Matrix Tricks for Linear Statistical Models

CERN Document Server

Puntanen, Simo; Styan, George PH

2011-01-01

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

Applied linear algebra and matrix analysis

CERN Document Server

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

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

Energy Technology Data Exchange (ETDEWEB)

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.

Mitochondrial function in engineered cardiac tissues is regulated by extracellular matrix elasticity and tissue alignment.

Science.gov (United States)

Lyra-Leite, Davi M; Andres, Allen M; Petersen, Andrew P; Ariyasinghe, Nethika R; Cho, Nathan; Lee, Jezell A; Gottlieb, Roberta A; McCain, Megan L

2017-10-01

Mitochondria in cardiac myocytes are critical for generating ATP to meet the high metabolic demands associated with sarcomere shortening. Distinct remodeling of mitochondrial structure and function occur in cardiac myocytes in both developmental and pathological settings. However, the factors that underlie these changes are poorly understood. Because remodeling of tissue architecture and extracellular matrix (ECM) elasticity are also hallmarks of ventricular development and disease, we hypothesize that these environmental factors regulate mitochondrial function in cardiac myocytes. To test this, we developed a new procedure to transfer tunable polydimethylsiloxane disks microcontact-printed with fibronectin into cell culture microplates. We cultured Sprague-Dawley neonatal rat ventricular myocytes within the wells, which consistently formed tissues following the printed fibronectin, and measured oxygen consumption rate using a Seahorse extracellular flux analyzer. Our data indicate that parameters associated with baseline metabolism are predominantly regulated by ECM elasticity, whereas the ability of tissues to adapt to metabolic stress is regulated by both ECM elasticity and tissue alignment. Furthermore, bioenergetic health index, which reflects both the positive and negative aspects of oxygen consumption, was highest in aligned tissues on the most rigid substrate, suggesting that overall mitochondrial function is regulated by both ECM elasticity and tissue alignment. Our results demonstrate that mitochondrial function is regulated by both ECM elasticity and myofibril architecture in cardiac myocytes. This provides novel insight into how extracellular cues impact mitochondrial function in the context of cardiac development and disease. NEW & NOTEWORTHY A new methodology has been developed to measure O 2 consumption rates in engineered cardiac tissues with independent control over tissue alignment and matrix elasticity. This led to the findings that matrix

Non-linear elastic thermal stress analysis with phase changes

International Nuclear Information System (INIS)

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.)

Covariance Matrix of a Double-Differential Doppler-Broadened Elastic Scattering Cross Section

Science.gov (United States)

Arbanas, G.; Becker, B.; Dagan, R.; Dunn, M. E.; Larson, N. M.; Leal, L. C.; Williams, M. L.

2012-05-01

Legendre moments of a double-differential Doppler-broadened elastic neutron scattering cross section on 238U are computed near the 6.67 eV resonance at temperature T = 103 K up to angular order 14. A covariance matrix of these Legendre moments is computed as a functional of the covariance matrix of the elastic scattering cross section. A variance of double-differential Doppler-broadened elastic scattering cross section is computed from the covariance of Legendre moments. Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

The influence of powder elasticity on the quality of pressed matrix bodies

International Nuclear Information System (INIS)

Heit, W.; Herrmann, F.J.

1976-01-01

The production of electrographite powder has dominating influence on the powder elasticity and the quality of pressed resin bonded bodies. The quality increases with increasing degree of graphitization and additionally depends strongly on the sequence of the process steps gruinding and graphitization. It could be shown that elasticity is the only property of the graphite powder correlating with the quality of pressed matrix bodies. (orig.) [de

Deposition of tropoelastin into the extracellular matrix requires a competent elastic fiber scaffold but not live cells.

Science.gov (United States)

Kozel, Beth A; Ciliberto, Christopher H; Mecham, Robert P

2004-04-01

The initial steps of elastic fiber assembly were investigated using an in vitro assembly model in which purified recombinant tropoelastin (rbTE) was added to cultures of live or dead cells. The ability of tropoelastin to associate with preexisting elastic fibers or microfibrils in the extracellular matrix was then assessed by immunofluorescence microscopy using species-specific tropoelastin antibodies. Results show that rbTE can associate with elastic fiber components in the absence of live cells through a process that does not depend on crosslink formation. Time course studies show a transformation of the deposited protein from an initial globular appearance early in culture to a more fibrous structure as the matrix matures. Deposition required the C-terminal region of tropoelastin and correlated with the presence of preexisting elastic fibers or microfibrils. Association of exogenously added tropoelastin to the cellular extracellular matrix was inhibited by the addition of heparan sulfate but not chondroitin sulfate sugars. Together, these results suggest that the matrix elaborated by the cell is sufficient for the initial deposition of tropoelastin in the extracellular space and that elastin assembly may be influenced by the composition of sulfated proteoglycans in the matrix.

Generating Nice Linear Systems for Matrix Gaussian Elimination

Science.gov (United States)

Homewood, L. James

2004-01-01

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

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

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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.

Generation of discrete inelastic and elastic transfer matrix

International Nuclear Information System (INIS)

Garcia, R.D.M.; Santina, M.D.

1985-01-01

A technique developed for the calculation of the isotropic and linearly anisotropic components components of elastic and discrete inelastic transfer matrices is presented in this work. The implementation of the technique is discussed in detail and numerical results obtained for some examples are compared with results reported in the literature or generated with the use of several processing codes. (author) [pt

Designing Linear Feedback Controller for Elastic Inverted Pendulum with Tip Mass

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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.

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

International Nuclear Information System (INIS)

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

A Galerkin approximation for linear elastic shallow shells

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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.

Non-linear elastic deformations

CERN Document Server

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.

Matrix model and time-like linear dila ton matter

International Nuclear Information System (INIS)

Takayanagi, Tadashi

2004-01-01

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

The ultra-structural organization of the elastic network in the intra- and inter-lamellar matrix of the intervertebral disc.

Science.gov (United States)

Tavakoli, J; Elliott, D M; Costi, J J

2017-08-01

The inter-lamellar matrix (ILM)-located between adjacent lamellae of the annulus fibrosus-consists of a complex structure of elastic fibers, while elastic fibers of the intra-lamellar region are aligned predominantly parallel to the collagen fibers. The organization of elastic fibers under low magnification, in both inter- and intra-lamellar regions, was studied by light microscopic analysis of histologically prepared samples; however, little is known about their ultrastructure. An ultrastructural visualization of elastic fibers in the inter-lamellar matrix is crucial for describing their contribution to structural integrity, as well as mechanical properties of the annulus fibrosus. The aims of this study were twofold: first, to present an ultrastructural analysis of the elastic fiber network in the ILM and intra-lamellar region, including cross section (CS) and in-plane (IP) lamellae, of the AF using Scanning Electron Microscopy (SEM) and second, to -compare the elastic fiber orientation between the ILM and intra-lamellar region. Four samples (lumbar sheep discs) from adjacent sections (30μm thickness) of anterior annulus were partially digested by a developed NaOH-sonication method for visualization of elastic fibers by SEM. Elastic fiber orientation and distribution were quantified relative to the tangential to circumferential reference axis. Visualization of the ILM under high magnification revealed a dense network of elastic fibers that has not been previously described. Within the ILM, elastic fibers form a complex network, consisting of different size and shape fibers, which differed to those located in the intra-lamellar region. For both regions, the majority of fibers were oriented near 0° with respect to tangential to circumferential (TCD) direction and two minor symmetrical orientations of approximately±45°. Statistically, the orientation of elastic fibers between the ILM and intra-lamellar region was not different (p=0.171). The present study used

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space

International Nuclear Information System (INIS)

Parzen, G.

1997-01-01

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. A set of equations is given from which the 12 elements of R can be computed form the one period transfer matrix. This set of equations also allows the linear parameters, the β i , α i , i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix

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

CERN Document Server

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.

Effects of matrix elasticity and cell density on human mesenchymal stem cells differentiation.

