electrode field-distortion gas switch, with two 8 mm gaps and pressurized with nitrogen. An ultrasonic probe is employed to monitor the bounce signals. In pre-firing incidents, the bounce is detected shortly before the collapse of the voltage waveform, which demonstrates that free microparticles contribute significantly to the mechanism that induces pre-firing in FLTD gas switches.

  15. Elastic Anisotropy of Basalt

    Becker, K.; Shapiro, S.; Stanchits, S.; Dresen, G.; Kaselow, A.; Vinciguerra, S.

    2005-12-01

    Elastic properties of rocks are sensitive to changes of the in-situ stress and damage state. In particular, seismic velocities are strongly affected by stress-induced formation and deformation of cracks or shear-enhanced pore collapse. The effect of stress on seismic velocities as a result of pore space deformation in isotropic rock at isostatic compression may be expressed by the equation: A+K*P-B*exp (-D*P) (1), where P=Pc-Pp is the effective pressure, the pure difference between confining pressure and pore pressure. The parameter A, K, B and D describe material constants determined using experimental data. The physical meaning of the parameters is given by Shapiro (2003, in Geophysics Vol.68(Nr.2)). Parameter D is related to the stress sensitivity of the rock. A similar relation was derived by Shapiro and Kaselow (2005, in Geophysics in press) for weak anisotropic rocks under arbitrary load. They describe the stress dependent anisotropy in terms of Thomson's (1986, in Geophysics, Vol. 51(Nr.10)) anisotropy parameters ɛ and γ as a function of stress in the case of an initially isotropic rock: ɛ ∝ E2-E3, γ ∝ E3-E2 (2) with Ei=exp (D*Pi). The exponential terms Ei are controlled by the effective stress components Pi. To test this relation, we have conducted a series of triaxial compression tests on dry samples of initially isotropic Etnean Basalt in a servo-controlled MTS loading frame equipped with a pressure cell. Confining pressure was 60, 40 and 20 MPa. Samples were 5 cm in diameter and 10 cm in length. Elastic anisotropy was induced by axial compression of the samples through opening and growth of microcracks predominantly oriented parallel to the sample axis. Ultrasonic P- and S- wave velocities were monitored parallel and normal to the sample axis by an array of 20 piezoceramic transducers glued to the surface. Preamplified full waveform signals were stored in two 12 channel transient recorders. According to equation 2 the anisotropy parameters are

  16. Dynamic elasticity measurement for prosthetic socket design.

    Kim, Yujin; Kim, Junghoon; Son, Hyeryon; Choi, Youngjin

    2017-07-01

    The paper proposes a novel apparatus to measure the dynamic elasticity of human limb in order to help the design and fabrication of the personalized prosthetic socket. To take measurements of the dynamic elasticity, the desired force generated as an exponential chirp signal in which the frequency increases and amplitude is maintained according to time progress is applied to human limb and then the skin deformation is recorded, ultimately, to obtain the frequency response of its elasticity. It is referred to as a Dynamic Elasticity Measurement Apparatus (DEMA) in the paper. It has three core components such as linear motor to provide the desired force, loadcell to implement the force feedback control, and potentiometer to record the skin deformation. After measuring the force/deformation and calculating the dynamic elasticity of the limb, it is visualized as 3D color map model of the limb so that the entire dynamic elasticity can be shown at a glance according to the locations and frequencies. For the visualization, the dynamic elasticities measured at specific locations and frequencies are embodied using the color map into 3D limb model acquired by using 3D scanner. To demonstrate the effectiveness, the visualized dynamic elasticities are suggested as outcome of the proposed system, although we do not have any opportunity to apply the proposed system to the amputees. Ultimately, it is expected that the proposed system can be utilized to design and fabricate the personalized prosthetic socket in order for releasing the wearing pain caused by the conventional prosthetic socket.

  17. Elastic least-squares reverse time migration

    Feng, Zongcai

    2017-03-08

    We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

  18. Elastic least-squares reverse time migration

    Feng, Zongcai; Schuster, Gerard T.

    2017-01-01

    We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.