Science.gov (United States)

Xue, Ruyue; Li, Julie Yi-Shuan; Yeh, Yiting; Yang, Li; Chien, Shu

2013-09-01

Human mesenchymal stem cells (hMSCs) can differentiate into various cell types, including osteogenic and chondrogenic cells. The matrix elasticity and cell seeding density are important factors in hMSCs differentiation. We cultured hMSCs at different seeding densities on polyacrylamide hydrogels with different stiffness corresponding to Young's moduli of 1.6 ± 0.3 and 40 ± 3.6 kPa. The promotion of osteogenic marker expression by hard gel is overridden by a high seeding density. Cell seeding density, however, did not influence the chondrogenic marker expressions induced by soft gel. These findings suggest that interplays between cell-matrix and cell-cell interactions contribute to hMSCs differentiation. The promotion of osteogenic differentiation on hard matrix was shown to be mediated through the Ras pathway. Inhibition of Ras (RasN17) significantly decreased ERK, Smad1/5/8 and AKT activation, and osteogenic markers expression. However, constitutively active Ras (RasV12) had little effect on osteogenic marker expression, suggesting that the Ras pathways are necessary but not sufficient for osteogenesis. Taken together, our results indicate that matrix elasticity and cell density are important microenvironmental cues driving hMSCs proliferation and differentiation. Copyright © 2013 Orthopaedic Research Society.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

Science.gov (United States)

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Linear matrix differential equations of higher-order and applications

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Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Continuum mechanics elasticity, plasticity, viscoelasticity

CERN Document Server

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...

Particles geometry influence in the thermal stress level in an SiC reinforced aluminum matrix composite considering the material non-linear behavior

International Nuclear Information System (INIS)

Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.

2009-01-01

An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)

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

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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

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

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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.

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

DEFF Research Database (Denmark)

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...

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

Science.gov (United States)

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

Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

DEFF Research Database (Denmark)

Garde, Henrik

2018-01-01

. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

Fracture toughness in metal matrix composites

Directory of Open Access Journals (Sweden)

Perez Ipiña J.E.

2000-01-01

Full Text Available Evaluations of the fracture toughness in metal matrix composites (Duralcan reinforced with 15% of Al(20(3 and SiC are presented in this work. The application of Elastic Plastic Fracture Mechanics is discussed and the obtained values are compared with the ones obtained by means of Linear Elastic Fracture Mechanics. Results show that J IC derived K JC values are higher than the corresponding values obtained by direct application of the linear elastic methodology. The effect of a heat treatment on the material fracture toughness was also evaluated in which the analyzed approaches showed, not only different toughness values, but also opposite tendencies. A second comparison of the J IC and K JC values obtained in this work with toughness values reported in the literature is presented and discussed.

Linear elastic properties derivation from microstructures representative of transport parameters.

Science.gov (United States)

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.

The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

International Nuclear Information System (INIS)

Kim, Jeong Soo; Kim, Moon Kyum

2012-01-01

In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

A reexamination of some puzzling results in linearized elasticity

Indian Academy of Sciences (India)

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 ...

Elastic properties of Cs2HgBr4 and Cs2CdBr4 crystals

International Nuclear Information System (INIS)

Kityk, A.V.; Zadorozhna, A.V.; Shchur, Y.I.; Martynyuk-Lototska, Y.I.; Burak, Y.; Vlokh, O.G.

1998-01-01

Using ultrasonic velocity measurements, all components of the elastic constant matrix C ij , elastic compliances matrix S ij , and linear compressibility constants matrix K ij of orthorhombic Cs 2 HgBr 4 and Cs 2 CdBr 4 crystals have been determined over a wide temperature range, including the region of the phase transition from the normal to the incommensurate phase. Results obtained are considered within the framework of the phenomenological theory. Preliminary analysis of the acoustical properties at room temperature clearly indicates that both crystals are relatively important materials for acousto-optical applications. Copyright (1998) CSIRO Australia

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

Science.gov (United States)

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Non-linear dynamic response of reactor containment

International Nuclear Information System (INIS)

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

Compressor Surge Control Design Using Linear Matrix Inequality Approach

OpenAIRE

Uddin, Nur; Gravdahl, Jan Tommy

2017-01-01

A novel design for active compressor surge control system (ASCS) using linear matrix inequality (LMI) approach is presented and including a case study on piston-actuated active compressor surge control system (PAASCS). The non-linear system dynamics of the PAASCS is transformed into linear parameter varying (LPV) system dynamics. The system parameters are varying as a function of the compressor performance curve slope. A compressor surge stabilization problem is then formulated as a LMI probl...

Chosen interval methods for solving linear interval systems with special type of matrix

Science.gov (United States)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

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

Energy Technology Data Exchange (ETDEWEB)

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.

A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

DEFF Research Database (Denmark)

Harrod, Steven

2009-01-01

The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

H∞ /H2 model reduction through dilated linear matrix inequalities

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2012-01-01

This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arb......This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...

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

Directory of Open Access Journals (Sweden)

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.

An analysis of hypercritical states in elastic and inelastic systems

Science.gov (United States)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

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Bin Wang

2015-01-01

Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

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

Institute of Scientific and Technical Information of China (English)

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.

Price elasticity matrix of demand in power system considering demand response programs

Science.gov (United States)

Qu, Xinyao; Hui, Hongxun; Yang, Shengchun; Li, Yaping; Ding, Yi

2018-02-01

The increasing renewable energy power generations have brought more intermittency and volatility to the electric power system. Demand-side resources can improve the consumption of renewable energy by demand response (DR), which becomes one of the important means to improve the reliability of power system. In price-based DR, the sensitivity analysis of customer’s power demand to the changing electricity prices is pivotal for setting reasonable prices and forecasting loads of power system. This paper studies the price elasticity matrix of demand (PEMD). An improved PEMD model is proposed based on elasticity effect weight, which can unify the rigid loads and flexible loads. Moreover, the structure of PEMD, which is decided by price policies and load types, and the calculation method of PEMD are also proposed. Several cases are studied to prove the effectiveness of this method.

Co-effects of matrix low elasticity and aligned topography on stem cell neurogenic differentiation and rapid neurite outgrowth

Science.gov (United States)

Yao, Shenglian; Liu, Xi; Yu, Shukui; Wang, Xiumei; Zhang, Shuming; Wu, Qiong; Sun, Xiaodan; Mao, Haiquan

2016-05-01

The development of novel biomaterials that deliver precise regulatory signals to direct stem cell fate for nerve regeneration is the focus of current intensive research efforts. In this study, a hierarchically aligned fibrillar fibrin hydrogel (AFG) that was fabricated through electrospinning and the concurrent molecular self-assembly process mimics both the soft and oriented features of nerve tissue, thus providing hybrid biophysical cues to instruct cell behavior in vitro and in vivo. The electrospun hydrogels were examined by scanning electron microscopy (SEM), polarized light microscopy, small angle X-ray scattering assay and atomic force microscopy (AFM), showing a hierarchically linear-ordered structure from the nanoscale to the macroscale with a soft elastic character (elasticity ~1 kPa). We found that this low elasticity and aligned topography of AFG exhibit co-effects on promoting the neurogenic differentiation of human umbilical cord mesenchymal stem cells (hUMSCs) in comparison to random fibrin hydrogel (RFG) and tissue culture plate (TCP) control after two week cell culture in growth medium lacking supplementation with soluble neurogenic induction factors. In addition, AFG also induces dorsal root ganglion (DRG) neurons to rapidly project numerous long neurite outgrowths longitudinally along the AFG fibers for a total neurite extension distance of 1.96 mm in three days in the absence of neurotrophic factor supplementation. Moreover, the AFG implanted in a rat T9 dorsal hemisection spinal cord injury model was found to promote endogenous neural cell fast migration and axonal invasion along AFG fibers, resulting in aligned tissue cables in vivo. Our results suggest that matrix stiffness and aligned topography may instruct stem cell neurogenic differentiation and rapid neurite outgrowth, providing great promise for biomaterial design for applications in nerve regeneration.The development of novel biomaterials that deliver precise regulatory signals to

Integrodifferential relations in linear elasticity

CERN Document Server

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.