  19. Elastic emission polishing

    Loewenthal, M.; Loseke, K.; Dow, T.A.; Scattergood, R.O.

    1988-12-01

    Elastic emission polishing, also called elastic emission machining (EEM), is a process where a stream of abrasive slurry is used to remove material from a substrate and produce damage free surfaces with controlled surface form. It is a noncontacting method utilizing a thick elasto-hydrodynamic film formed between a soft rotating ball and the workpiece to control the flow of the abrasive. An apparatus was built in the Center, which consists of a stationary spindle, a two-axis table for the workpiece, and a pump to circulate the working fluid. The process is controlled by a programmable computer numerical controller (CNC), which presently can operate the spindle speed and movement of the workpiece in one axis only. This apparatus has been used to determine material removal rates on different material samples as a function of time, utilizing zirconium oxide (ZrO{sub 2}) particles suspended in distilled water as the working fluid. By continuing a study of removal rates the process should become predictable, and thus create a new, effective, yet simple tool for ultra-precision mechanical machining of surfaces.

  20. A method for determination of X-ray elastic constants of materials showing non-linear sin2ψ diagrams and its application to Zn-Ni-alloy electroplate

    Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.

    1990-01-01

    This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)

  1. Elastic Composite, Reinforced Lightweight Concrete as a Type of Resilient Composite Systems

    Esmaeili, Kamyar

    2015-01-01

    . A kind of "Elastic Composite, Reinforced Lightweight Concrete (ECRLC)" with the mentioned specifics is a type of "Resilient Composite Systems (RCS)" in which, contrary to the basic geometrical assumption of flexure theory in Solid Mechanics, "the strain changes in the beam height during bending" is typically "Non-linear". . Through employing this integrated structure, with significant high strain capability and modulus of resilience in bending, we could constructively achieve high bearing c...

  2. Theoretical basis for a transient thermal elastic-plastic stress analysis of nuclear reactor fuel elements

    Hsu, T.R.; Bertels, A.W.M.; Banerjee, S.; Harrison, W.C.

    1976-07-01

    This report presents the theoretical basis for a transient thermal elastic-plastic stress analysis of a nuclear reactor fuel element subject to severe transient thermo-mechanical loading. A finite element formulation is used for both the non-linear stress analysis and thermal analysis. These two major components are linked together to form an integrated program capable of predicting fuel element transient behaviour in two dimensions. Specific case studies are presented to illustrate capabilities of the analysis. (author)

  3. Treatise on classical elasticity theory and related problems

    Teodorescu, Petre P

    2013-01-01

    Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University o...

  4. Mechanical design in arteries.

    Shadwick, R E

    1999-12-01

    The most important mechanical property of the artery wall is its non-linear elasticity. Over the last century, this has been well-documented in vessels in many animals, from humans to lobsters. Arteries must be distensible to provide capacitance and pulse-smoothing in the circulation, but they must also be stable to inflation over a range of pressure. These mechanical requirements are met by strain-dependent increases in the elastic modulus of the vascular wall, manifest by a J-shaped stress-strain curve, as typically exhibited by other soft biological tissues. All vertebrates and invertebrates with closed circulatory systems have arteries with this non-linear behaviour, but specific tissue properties vary to give correct function for the physiological pressure range of each species. In all cases, the non-linear elasticity is a product of the parallel arrangement of rubbery and stiff connective tissue elements in the artery wall, and differences in composition and tissue architecture can account for the observed variations in mechanical properties. This phenomenon is most pronounced in large whales, in which very high compliance in the aortic arch and exceptionally low compliance in the descending aorta occur, and is correlated with specific modifications in the arterial structure.

  5. Structural and elastic anisotropy of crystals at high pressures and temperatures from quantum mechanical methods: The case of Mg{sub 2}SiO{sub 4} forsterite

    Erba, A., E-mail: alessandro.erba@unito.it; Dovesi, R. [Dipartimento di Chimica and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, IT-10125 Torino (Italy); Maul, J. [Dipartimento di Chimica and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, IT-10125 Torino (Italy); Laboratório de Combustíveis e Materiais, INCTMN-UFPB, Universidade Federal da Paraíba, CEP 58051-900 João Pessoa, PB (Brazil); De La Pierre, M. [Nanochemistry Research Institute, Curtin Institute for Computation, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845 (Australia)

    2015-05-28

    We report accurate ab initio theoretical predictions of the elastic, seismic, and structural anisotropy of the orthorhombic Mg{sub 2}SiO{sub 4} forsterite crystal at high pressures (up to 20 GPa) and temperatures (up to its melting point, 2163 K), which constitute earth’s upper mantle conditions. Single-crystal elastic stiffness constants are evaluated up to 20 GPa and their first- and second-order pressure derivatives reported. Christoffel’s equation is solved at several pressures: directional seismic wave velocities and related properties (azimuthal and polarization seismic anisotropies) discussed. Thermal structural and average elastic properties, as computed within the quasi-harmonic approximation of the lattice potential, are predicted at high pressures and temperatures: directional thermal expansion coefficients, first- and second-order pressure derivatives of the isothermal bulk modulus, and P-V-T equation-of-state. The effect on computed properties of five different functionals, belonging to three different classes of approximations, of the density functional theory is explicitly investigated.

  6. Diffuso-Kinetics and Diffuso-Mechanics of Carbon Dioxide / Polyvinylidene Fluoride System under Explosive Gas Decompression: Identification of Key Diffuso-Elastic Couplings by Numerical and Experimental Confrontation

    Grandidier Jean-Claude

    2015-02-01

    Full Text Available The work aims at identifying the key diffuso-elastic couplings which characterize a numerical tool developed to simulate the irreversible ‘Explosive Decompression Failure’ (XDF in semi-crystalline polymer. The model proposes to predict the evolution of the gas concentration and of the stress field in the polymer during the gas desorption [DOI: 10.1016/j.compositesa.2005.05.021]. Main difficulty is to couple thermal, mechanical and diffusive effects that occur simultaneously during the gas desorption. The couplings are splitting into two families: indirect coupling (i.e., phenomenology that is state variables (gas concentration, temperature, and pressure dependent. direct coupling, (i.e., diffuso-elastic coupling as polymer volume changes because of gas diffusion; The numerical prediction of the diffusion kinetics and of the volume strain (swelling of PVF2 (polyvinylidene fluoride under CO2 (carbon dioxide environment is concerned. The prediction is carried out by studying selected combinations of couplings for a broad range of CO2 pressures. The modeling relevance is evaluated by a comparison with experimental transport parameters analytically identify from solubility tests. A pertinent result of the present study is to have demonstrated the non-uniqueness of the coefficients of diffusion (D and solubility (Sg between the diffuso-elastic coupling (direct coupling and indirect coupling. Main conclusion is that it is necessary to consider concomitantly the two types of couplings, the indirect and the direct couplings.

  7. Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models.

    Amano, Ken-Ichi; Yoshidome, Takashi; Iwaki, Mitsuhiro; Suzuki, Makoto; Kinoshita, Masahiro

    2010-07-28

    We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1

  8. Questions about elastic waves

    Engelbrecht, Jüri

    2015-01-01

    This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.

  9. Non-invasive determination of the complete elastic moduli of spider silks

    Koski, Kristie J.; Akhenblit, Paul; McKiernan, Keri; Yarger, Jeffery L.

    2013-03-01

    Spider silks possess nature’s most exceptional mechanical properties, with unrivalled extensibility and high tensile strength. Unfortunately, our understanding of silks is limited because the complete elastic response has never been measured—leaving a stark lack of essential fundamental information. Using non-invasive, non-destructive Brillouin light scattering, we obtain the entire stiffness tensors (revealing negative Poisson’s ratios), refractive indices, and longitudinal and transverse sound velocities for major and minor ampullate spider silks: Argiope aurantia, Latrodectus hesperus, Nephila clavipes, Peucetia viridans. These results completely quantify the linear elastic response for all possible deformation modes, information unobtainable with traditional stress-strain tests. For completeness, we apply the principles of Brillouin imaging to spatially map the elastic stiffnesses on a spider web without deforming or disrupting the web in a non-invasive, non-contact measurement, finding variation among discrete fibres, junctions and glue spots. Finally, we provide the stiffness changes that occur with supercontraction.