A virtual surgical training system that simulates cutting of soft tissue using a modified pre-computed elastic model.

Science.gov (United States)

Toe, Kyaw Kyar; Huang, Weimin; Yang, Tao; Duan, Yuping; Zhou, Jiayin; Su, Yi; Teo, Soo-Kng; Kumar, Selvaraj Senthil; Lim, Calvin Chi-Wan; Chui, Chee Kong; Chang, Stephen

2015-08-01

This work presents a surgical training system that incorporates cutting operation of soft tissue simulated based on a modified pre-computed linear elastic model in the Simulation Open Framework Architecture (SOFA) environment. A precomputed linear elastic model used for the simulation of soft tissue deformation involves computing the compliance matrix a priori based on the topological information of the mesh. While this process may require a few minutes to several hours, based on the number of vertices in the mesh, it needs only to be computed once and allows real-time computation of the subsequent soft tissue deformation. However, as the compliance matrix is based on the initial topology of the mesh, it does not allow any topological changes during simulation, such as cutting or tearing of the mesh. This work proposes a way to modify the pre-computed data by correcting the topological connectivity in the compliance matrix, without re-computing the compliance matrix which is computationally expensive.

Linearized inversion of two components seismic data; Inversion linearisee de donnees sismiques a deux composantes

Energy Technology Data Exchange (ETDEWEB)

Lebrun, D.

1997-05-22

The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Non-linear theory of elasticity

CERN Document Server

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.

Matrix preconditioning: a robust operation for optical linear algebra processors.

Science.gov (United States)

Ghosh, A; Paparao, P

1987-07-15

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

Some Differential Geometric Relations in the Elastic Shell

Directory of Open Access Journals (Sweden)

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.

Minimal solution of linear formed fuzzy matrix equations

Directory of Open Access Journals (Sweden)

Maryam Mosleh

2012-10-01

Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

Force sensing using 3D displacement measurements in linear elastic bodies

Science.gov (United States)

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.

Compressive elasticity of three-dimensional nanofiber matrix directs mesenchymal stem cell differentiation to vascular cells with endothelial or smooth muscle cell markers.

Science.gov (United States)

Wingate, K; Bonani, W; Tan, Y; Bryant, S J; Tan, W

2012-04-01

The importance of mesenchymal stem cells (MSC) in vascular regeneration is becoming increasingly recognized. However, few in vitro studies have been performed to identify the effects of environmental elasticity on the differentiation of MSC into vascular cell types. Electrospinning and photopolymerization techniques were used to fabricate a three-dimensional (3-D) polyethylene glycol dimethacrylate nanofiber hydrogel matrix with tunable elasticity for use as a cellular substrate. Compression testing demonstrated that the elastic modulus of the hydrated 3-D matrices ranged from 2 to 15 kPa, similar to the in vivo elasticity of the intima basement membrane and media layer. MSC seeded on rigid matrices (8-15 kPa) showed an increase in cell area compared with those seeded on soft matrices (2-5 kPa). Furthermore, the matrix elasticity guided the cells to express different vascular-specific phenotypes with high differentiation efficiency. Around 95% of MSC seeded on the 3-D matrices with an elasticity of 3 kPa showed Flk-1 endothelial markers within 24h, while only 20% of MSC seeded on the matrices with elasticity >8 kPa demonstrated Flk-1 marker. In contrast, ∼80% of MSC seeded on 3-D matrices with elasticity >8 kPa demonstrated smooth muscle α-actin marker within 24h, while fewer than 10% of MSC seeded on 3-D matrices with elasticity elasticity of the substrate could be a powerful tool for vascular tissue regeneration. Copyright © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Compressive Elasticity of Three-Dimensional Nanofiber Matrix Directs Mesenchymal Stem Cell Differentiation to Vascular Cells with Endothelial or Smooth Muscle Cell Markers

OpenAIRE

Wingate, Kathryn; Bonani, Walter; Tan, Yan; Bryant, Stephanie J.; Tan, Wei

2012-01-01

The importance of mesenchymal stem cell (MSC) in vascular regeneration is becoming increasingly recognized. However, few in vitro studies have been performed to identify the effects of environmental elasticity on the differentiation of MSC into vascular cell types. We utilized electrospinning and photopolymerization techniques to fabricate a 3D PEGdma nanofiber hydrogel matrix with a tunable elasticity for use as a cellular substrate. Compression testing demonstrated that the elastic modulus ...

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

Science.gov (United States)

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.

Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening

International Nuclear Information System (INIS)

Roche, R.

1983-12-01

A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

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

Directory of Open Access Journals (Sweden)

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.

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

A unified approach to fixed-order controller design via linear matrix inequalities

Directory of Open Access Journals (Sweden)

T. Iwasaki

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,-stabilization as a robust stabilization problem, and robust L∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type BGC+(BGCT+Q<0 for the unknown matrix G. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X∈1 and X−1∈2 where 1 and 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

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

Energy Technology Data Exchange (ETDEWEB)

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.

Elastic and piezoelectric fields around a quantum wire of zincblende heterostructures with interface elasticity effect

Science.gov (United States)

Ye, Wei; Liu, Yifei

2018-04-01

This work formulates the solutions to the elastic and piezoelectric fields around a quantum wire (QWR) with interface elasticity effect. Closed-form solutions to the piezoelectric potential field of zincblende QWR/matrix heterostructures grown along [111] crystallographic orientation are found and numerical results of InAs/InP heterostructures are provided as an example. The piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the QWR. Our results indicate that interface elasticity can significantly alter the elastic and piezoelectric fields near the interface. Additionally, when the elastic property of the QWR is considered to be anisotropic in contrary to the common isotropic assumption, piezoelectric potentials are found to be distinct near the interface, but the deviations are negligible at positions far away from the interface.

Two-Sided Estimates of Thermo-elastic Characteristics of Dispersed Inclusion Composites

Directory of Open Access Journals (Sweden)

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.

Isogeometric BDDC deluxe preconditioners for linear elasticity

KAUST Repository

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.

Isogeometric BDDC deluxe preconditioners for linear elasticity

KAUST Repository

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.

Co-effects of matrix low elasticity and aligned topography on stem cell neurogenic differentiation and rapid neurite outgrowth.

Science.gov (United States)

Yao, Shenglian; Liu, Xi; Yu, Shukui; Wang, Xiumei; Zhang, Shuming; Wu, Qiong; Sun, Xiaodan; Mao, Haiquan

2016-05-21

The development of novel biomaterials that deliver precise regulatory signals to direct stem cell fate for nerve regeneration is the focus of current intensive research efforts. In this study, a hierarchically aligned fibrillar fibrin hydrogel (AFG) that was fabricated through electrospinning and the concurrent molecular self-assembly process mimics both the soft and oriented features of nerve tissue, thus providing hybrid biophysical cues to instruct cell behavior in vitro and in vivo. The electrospun hydrogels were examined by scanning electron microscopy (SEM), polarized light microscopy, small angle X-ray scattering assay and atomic force microscopy (AFM), showing a hierarchically linear-ordered structure from the nanoscale to the macroscale with a soft elastic character (elasticity ∼1 kPa). We found that this low elasticity and aligned topography of AFG exhibit co-effects on promoting the neurogenic differentiation of human umbilical cord mesenchymal stem cells (hUMSCs) in comparison to random fibrin hydrogel (RFG) and tissue culture plate (TCP) control after two week cell culture in growth medium lacking supplementation with soluble neurogenic induction factors. In addition, AFG also induces dorsal root ganglion (DRG) neurons to rapidly project numerous long neurite outgrowths longitudinally along the AFG fibers for a total neurite extension distance of 1.96 mm in three days in the absence of neurotrophic factor supplementation. Moreover, the AFG implanted in a rat T9 dorsal hemisection spinal cord injury model was found to promote endogenous neural cell fast migration and axonal invasion along AFG fibers, resulting in aligned tissue cables in vivo. Our results suggest that matrix stiffness and aligned topography may instruct stem cell neurogenic differentiation and rapid neurite outgrowth, providing great promise for biomaterial design for applications in nerve regeneration.

Sonoelastography can be used to monitor the restoration of Achilles tendon elasticity after injury.

Science.gov (United States)

Gehmert, S; Jung, E M; Kügler, T; Klein, S; Gehmert, S; Zeitler, K; Loibl, M; Prantl, L

2012-12-01

The aim of the current study was to evaluate an ultrasound approach for depicting elastic recovery after stem cell application on injured Achilles tendons. A rabbit Achilles tendon injury model was used and randomized hind limbs received an extracellular matrix either with autologous mesenchymal stem cells (group 2, n = 6) or without (group 3, n = 6). The cells were harvested from the rabbits' nuchal fat body. Untreated Achilles tendons (group 1, n = 6) served as controls. Specimens were harvested after 8 weeks and analyzed longitudinally for elasticity using a high resolution 6-15 MHz matrix linear probe. For each tendon, real-time color-coded sonoelastography sequences were recorded for 20 seconds and 10 color histogram frames were obtained. Defined regions of interest (ROIs) were placed on the injury (n = 3) and on the adjacent uninjured tendon tissue (n = 3). In total, 180 measurements were obtained for semi-quantitative analysis. Repeated measures ANOVA demonstrated a higher elasticity for the stem cell-seeded matrix (group 2) in comparison to the unseeded matrix (group 3) (p tendon tissue treated with stem cell-seeded matrix (group 2) and the uninjured Achilles tendons (group 1) (p > 0.05). Moreover, no differences were found between the measurements at different points in time (p > 0.05). Our results indicate that autologous mesenchymal stem cell application successfully restores the mechanical properties of injured tendon tissue. Furthermore, sonoelastography makes it possible to monitor the elasticity of injured Achilles tendons. © Georg Thieme Verlag KG Stuttgart · New York.

Linear models in matrix form a hands-on approach for the behavioral sciences

CERN Document Server

Brown, Jonathon D

2014-01-01

This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum ...

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

Science.gov (United States)

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.

A unified approach to fixed-order controller design via linear matrix inequalities

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Iwasaki T.

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type B G C + ( B G C T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

International Nuclear Information System (INIS)

Garbow, B.

1984-01-01

Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

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

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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.

Exploiting elastic anharmonicity in aluminum nitride matrix for phase-synchronous frequency reference generation

Science.gov (United States)

Ghatge, Mayur; Tabrizian, Roozbeh

2018-03-01

A matrix of aluminum-nitride (AlN) waveguides is acoustically engineered to realize electrically isolated phase-synchronous frequency references through nonlinear wave-mixing. AlN rectangular waveguides are cross-coupled through a periodically perforated plate that is engineered to have a wide acoustic bandgap around a desirable frequency ( f1≈509 MHz). While the coupling plate isolates the matrix from resonant vibrations of individual waveguide constituents at f1, it is transparent to the third-order harmonic waves (3f1) that are generated through nonlinear wave-mixing. Therefore, large-signal excitation of the f1 mode in a constituent waveguide generates acoustic waves at 3f1 with an efficiency defined by elastic anharmonicity of the AlN film. The phase-synchronous propagation of the third harmonic through the matrix is amplified by a high quality-factor resonance mode at f2≈1529 MHz, which is sufficiently close to 3f1 (f2 ≅ 3f1). Such an architecture enables realization of frequency-multiplied and phase-synchronous, yet electrically and spectrally isolated, references for multi-band/carrier and spread-spectrum wireless communication systems.

Involutional ectropion and entropion: clinicopathologic correlation between horizontal eyelid laxity and eyelid extracellular matrix.

Science.gov (United States)

Damasceno, Renato Wendell; Osaki, Midori Hentona; Dantas, Paulo Elias Correa; Belfort, Rubens

2011-01-01

To investigate the clinicopathologic correlation between horizontal eyelid laxity and extracellular matrix components, such as collagen and elastic fibers, in involutional ectropion and entropion. Another goal was to compare the differences between involutional ectropion and entropion in regard to extracellular matrix content using computer-assisted morphometry. This clinicopathologic study included 20 consecutive patients with involutional ectropion (group 1) and 20 consecutive patients with involutional entropion (group 2). The pinch test was performed to measure horizontal eyelid laxity in both groups. Full-thickness eyelid biopsy specimens were examined by light microscopy and computer-assisted morphometry. The Mann-Whitney U test, the Pearson chi-square test, the Pearson correlation coefficient calculation, and a linear regression analysis were performed. All sections of specimens from patients in groups 1 and 2 revealed abnormal collagen and elastic fibers. The Pearson correlation coefficient revealed a significant negative correlation between horizontal eyelid laxity and extracellular matrix content in the eyelid skin, the pretarsal orbicularis oculi muscle, the perimeibomian tarsal stroma, and the intermeibomian tarsal stroma. Linear regression demonstrated that horizontal eyelid laxity is dependent upon extracellular matrix components in all eyelid regions. Collagen fiber content was significantly increased in specimens from patients in group 1 compared with specimens from patients in group 2. The present findings suggest that a reduction of collagen and elastic fibers may contribute to the development of excessive horizontal eyelid laxity in patients with involutional ectropion and entropion of the lower eyelid.

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

Czech Academy of Sciences Publication Activity Database

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

Elastic modulus of Al-Si/SiC metal matrix composites as a function of volume fraction

Energy Technology Data Exchange (ETDEWEB)

Santhosh Kumar, S; Rajasekharan, T [Powder Metallurgy Group, Defence Metallurgical Research Laboratory, Kanchanbagh PO, Hyderabad-500 058 (India); Seshu Bai, V [School of Physics, University of Hyderabad, Central University PO, Hyderabad-500 046 (India); Rajkumar, K V; Sharma, G K; Jayakumar, T, E-mail: dearsanthosh@gmail.co [Non-Destructive Evaluation Division, Indira Gandhi Center for Atomic Research, Kalpakkam, Chennai-603 102 (India)

2009-09-07

Aluminum alloy matrix composites have emerged as candidate materials for electronic packaging applications in the field of aerospace semiconductor electronics. Composites prepared by the pressureless infiltration technique with high volume fractions in the range 0.41-0.70 were studied using ultrasonic velocity measurements. For different volume fractions of SiC, the longitudinal velocity and shear velocity were found to be in the range of 7600-9300 m s{sup -1} and 4400-5500 m s{sup -1}, respectively. The elastic moduli of the composites were determined from ultrasonic velocities and were analysed as a function of the volume fraction of the reinforcement. The observed variation is discussed in the context of existing theoretical models for the effective elastic moduli of two-phase systems.

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

International Nuclear Information System (INIS)

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)

Microstructural evolution in inhomogeneous elastic media

International Nuclear Information System (INIS)

Jou, H.J.; Leo, P.H.; Lowengrub, J.S.

1997-01-01

We simulate the diffusional evolution of microstructures produced by solid state diffusional transformations in elastically stressed binary alloys in two dimensions. The microstructure consists of arbitrarily shaped precipitates embedded coherently in an infinite matrix. The precipitate and matrix are taken to be elastically isotropic, although they may have different elastic constants (elastically inhomogeneous). Both far-field applied strains and mismatch strains between the phases are considered. The diffusion and elastic fields are calculated using the boundary integral method, together with a small scale preconditioner to remove ill-conditioning. The precipitate-matrix interfaces are tracked using a nonstiff time updating method. The numerical method is spectrally accurate and efficient. Simulations of a single precipitate indicate that precipitate shapes depend strongly on the mass flux into the system as well as on the elastic fields. Growing shapes (positive mass flux) are dendritic while equilibrium shapes (zero mass flux) are squarish. Simulations of multiparticle systems show complicated interactions between precipitate morphology and the overall development of microstructure (i.e., precipitate alignment, translation, merging, and coarsening). In both single and multiple particle simulations, the details of the microstructural evolution depend strongly o the elastic inhomogeneity, misfit strain, and applied fields. 57 refs., 24 figs

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

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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.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Computation of the lamina stacking sequence effect on elastic moduli of a plain-weave Nicalon/SiC laminated composite with a [0/30/60] lay-up

International Nuclear Information System (INIS)

Zhao Wei; Yu Niann-i

1998-01-01

Estimation of the elastic modulus is important in engineering design. One difference between CFCCs (continuous fiber-reinforced ceramic-matrix composites), and CMCs (whisker, particulate, or short fiber-reinforced ceramic-matrix composites), is that the anisotropic behavior of CFCCs plays an important role in affecting their mechanical behavior. This feature may also contribute to the variation of elastic properties and strengths of CFCC. In this paper, a Fortran program is developed to quantify the lamina stacking sequence effect on the effective elastic moduli of the laminated CFCCs. The material for modeling is a plain-weave Nicalon fiber-reinforced silicon carbide (Nicalon/SiC) CFCCs. Results show that various stacking sequences within the CFCC (a [0/30/60] lay-up) will give different effective elastic moduli of the CFCCs. This trend leads to a variation of the slope of the linear portion on the flexural stress-strain curve, i.e., changing the position of the starting point of the non-linear portion, and the shape of the whole curve, which gives a different value of the peak stress in the curve. (orig.)