  10. Growth and decay of weak disturbances in visco-elastic arteries

    Gaur, M.; Rai, S.K.

    1996-01-01

    In non-linear mathematical models of the arterial circulation, the visco-elasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. The object of the present paper is to provide a mathematical model for the propagation of weak disturbances in visco-elastic arteries. A differential equation governing the growth and decay of the waves has been obtained and solved analytically. It is observed that compressive pulses may grow into shock waves. A mathematical model which is based on geometrical and mechanical properties of arteries admits disturbances in the propagating pulses which are not observed in human beings under normal physiological conditions. It is also predicted that visco-elasticity delays the shock wave formation in the model. The shock wave may appear in periphery in the case of aortic insufficiency due to increased pressure at the root of aorta. The corresponding predictions are in much better agreement with in vivo measurements

  11. Structural phase transition and elastic properties of mercury chalcogenides

    Varshney, Dinesh, E-mail: vdinesh33@rediffmail.com [School of Physics, Vigyan Bhavan, Devi Ahilya University, Khandwa Road Campus, Indore 452001 (India); Shriya, S. [School of Physics, Vigyan Bhavan, Devi Ahilya University, Khandwa Road Campus, Indore 452001 (India); Khenata, R. [Laboratoire de Physique Quantique et de Modelisation Mathematique (LPQ3M), Departement de Technologie, Universite de Mascara, 29000 Mascara (Algeria)

    2012-08-15

    Pressure induced structural transition and elastic properties of ZnS-type (B3) to NaCl-type (B1) structure in mercury chalcogenides (HgX; X = S, Se and Te) are presented. An effective interionic interaction potential (EIOP) with long-range Coulomb, as well charge transfer interactions, Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and van der Waals interactions are considered. Emphasis is on the evaluation of the pressure dependent Poisson's ratio {nu}, the ratio R{sub BT/G} of B (bulk modulus) over G (shear modulus), anisotropy parameter, Shear and Young's modulus, Lame constant, Kleinman parameter, elastic wave velocity and thermodynamical property as Debye temperature. The Poisson's ratio behavior infers that Mercury chalcogenides are brittle in nature. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of elastic and thermodynamical properties explicitly the ductile (brittle) nature of HgX and still awaits experimental confirmations. Highlights: Black-Right-Pointing-Pointer Vast volume discontinuity in phase diagram infers transition from ZnS to NaCl structure. Black-Right-Pointing-Pointer The shear elastic constant C{sub 44} is nonzero confirms the mechanical stability. Black-Right-Pointing-Pointer Pressure dependence of {theta}{sub D} infers the softening of lattice with increasing pressure. Black-Right-Pointing-Pointer Estimated bulk, shear and tetragonal moduli satisfied elastic stability criteria. Black-Right-Pointing-Pointer In both B3 and B1 phases, C{sub 11} and C{sub 12} increase linearly with pressure.

  12. Effects of Host-rock Fracturing on Elastic-deformation Source Models of Volcano Deflation.

    Holohan, Eoghan P; Sudhaus, Henriette; Walter, Thomas R; Schöpfer, Martin P J; Walsh, John J

    2017-09-08

    Volcanoes commonly inflate or deflate during episodes of unrest or eruption. Continuum mechanics models that assume linear elastic deformation of the Earth's crust are routinely used to invert the observed ground motions. The source(s) of deformation in such models are generally interpreted in terms of magma bodies or pathways, and thus form a basis for hazard assessment and mitigation. Using discontinuum mechanics models, we show how host-rock fracturing (i.e. non-elastic deformation) during drainage of a magma body can progressively change the shape and depth of an elastic-deformation source. We argue that this effect explains the marked spatio-temporal changes in source model attributes inferred for the March-April 2007 eruption of Piton de la Fournaise volcano, La Reunion. We find that pronounced deflation-related host-rock fracturing can: (1) yield inclined source model geometries for a horizontal magma body; (2) cause significant upward migration of an elastic-deformation source, leading to underestimation of the true magma body depth and potentially to a misinterpretation of ascending magma; and (3) at least partly explain underestimation by elastic-deformation sources of changes in sub-surface magma volume.