Elastic properties of Cs{sub 2}HgBr{sub 4} and Cs{sub 2}CdBr{sub 4} crystals

Energy Technology Data Exchange (ETDEWEB)

Kityk, A.V.; Zadorozhna, A.V.; Shchur, Y.I.; Martynyuk-Lototska, Y.I.; Burak, Y.; Vlokh, O.G. [Institute of Physical Optics, Lvov (Ukraine)

1998-12-31

Using ultrasonic velocity measurements, all components of the elastic constant matrix C{sub ij} , elastic compliances matrix S{sub ij}, and linear compressibility constants matrix K{sub ij} of orthorhombic Cs{sub 2}HgBr{sub 4} and Cs{sub 2}CdBr{sub 4} crystals have been determined over a wide temperature range, including the region of the phase transition from the normal to the incommensurate phase. Results obtained are considered within the framework of the phenomenological theory. Preliminary analysis of the acoustical properties at room temperature clearly indicates that both crystals are relatively important materials for acousto-optical applications. Copyright (1998) CSIRO Australia 16 refs., 1 tab. 8 figs. The URL for the electronic version of this article is http://www.publish.csiro.au/journals/ajp/electronic.html

Phase properties of elastic waves in systems constituted of adsorbed diatomic molecules on the (001) surface of a simple cubic crystal

Science.gov (United States)

Deymier, P. A.; Runge, K.

2018-03-01

A Green's function-based numerical method is developed to calculate the phase of scattered elastic waves in a harmonic model of diatomic molecules adsorbed on the (001) surface of a simple cubic crystal. The phase properties of scattered waves depend on the configuration of the molecules. The configurations of adsorbed molecules on the crystal surface such as parallel chain-like arrays coupled via kinks are used to demonstrate not only linear but also non-linear dependency of the phase on the number of kinks along the chains. Non-linear behavior arises for scattered waves with frequencies in the vicinity of a diatomic molecule resonance. In the non-linear regime, the variation in phase with the number of kinks is formulated mathematically as unitary matrix operations leading to an analogy between phase-based elastic unitary operations and quantum gates. The advantage of elastic based unitary operations is that they are easily realizable physically and measurable.

Linear Matrix Inequalities in Multirate Control over Networks

Directory of Open Access Journals (Sweden)

Ángel Cuenca

2012-01-01

Full Text Available This paper faces two of the main drawbacks in networked control systems: bandwidth constraints and timevarying delays. The bandwidth limitations are solved by using multirate control techniques. The resultant multirate controller must ensure closed-loop stability in the presence of time-varying delays. Some stability conditions and a state feedback controller design are formulated in terms of linear matrix inequalities. The theoretical proposal is validated in two different experimental environments: a crane-based test-bed over Ethernet, and a maglev based platform over Profibus.

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

Science.gov (United States)

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.

Matrix of transmission in structural dynamics

International Nuclear Information System (INIS)

Mukherjee, S.

1975-01-01

Within the last few years numerous papers have been published on the subject of matrix method in elasto-mechanics. 'Matrix of Transmission' is one of the methods in this field which has gained considerable attention in recent years. The basic philosophy adopted in this method is based on the idea of breaking up a complicated system into component parts with simple elastic and dynamic properties which can be readily expressed in matrix form. These component matrices are considered as building blocks, which are fitted together according to a set of predetermined rules which then provide the static and dynamic properties of the entire system. A common type of system occuring in engineering practice consists of a number of elements linked together end to end in the form of a chain. The 'Transfer Matrix' is ideally suited for such a system, because only successive multiplication is necessary to connect these elements together. The number of degrees of freedom and intermediate conditions present no difficulty. Although the 'Transfer Matrix' method is suitable for the treatment of branched and coupled systems its application to systems which do not have predominant chain topology is not effective. Apart from the requirement that the system be linearely elastic, no other restrictions are made. In this paper, it is intended to give a general outline and theoretical formulation of 'Transfer Matrix' and then its application to actual problems in structural dynamics related to seismic analysis. The natural frequencies of a freely vibrating elastic system can be found by applying proper end conditions. The end conditions will yield the frequency determinate to zero. By using a suitable numerical method, the natural frequencies and mode shapes are determined by making a frequency sweep within the range of interest. Results of an analysis of a typical nuclear building by this method show very close agreement with the results obtained by using ASKA and SAP IV program. Therefore

New computational method for non-LTE, the linear response matrix

International Nuclear Information System (INIS)

Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

1998-01-01

My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

Science.gov (United States)

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.

FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

Directory of Open Access Journals (Sweden)

N. A. Dudarenko

2014-09-01

Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.

Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

CERN Document Server

Li, Deng-Feng

2016-01-01

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

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

Science.gov (United States)

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.

Linear and Nonlinear Finite Elements.

Science.gov (United States)

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

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

International Nuclear Information System (INIS)

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

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

Science.gov (United States)

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

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

Science.gov (United States)

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.

Elastic-plastic dynamic analysis of a reactor building

International Nuclear Information System (INIS)

Umemura, Hajime; Tanaka, Hiroshi.

1976-01-01

The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)

Theory of atom displacements induced by fast electron elastic scattering in solids

International Nuclear Information System (INIS)

Cruz, C. M.; Pinera, I.; Abreu, Y.; Leyva, A.

2006-01-01

Present contribution deals with the theoretical description of the conditions favoring the occurrence of single fast electron elastic scattering in solids, leading to the displacement of atoms from their crystalline sites. Firstly, the Moliere-Bethe-Goudsmit-Saunderson theory of Multiple Electron Scattering is applied, determining the limiting angle θ l over which the single electron elastic scattering prevails over the multiple one, leading to the evaluation of the total macroscopic cross-section for single electron elastic scattering on the basis of the Mott-Rutherford differential cross-section. On the basis of single electron elastic scattering by atoms in the solid matrix, it was determined the relative number of Atom Displacements produced by the Gamma Radiation as a primary act, as well as the energy and linear momentum of the ejected atoms. The statistical distributions of single electron elastic scattering and of those inducing Atom Displacements at different electron initial energies in comparison with the others electron inelastic scattering channels are discussed, where the statistical sampling methods on the basis of the rejection one where applied simulating different practical situations. (Full text)

Filamin A Mediates Wound Closure by Promoting Elastic Deformation and Maintenance of Tension in the Collagen Matrix

Science.gov (United States)

Mohammadi, Hamid; Pinto, Vanessa I.; Wang, Yongqiang; Hinz, Boris; Janmey, Paul A.; McCulloch, Christopher A.