  13. Code conforming determination of cumulative usage factors for general elastic-plastic finite element analyses

    Rudolph, Juergen; Goetz, Andreas; Hilpert, Roland

    2012-01-01

    The procedures of fatigue analyses of several relevant nuclear and conventional design codes (ASME, KTA, EN, AD) for power plant components differentiate between an elastic, simplified elastic-plastic and elastic-plastic fatigue check. As a rule, operational load levels will exclude the purely elastic fatigue check. The application of the code procedure of the simplified elastic-plastic fatigue check is common practice. Nevertheless, resulting cumulative usage factors may be overly conservative mainly due to high code based plastification penalty factors Ke. As a consequence, the more complex and still code conforming general elastic-plastic fatigue analysis methodology based on non-linear finite element analysis (FEA) is applied for fatigue design as an alternative. The requirements of the FEA and the material law to be applied have to be clarified in a first step. Current design codes only give rough guidelines on these relevant items. While the procedure for the simplified elastic-plastic fatigue analysis and the associated code passages are based on stress related cycle counting and the determination of pseudo elastic equivalent stress ranges, an adaptation to elastic-plastic strains and strain ranges is required for the elastic-plastic fatigue check. The associated requirements are explained in detail in the paper. If the established and implemented evaluation mechanism (cycle counting according to the peak and valley respectively the rainflow method, calculation of stress ranges from arbitrary load-time histories and determination of cumulative usage factors based on all load events) is to be retained, a conversion of elastic-plastic strains and strain ranges into pseudo elastic stress ranges is required. The algorithm to be applied is described in the paper. It has to be implemented in the sense of an extended post processing operation of FEA e.g. by APDL scripts in ANSYS registered . Variations of principal stress (strain) directions during the loading

  14. Why ductile fracture mechanics

    Ritchie, R.O.

    1983-01-01

    Until recently, the engineering application of fracture mechanics has been specific to a description of macroscopic fracture behavior in components and structural parts which remain nominally elastic under loading. While this approach, termed linear elastic fracture mechanics, has been found to be invaluable for the continuum analysis of crack growth in brittle and high strength materials, it is clearly inappropriate for characterizing failure in lower strength ductile alloys where extensive inelastic deformation precedes and accompanies crack initiation and subsequent propagation. Accordingly, much effort has been devoted in recent years toward the development of nonlinear or ductile fracture mechanics methodology to characterize fracture behavior under elastic/plastic conditions; an effort which has been principally motivated by problems in nuclear industry. In this paper, the concepts of ductile (elastic/plastic) fracture mechanics are introduced and applied to the problem of both stationary and nonstationary cracks. Specifically, the limitations inherent in this approach are defined, together with a description of the microstructural considerations and applications relevant to the failure of ductile materials by fracture, fatigue, and creep

  15. Elastic scattering and quasi-elastic transfers

    Mermaz, M.C.

    1978-01-01

    Experiments are presented which it will be possible to carry out at GANIL on the elastic scattering of heavy ions: diffraction phenomena if the absorption is great, refraction phenomena if absorption is low. The determination of the optical parameters can be performed. The study of the quasi-elastic transfer reactions will make it possible to know the dynamics of the nuclear reactions, form exotic nuclei and study their energy excitation spectrum, and analyse the scattering and reaction cross sections [fr

  16. Notes on continuum mechanics

    Chaves, Eduardo W V

    2013-01-01

    This publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately.   The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.

  17. Elastic-plastic FEM-analysis of a nozzle corner crack and discussion of the results by some fracture mechanics concepts

    Aurich, D.; Brocks, W.; Noack, D.; Veith, H.

    1981-01-01

    From a three-dimensional elastic-plastic stress-distortion analysis according to the finite element method (FEM) for a straight inner edge crack at room temperature in a nozzle of the intermediate vessel ZB 2 made of 22 NiMoCr 37 steel, the results obtained for stresses and strains in the ligament before the crack front, the crack opening profile, and the propagation of the plastic zone as a function of internal pressure until through-plastifying of the ligament are shown and explained. (orig.) [de

  18. Mechanics of ultrasound elastography

    Li, Guo-Yang

    2017-01-01

    Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues. PMID:28413350

  19. Semidefinite linear complementarity problems

    Eckhardt, U.

    1978-04-01

    Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

  20. Elastic properties of suspended multilayer WSe{sub 2}

    Zhang, Rui, E-mail: rui.zhang@ed.ac.uk; Cheung, Rebecca [Scottish Microelectronics Centre, Alexander Crum Brown Road, The University of Edinburgh, King' s Buildings, Edinburgh EH9 3FF (United Kingdom); Koutsos, Vasileios [Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King' s Buildings, Edinburgh EH9 3FB (United Kingdom)

    2016-01-25

    We report the experimental determination of the elastic properties of suspended multilayer WSe{sub 2}, a promising two-dimensional (2D) semiconducting material combined with high optical quality. The suspended WSe{sub 2} membranes have been fabricated by mechanical exfoliation of bulk WSe{sub 2} and transfer of the exfoliated multilayer WSe{sub 2} flakes onto SiO{sub 2}/Si substrates pre-patterned with hole arrays. Then, indentation experiments have been performed on these membranes with an atomic force microscope. The results show that the 2D elastic modulus of the multilayer WSe{sub 2} membranes increases linearly while the prestress decreases linearly as the number of layers increases. The interlayer interaction in WSe{sub 2} has been observed to be strong enough to prevent the interlayer sliding during the indentation experiments. The Young's modulus of multilayer WSe{sub 2} (167.3 ± 6.7 GPa) is statistically independent of the thickness of the membranes, whose value is about two thirds of other most investigated 2D semiconducting transition metal dichalcogenides, namely, MoS{sub 2} and WS{sub 2}. Moreover, the multilayer WSe{sub 2} can endure ∼12.4 GPa stress and ∼7.3% strain without fracture or mechanical degradation. The 2D WSe{sub 2} can be an attractive semiconducting material for application in flexible optoelectronic devices and nano-electromechanical systems.

  1. Continuum mechanics of electromagnetic solids

    Maugin, GA

    1988-01-01

    This volume is a rigorous cross-disciplinary theoretical treatment of electromechanical and magnetomechanical interactions in elastic solids. Using the modern style of continuum thermomechanics (but without excessive formalism) it starts from basic principles of mechanics and electromagnetism, and goes on to unify these two fields in a common framework. It treats linear and nonlinear static and dynamic problems in a variety of elastic solids such as piezoelectrics, electricity conductors, ferromagnets, ferroelectrics, ionic crystals and ceramics. Chapters 1-3 are introductory, describing the e

  2. Low temperature uniform plastic deformation of metallic glasses during elastic iteration

    Fujita, Takeshi; Wang Zheng; Liu Yanhui; Sheng, Howard; Wang Weihua; Chen Mingwei

    2012-01-01

    Molecular dynamics simulations and dynamic mechanical analysis experiments were employed to investigate the mechanical behavior of metallic glasses subjected to iteration deformation in a nominally elastic region. It was found that cyclic deformation leads to the formation of irreversible shear transformation zones (STZs) and a permanent uniform strain. The initiation of STZs is directly correlated with the atomic heterogeneity of the metallic glass and the accumulated permanent strain has a linear relation with the number of STZs. This study reveals a new deformation mode and offers insights into the atomic mechanisms of STZ formation and low temperature uniform plastic deformation of metallic glasses.

  3. Efficient education policy: A second-order elasticity rule

    Richter, Wolfram F.

    2010-01-01

    Assuming a two-period model with endogenous choices of labour, education, and saving, efficient education policy is characterized for a Ramsey-like scenario in which the government is constrained to use linear instruments. It is shown that education should be effectively subsidized if, and only if, the elasticity of the earnings function is increasing in education. The strength of second-best subsidization increases in the elasticity of the elasticity of the earnings function. This second-ord...