2016-01-01

Cell-mediated remodeling and wound closure are critical for efficient wound healing, but the contribution of actin-binding proteins to contraction of the extracellular matrix is not defined. We examined the role of filamin A (FLNa), an actin filament cross-linking protein, in wound contraction and maintenance of matrix tension. Conditional deletion of FLNa in fibroblasts in mice was associated with ~ 4 day delay of full-thickness skin wound contraction compared with wild-type (WT) mice. We modeled the healing wound matrix using cultured fibroblasts plated on grid-supported collagen gels that create lateral boundaries, which are analogues to wound margins. In contrast to WT cells, FLNa knockdown (KD) cells could not completely maintain tension when matrix compaction was resisted by boundaries, which manifested as relaxed matrix tension. Similarly, WT cells on cross-linked collagen, which requires higher levels of sustained tension, exhibited approximately fivefold larger deformation fields and approximately twofold greater fiber alignment compared with FLNa KD cells. Maintenance of boundary-resisted tension markedly influenced the elongation of cell extensions: in WT cells, the number (~50%) and length (~300%) of cell extensions were greater than FLNa KD cells. We conclude that FLNa is required for wound contraction, in part by enabling elastic deformation and maintenance of tension in the matrix. PMID:26134946

The detection of influential subsets in linear regression using an influence matrix

OpenAIRE

Peña, Daniel; Yohai, Víctor J.

1991-01-01

This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...

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

International Nuclear Information System (INIS)

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)

Blocky inversion of multichannel elastic impedance for elastic parameters

Science.gov (United States)

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.

Elasticity problems in domains with nonsmooth boundaries

International Nuclear Information System (INIS)

Esparza, David

2001-01-01

In the present work we study the behaviour of elastic stress fields in domains with non-regular boundaries. We consider three-dimensional problems in elastic media with thin conical defects (inclusions or cavities) and analyse the stress singularity at their vertices. To construct asymptotic expansions for the stress and displacement fields in terms of a small parameter ε related to the 'thickness' of the defect, we employ a technique based on the work by Kondrat'ev, Maz'ya, Nazarov and Plamenevskii. We first study the stress distribution in an elastic body with a thin conical notch. We derive an asymptotic representation for the stress singularity exponent by reducing the original problem to a spectral problem for a 9x9 matrix. The elements of this matrix are found to depend upon the geometry of the cross-section of the notch and the elastic properties of the medium. We specify the sets of eigenvalues and the corresponding eigenvectors for a circular, elliptical, 'triangular' and 'square' cross-section, and show that the strongest singularity is associated with the 'triangular' cross-section, and is generated by a non-axisymmetric load. We then analyse the stress distribution near a thin conical inclusion which is allowed to slide freely along its axis. We derive the representation for the stress singularity exponent for the case of a circular conical inclusion whose elastic properties differ from those of the medium. In the last chapter we study the stress distribution in the vicinity of a thin 'coated' conical inclusion. We show that a soft thin coating (perfectly bonded to the inclusion and the surrounding material) can be replaced by a so-called linear interface at which the normal displacement is discontinuous, and the stresses are proportional to the 'jump' in the normal displacement across the coating. We analyse the effect of the properties of the coating on the stress singularity exponent and compare the results with those for a perfectly bonded

Finite element historical deformation analysis in piecewise linear plasticity by mathematical programming

International Nuclear Information System (INIS)

De Donato, O.; Parisi, M.A.

1977-01-01

When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)

Classification of the linear canonical transformation and its associated real symplectic matrix

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2007-01-01

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

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

OpenAIRE

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...

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

Directory of Open Access Journals (Sweden)

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.

Positron interactions with water–total elastic, total inelastic, and elastic differential cross section measurements

International Nuclear Information System (INIS)

Tattersall, Wade; Chiari, Luca; Machacek, J. R.; Anderson, Emma; Sullivan, James P.; White, Ron D.; Brunger, M. J.; Buckman, Stephen J.; Garcia, Gustavo; Blanco, Francisco

2014-01-01

Utilising a high-resolution, trap-based positron beam, we have measured both elastic and inelastic scattering of positrons from water vapour. The measurements comprise differential elastic, total elastic, and total inelastic (not including positronium formation) absolute cross sections. The energy range investigated is from 1 eV to 60 eV. Comparison with theory is made with both R-Matrix and distorted wave calculations, and with our own application of the Independent Atom Model for positron interactions

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry.

Science.gov (United States)

Sherrit, Stewart; Masys, Tony J; Wiederick, Harvey D; Mukherjee, Binu K

2011-09-01

We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present the transform equations, in reduced matrix form, to other consistent material constant sets. We discuss the propagation of errors in going from one material data set to another and look at the limitations inherent in direct calculations of other useful coefficients from the data.

Emergence of linear elasticity from the atomistic description of matter

Energy Technology Data Exchange (ETDEWEB)

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.

Emergence of linear elasticity from the atomistic description of matter

International Nuclear Information System (INIS)

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.

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

International Nuclear Information System (INIS)

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.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

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

International Nuclear Information System (INIS)

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

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Advanced topics in linear algebra weaving matrix problems through the Weyr form

CERN Document Server

O'Meara, Kevin; Vinsonhaler, Charles

2011-01-01

The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the

Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

Directory of Open Access Journals (Sweden)

Darunee Hunwisai

2017-01-01

Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

Printing Three-Dimensional Heterogeneities in the Elastic Modulus of an Elastomeric Matrix.

Science.gov (United States)

Abdel Fattah, Abdel Rahman; Ghosh, Suvojit; Puri, Ishwar K

2016-05-04

We present a rapid and controllable method to create microscale heterogeneities in the 3D stiffness of a soft material by printing patterns with a ferrofluid ink. An ink droplet moved through a liquid polydimethylsiloxane (PDMS) volume using an externally applied magnetic field sheds clusters of magnetic nanoparticles (MNPs) in its wake. By varying the field spatiotemporally, a well-defined three-dimensional curvilinear feature is printed that contains MNP clusters. Subsequent cross-linking of the PDMS preserves the feature in place after the magnetic field is removed. Since the ferrofluid ink interferes with the cross-linking of PDMS, a 3D print containing ink density variations leads to corresponding spatial deviations in the elastic modulus of the matrix. The modulus is mapped in the experiments with atomic force microscopy. This rapid method to print 3D heterogeneities in soft matter promises the ability to mimic mechanical variations that occur in natural biomaterials.

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

International Nuclear Information System (INIS)

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

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

Science.gov (United States)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

A Linear Theory for Pretwisted Elastic Beams

DEFF Research Database (Denmark)

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...

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

Directory of Open Access Journals (Sweden)

N. S. Dzhaliuk

2017-07-01

Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

Fundamental Matrix for a Class of Point Delay Linear Systems

International Nuclear Information System (INIS)

Sen, M. de la; Alastruey, C. F.

1998-01-01

It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)

Comparison of Damage Models for Predicting the Non-Linear Response of Laminates Under Matrix Dominated Loading Conditions

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Rose, Cheryl A.

2010-01-01

Five models for matrix damage in fiber reinforced laminates are evaluated for matrix-dominated loading conditions under plane stress and are compared both qualitatively and quantitatively. The emphasis of this study is on a comparison of the response of embedded plies subjected to a homogeneous stress state. Three of the models are specifically designed for modeling the non-linear response due to distributed matrix cracking under homogeneous loading, and also account for non-linear (shear) behavior prior to the onset of cracking. The remaining two models are localized damage models intended for predicting local failure at stress concentrations. The modeling approaches of distributed vs. localized cracking as well as the different formulations of damage initiation and damage progression are compared and discussed.

Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

KAUST Repository

Charara, Ali; Keyes, David E.; Ltaief, Hatem

2017-01-01

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

KAUST Repository

Charara, Ali

2017-03-06

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

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

International Nuclear Information System (INIS)

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

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

International Nuclear Information System (INIS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-01-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders. -- Highlights: ► New superposition T-matrix code is applied to soot aerosols. ► Quasi-Rayleigh side-scattering peak in linear depolarization (LD) is explained. ► LD measurements can be used for morphological characterization of soot aerosols

A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

Science.gov (United States)

Liu, Tao; Huang, Jie

2017-04-17

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

Aging linear viscoelasticity of matrix-inclusion composite materials featuring ellipsoidal inclusions

OpenAIRE

LAVERGNE, Francis; SAB, Karam; SANAHUJA, Julien; BORNERT, Michel; TOULEMONDE, Charles

2016-01-01

A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-a...

Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

DEFF Research Database (Denmark)

Tarp-Johansen, Niels Jacob; Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.......Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under......-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure...

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

Science.gov (United States)

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.

Phason elasticity and surface roughening

International Nuclear Information System (INIS)

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

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

International Nuclear Information System (INIS)

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

Matrix dimensions bias demographic inferences: implications for comparative plant demography.

Science.gov (United States)

Salguero-Gómez, Roberto; Plotkin, Joshua B

2010-12-01

While the wealth of projection matrices in plant demography permits comparative studies, variation in matrix dimensions complicates interspecific comparisons. Collapsing matrices to a common dimension may facilitate such comparisons but may also bias the inferred demographic parameters. Here we examine how matrix dimension affects inferred demographic elasticities and how different collapsing criteria perform. We analyzed 13 x 13 matrices representing nine plant species, collapsing these matrices (i) into even 7 x 7, 5 x 5, 4 x 4, and 3 x 3 matrices and (ii) into 5 x 5 matrices using different criteria. Stasis and fecundity elasticities increased when matrix dimension was reduced, whereas those of progression and retrogression decreased. We suggest a collapsing criterion that minimizes dissimilarities between the original- and collapsed-matrix elasticities and apply it to 66 plant species to study how life span and growth form influence the relationship between matrix dimension and elasticities. Our analysis demonstrates that (i) projection matrix dimension has significant effects on inferred demographic parameters, (ii) there are better-performing methods than previously suggested for standardizing matrix dimension, and (iii) herbaceous perennial projection matrices are particularly sensitive to changes in matrix dimensionality. For comparative demographic studies, we recommend normalizing matrices to a common dimension by collapsing higher classes and leaving the first few classes unaltered.

Matrix completion by deep matrix factorization.

Science.gov (United States)

Fan, Jicong; Cheng, Jieyu

2018-02-01

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

Directory of Open Access Journals (Sweden)

P. Bumroongsri

2014-01-01

Full Text Available An offline model predictive control (MPC algorithm for linear parameter varying (LPV systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

Collusion and the elasticity of demand

OpenAIRE

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.

Elastic properties of spherically anisotropic piezoelectric composites

International Nuclear Information System (INIS)

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)

Elastic metamaterial beam with remotely tunable stiffness

Energy Technology Data Exchange (ETDEWEB)

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.

Elastic metamaterial beam with remotely tunable stiffness

Science.gov (United States)

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.

Wave chaos in acoustics and elasticity

International Nuclear Information System (INIS)

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)

Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix --- The full report.

OpenAIRE

Ben Gharbia , Ibtihel; Gilbert , Jean Charles

2012-01-01

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q)=0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may...

Elastic-plastic deformation of fiber composites with a tetragonal structure

Energy Technology Data Exchange (ETDEWEB)

Makarova, E.IU.; Svistkova, L.A. (Permskii Politekhnicheskii Institut, Perm (USSR))

1991-02-01

Results of numerical solutions are presented for elastic-plastic problems concerning arbitrary loading of unidirectional composites in the transverse plane. The nucleation and evolution of microplastic zones in the matrix and the effect of this process on the macroscopic characteristics of the composite are discussed. Attention is also given to the effect of the fiber shape on the elastic-plastic deformation of the matrix and to deformation paths realized in simple microdeformation processes. The discussion is illustrated by results obtained for a composite consisting of a VT1-0 titanium alloy matrix reinforced by Ti-Mo fibers.

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

KAUST Repository

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

The visco-elastic multilayer program VEROAD

NARCIS (Netherlands)

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

Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour

DEFF Research Database (Denmark)

Ottosen, N. Saabye; Gunneskov, O.

1985-01-01

to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

Science.gov (United States)

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.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Elastic K-means using posterior probability.

Science.gov (United States)

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model.

Unified approach to numerical transfer matrix methods for disordered systems: applications to mixed crystals and to elasticity percolation

International Nuclear Information System (INIS)

Lemieux, M.A.; Breton, P.; Tremblay, A.M.S.

1985-01-01

It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size analysis of critical exponents for the central force percolation universality class are presented

A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber-Reinforced Composites

Directory of Open Access Journals (Sweden)

Melek Usal

2010-01-01

Full Text Available The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.

Hyperplasia of elastic tissue in hepatic schistosomal fibrosis

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Zilton A. Andrade

1991-12-01

Full Text Available Elastic tissue hyperplasia, revealed by means of histological, immunocytochemical and ultrastructural methods, appeared as a prominent change in surgical liver biopsies taken from 61 patients with schistosomal periportal and septal fibrosis. Such hyperplasia was absent in ecperimental murine schistosomiasis, including mice with "pipe-stem" fibrosis. Displaced connective tissue cells in periportal areas, such as smooth muscle cells, more frequently observed in human material, could be the site of excessive elastin synthesis, and could explain the differences observed in human and experimental materials. Elastic tissue, sometimes represented by its microfibrillar components, also appeared to be more condensed in areas of matrix (collagen degradation, suggesting a participation of this tissue in the remodelling of the extracellular matrix. By its rectratile properties elastic tissue hyperplasia in hepatic schistosomiasis can cause vascular narrowing and thus play a role in the pathogenesis of portal hypeertension.

How can cells sense the elasticity of a substrate? An analysis using a cell tensegrity model

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G De Santis

2011-10-01

Full Text Available A eukaryotic cell attaches and spreads on substrates, whether it is the extracellular matrix naturally produced by the cell itself, or artificial materials, such as tissue-engineered scaffolds. Attachment and spreading require the cell to apply forces in the nN range to the substrate via adhesion sites, and these forces are balanced by the elastic response of the substrate. This mechanical interaction is one determinant of cell morphology and, ultimately, cell phenotype. In this paper we use a finite element model of a cell, with a tensegrity structure to model the cytoskeleton of actin filaments and microtubules, to explore the way cells sense the stiffness of the substrate and thereby adapt to it. To support the computational results, an analytical 1D model is developed for comparison. We find that (i the tensegrity hypothesis of the cytoskeleton is sufficient to explain the matrix-elasticity sensing, (ii cell sensitivity is not constant but has a bell-shaped distribution over the physiological matrix-elasticity range, and (iii the position of the sensitivity peak over the matrix-elasticity range depends on the cytoskeletal structure and in particular on the F-actin organisation. Our model suggests that F-actin reorganisation observed in mesenchymal stem cells (MSCs in response to change of matrix elasticity is a structural-remodelling process that shifts the sensitivity peak towards the new value of matrix elasticity. This finding discloses a potential regulatory role of scaffold stiffness for cell differentiation.

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

Science.gov (United States)

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

Science.gov (United States)

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Linear algebra

CERN Document Server

Liesen, Jörg

2015-01-01

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

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

International Nuclear Information System (INIS)

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

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

International Nuclear Information System (INIS)

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.

Numerical Modeling and Experimental Study of Elastic-Plastic Behavior of Carbon Nanotubes Reinforced Nanocompsites of PA6/NBR Using a Microfinite Element Model

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Mir Hamid Reza Ghoreishy

2014-12-01

Full Text Available A theoretical and experimental study was conducted on the mechanical behavior of nanocomposites based on PA6/NBR thermoplastic elastomer reinforced by single wall carbon nanotubes (SWNTs. The selected samples include 60 and 40% NBR with 0.5, 1.0 and 1.5% SWNT. The modeling methodology was based on the use of two-dimensional "representative volume elements" (RVE. The Abaqus/standard code was employed to carry out the non-linear finite element calculations. Plane stress elements were selected for discretization of the domain. Linear elastic and isotropic hardening elastic-plastic models were utilized to describe the mechanical behaviors of the carbon nanotubes and polymer matrix, respectively. The samples were simultaneously prepared using melt mixing method in a laboratory internal mixer. Different orientations including regular in both longitudinal and transverse directions and random were selected for the nanotubes in the matrix. Also, two structural forms including hollow and solid for the carbon nanotubes were chosen. The highest and lowest predicted moduli were obtained from models with regular orientation in longitudinal and transverse directions, respectively. On the other hand, comparison between the predicted elastic modulus and elastic-plastic behaviors of the samples with their corresponding experimental data revealed that the random orientation in conjunction with hollow structural form gives the best results. Moreover, the selected material model for the thermoplastic elastomer i.e., isotropic hardening can precisely describe the mechanical behavior in both tension and compression modes. It is also concluded that the main source of error in this modeling methodology can be attributed to the effects of interface between polymer and nanotubes and orientation in perpendicular directions.