  4. Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies

    Boer, Jan de; Peeters, Bas; Skenderis, Kostas; Nieuwenhuizen, Peter van

    1995-01-01

    We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct Feynman rules which differ from those often assumed. These

  5. The 1 Repetition Maximum Mechanics of a High-Handle Hexagonal Bar Deadlift Compared With a Conventional Deadlift as Measured by a Linear Position Transducer.

    Lockie, Robert G; Moreno, Matthew R; Lazar, Adrina; Risso, Fabrice G; Liu, Tricia M; Stage, Alyssa A; Birmingham-Babauta, Samantha A; Torne, Ibett A; Stokes, John J; Giuliano, Dominic V; Davis, DeShaun L; Orjalo, Ashley J; Callaghan, Samuel J

    2018-01-01

    Lockie, RG, Moreno, MR, Lazar, A, Risso, FG, Liu, TM, Stage, AA, Birmingham-Babauta, SA, Torne, IA, Stokes, JJ, Giuliano, DV, Davis, DL, Orjalo, AJ, and Callaghan, SJ. The 1 repetition maximum mechanics of a high-handle hexagonal bar deadlift compared with a conventional deadlift as measured by a linear position transducer. J Strength Cond Res 32(1): 150-161, 2018-The high-handle hexagonal bar deadlift (HHBD), a variation of the conventional deadlift (CD), is said to reduce the lift range of motion, which may change the mechanics of the lift. However, no research has investigated this. This study compared the mechanics between a 1 repetition maximum (1RM) CD and HHBD. Thirty-one strength-trained subjects (21 men, 10 women) completed a 1RM CD and HHBD. A linear position transducer measured lift distance, duration, and work; and peak and mean power, velocity, and force. The presence of a sticking region (SR) was determined for each lift. A repeated-measures analysis of variance (ANOVA) calculated differences between 1RM CD and HHBD mechanics. A one-way ANOVA compared the mechanics of each lift between subjects who exhibited an SR or not, and the SR between the CD and HHBD. Significance was set at p mechanics between subjects with or without an SR, and no differences in SR region distance or duration between the CD and HHBD. Greater force can be generated in the HHBD, which could have implications for strength-training adaptations over time.

  6. Investigation on crack growth parameters in the elastic plastic region (interim report)

    Prij, J.

    1982-03-01

    Some theoretical as well as numerical results are presented with respect to the 2D and 3D application of linear elastic fracture mechanics. The application of the finite element method to calculate the stress and strain field in cracked bodies has been discussed with special attention to: singularity representation, parameter extraction and mesh refinement. Detailed 3D stress analyses of fracture mechanics test specimen are presented showing that: the stress intensity concept cannot be extended simply into a 3D concept, the energy release concept is more promising within this aspect and the plastic region along the crackfront will not have a dogbone shape. The 3D elastic fracture mechanics concept is applied to evaluate the consequences of the thermal stresses due to γ-heating in an in-pile crack growth experiment

  7. New constitutive equations to describe infinitesimal elastic-plastic deformations

    Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.

    1983-01-01

    A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)

  8. Controlling elastic waves with small phononic crystals containing rigid inclusions

    Peng, Pai

    2014-05-01

    We show that a two-dimensional elastic phononic crystal comprising rigid cylinders in a solid matrix possesses a large complete band gap below a cut-off frequency. A mechanical model reveals that the band gap is induced by negative effective mass density, which is affirmed by an effective medium theory based on field averaging. We demonstrate, by two examples, that such elastic phononic crystals can be utilized to design small devices to control low-frequency elastic waves. One example is a waveguide made of a two-layer anisotropic elastic phononic crystal, which can guide and bend elastic waves with wavelengths much larger than the size of the waveguide. The other example is the enhanced elastic transmission of a single-layer elastic phononic crystal loaded with solid inclusions. The effective mass density and reciprocal of the modulus of the single-layer elastic phononic crystal are simultaneously near zero. © CopyrightEPLA, 2014.

  9. Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

    Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

    2010-01-01

    Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.

  10. ElasticSearch cookbook

    Paro, Alberto

    2013-01-01

    Written in an engaging, easy-to-follow style, the recipes will help you to extend the capabilities of ElasticSearch to manage your data effectively.If you are a developer who implements ElasticSearch in your web applications, manage data, or have decided to start using ElasticSearch, this book is ideal for you. This book assumes that you've got working knowledge of JSON and Java

  11. A Smoothed Finite Element-Based Elasticity Model for Soft Bodies

    Juan Zhang

    2017-01-01

    Full Text Available One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.

  12. Uniqueness in inverse elastic scattering with finitely many incident waves

    Elschner, Johannes; Yamamoto, Masahiro

    2009-01-01

    We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)

  13. Support minimized inversion of acoustic and elastic wave scattering

    Safaeinili, A.

    1994-01-01

    This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

  14. Design and characterization of a microelectromechanical system electro-thermal linear motor with interlock mechanism for micro manipulators.

    Hu, Tengjiang; Zhao, Yulong; Li, Xiuyuan; Zhao, You; Bai, Yingwei

    2016-03-01

    The design, fabrication, and testing of a novel electro-thermal linear motor for micro manipulators is presented in this paper. The V-shape electro-thermal actuator arrays, micro lever, micro spring, and slider are introduced. In moving operation, the linear motor can move nearly 1 mm displacement with 100 μm each step while keeping the applied voltage as low as 17 V. In holding operation, the motor can stay in one particular position without consuming energy and no creep deformation is found. Actuation force of 12.7 mN indicates the high force generation capability of the device. Experiments of lifetime show that the device can wear over two million cycles of operation. A silicon-on-insulator wafer is introduced to fabricate a high aspect ratio structure and the chip size is 8.5 mm × 8.5 mm × 0.5 mm.

  15. Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

    Paulius Palevicius

    2014-01-01

    Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

  16. Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

    Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

    2014-01-01

    Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

  17. Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

    Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

    2014-01-21

    Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

  18. Mechanical design of a precision linear flexural stage for 3D x-ray diffraction microscope at the Advanced Photon Source

    Shu, D.; Liu, W.; Kearney, S.; Anton, J.; Tischler, J. Z.

    2015-09-01

    The 3-D X-ray diffraction microscope is a new nondestructive tool for the three-dimensional characterization of mesoscopic materials structure. A flexural-pivot-based precision linear stage has been designed to perform a wire scan as a differential aperture for the 3-D diffraction microscope at the Advanced Photon Source, Argonne National Laboratory. The mechanical design and finite element analyses of the flexural stage, as well as its initial mechanical test results with laser interferometer are described in this paper.

  19. Studies on the retention mechanism of solutes in hydrophilic interaction chromatography using stoichiometric displacement theory I. The linear relationship of lgk' vs. lg[H2O].

    Wang, Fei; Yang, Fan; Tian, Yang; Liu, Jiawei; Shen, Jiwei; Bai, Quan

    2018-01-01

    A stoichiometric displacement model for retention (SDM-R) of small solutes and proteins based on hydrophilic interaction chromatography (HILIC) was presented. A linear equation that related the logarithm of the capacity factor of the solute to the logarithm of the concentration of water in the mobile phase was derived. The stoichiometric displacement parameters, Z (the number of water molecules required to displace a solute from ligands) and lgI (containing a number of constants that relate to the affinity of solute to the ligands) could be obtained from the slope and the intercept of the linear plots of lgk' vs. lg[H 2 O]. The retention behaviors and retention mechanism of 15 kinds of small solutes and 6 kinds of proteins on 5 kinds HILIC columns with different ligands were investigated with SDM-R in typical range of water concentration in mobile phase. A good linear relationship between lgk' and lg[H 2 O] demonstrated that the most rational retention mechanism of solute in HILIC was a stoichiometric displacement process between solute and solvent molecules with water as displacing agents, which was not only valid for small solutes, but also could be used to explain the retention mechanism of biopolymers in HILIC. Comparing with the partition and adsorption models in HILIC, SDM-R was superior to them. Copyright © 2017 Elsevier B.V. All rights reserved.

  20. Extremal Overall Elastic Response of Polycrystalline Materials

    Bendsøe, Martin P; Lipton, Robert

    1997-01-01

    Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...