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

Science.gov (United States)

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.

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

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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.

Remarks on orthotropic elastic models applied to wood

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Nilson Tadeu Mascia

2006-09-01

Full Text Available Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal, R( radial and T(tangential are coincident with the Cartesian axes (x, y, z, is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young´s modulus and shear modulus, with fiber orientation are presented.

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

Science.gov (United States)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Modeling of a light elastic beam by a system of rigid bodies

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Šalinić Slaviša

2004-01-01

Full Text Available This paper has shown that a light elastic beam, in the case of small elastic deformations, can be modeled by a kinematic chain without branching composed of rigid bodies which are connected by passive revolute or prismatic joints with corresponding springs in them. Elastic properties of the beam are modeled by the springs introduced. The potential energy of the elastic beam is expressed as a function of components of the vector of elastic displacement and the vector of elastic rotation calculated for the elastic centre of the beam, which results in the diagonal stiffness matrix of the beam. As the potential energy of the introduced system of bodies with springs is expressed in the function of relative joint displacements, the diagonal stiffness matrix is obtained. In addition, these two stiffness matrices are equal. The modeling process has been demonstrated on the example of an elastic beam rotating about a fixed vertical axis, with a rigid body whose mass is considerably larger than the beam mass fixed to its free end. Differential equations of motion have been formed for this mechanical system. The modeling technique described here aims at expanding of usage of well developed methods of dynamics of systems of rigid bodies to the analysis of systems with elastic bodies. .

Elastic least-squares reverse time migration

KAUST Repository

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.

Elastic least-squares reverse time migration

KAUST Repository

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.

Parallelism in matrix computations

CERN Document Server

Gallopoulos, Efstratios; Sameh, Ahmed H

2016-01-01

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

Sensitivity of the elastic scattering matrix elements to the range of the inelastic potentials

International Nuclear Information System (INIS)

Rawitscher, G.H.; Rasoanaivo, R.Y.

1983-01-01

The solution to a system of coupled equations is examined with regard to the effect of the long range part of the inelastic potentials upon the elastic phase shifts. It is found that those parts of the inelastic potentials which occur beyond the range of the elastic to inelastic transition potentials affect the elastic phase shifts in only a minor way. The proof is given theoretically by means of a Green's function formulation which includes the long range part of the inelastic potentials perturbatively. When applied to the calculation of the effect of breakup on the deuteron-nucleus elastic scattering, the argument confirms the finding that errors in the long range part of the potentials in the breakup channels do not sensitively affect the elastic deuteron scattering cross section. This result explains why the elastic scattering is not very sensitive to the choice of the discretization procedure of the breakup space

A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

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Min Sun

2014-01-01

Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

Effects of ionizing radiation on extracellular matrix

Energy Technology Data Exchange (ETDEWEB)

Mohamed, F. [School of Physics, University of Exeter, Exeter EX44QL (United Kingdom)], E-mail: f.mohamed@ex.ac.uk; Bradley, D.A. [Department of Physics, University of Surrey, Guildford GU72XH (United Kingdom); Winlove, C.P. [School of Physics, University of Exeter, Exeter EX44QL (United Kingdom)

2007-09-21

The extracellular matrix is a ubiquitous and important component of tissues. We investigated the effects of ionizing radiation on the physical properties of its principal macromolecular components, pericardial collagen, ligament elastin and hyaluronan, a representative glycosaminoglycan. Samples were exposed to X-rays from an electron linear accelerator in the range of 10-100 Gy to cover the range of irradiation exposure during radiotherapy. A uniaxial mechanical testing protocol was used to characterize the fibrous proteins. For pericardial tissue the major change was an increase in the elastic modulus in the toe region of the curve ({<=}20% strain), from 23{+-}18 kPa for controls to 57{+-}22 kPa at a dose of 10 Gy (p=0.01, {alpha}=0.05). At larger strain ({>=}20% strain), the elastic modulus in the linear region decreased from 1.92{+-}0.70 MPa for control pericardium tissue to 1.31{+-}0.56 MPa (p=0.01, {alpha}=0.05) for 10 Gy X-irradiated sample. Similar observations have been made previously on tendon collagen at larger strains. For elastin, the stress-strain relationship was linear up to 30% strain, but the elastic modulus decreased significantly with irradiation (controls 626{+-}65 kPa, irradiated 474{+-}121 kPa (p=0.02, {alpha}=0.05), at 10 Gy X-irradiation). The results suggest that for collagen the primary effect of irradiation is generation of additional cross-links, while for elastin chain scissions are important. The viscosity of HA (at 1.25% w/v and 0.125% w/v) was measured by both cone and plate and capillary viscometry, the former providing measurement at uniform shear rate and the latter providing a more sensitive indication of changes at low viscosity. Both techniques revealed a dose-dependent reduction in viscosity (from 3400{+-}194 cP for controls to 1500{+-}88 cP at a shear rate of 2 s{sup -1} and dose of 75 Gy), again suggesting depolymerization.

Effects of ionizing radiation on extracellular matrix

International Nuclear Information System (INIS)

Mohamed, F.; Bradley, D.A.; Winlove, C.P.

2007-01-01

The extracellular matrix is a ubiquitous and important component of tissues. We investigated the effects of ionizing radiation on the physical properties of its principal macromolecular components, pericardial collagen, ligament elastin and hyaluronan, a representative glycosaminoglycan. Samples were exposed to X-rays from an electron linear accelerator in the range of 10-100 Gy to cover the range of irradiation exposure during radiotherapy. A uniaxial mechanical testing protocol was used to characterize the fibrous proteins. For pericardial tissue the major change was an increase in the elastic modulus in the toe region of the curve (≤20% strain), from 23±18 kPa for controls to 57±22 kPa at a dose of 10 Gy (p=0.01, α=0.05). At larger strain (≥20% strain), the elastic modulus in the linear region decreased from 1.92±0.70 MPa for control pericardium tissue to 1.31±0.56 MPa (p=0.01, α=0.05) for 10 Gy X-irradiated sample. Similar observations have been made previously on tendon collagen at larger strains. For elastin, the stress-strain relationship was linear up to 30% strain, but the elastic modulus decreased significantly with irradiation (controls 626±65 kPa, irradiated 474±121 kPa (p=0.02, α=0.05), at 10 Gy X-irradiation). The results suggest that for collagen the primary effect of irradiation is generation of additional cross-links, while for elastin chain scissions are important. The viscosity of HA (at 1.25% w/v and 0.125% w/v) was measured by both cone and plate and capillary viscometry, the former providing measurement at uniform shear rate and the latter providing a more sensitive indication of changes at low viscosity. Both techniques revealed a dose-dependent reduction in viscosity (from 3400±194 cP for controls to 1500±88 cP at a shear rate of 2 s -1 and dose of 75 Gy), again suggesting depolymerization

Advanced linear algebra for engineers with Matlab

CERN Document Server

Dianat, Sohail A

2009-01-01

Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu

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

Science.gov (United States)

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.

Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer-matrix composite.

Science.gov (United States)

Duan, Yuanyuan; Griggs, Jason A

2015-06-01

Further investigations are required to evaluate the mechanical behaviour of newly developed polymer-matrix composite (PMC) blocks for computer-aided design/computer-aided manufacturing (CAD/CAM) applications. The purpose of this study was to investigate the effect of elasticity on the stress distribution in dental crowns made of glass-ceramic and PMC materials using finite element (FE) analysis. Elastic constants of two materials were determined by ultrasonic pulse velocity using an acoustic thickness gauge. Three-dimensional solid models of a full-coverage dental crown on a first mandibular molar were generated based on X-ray micro-CT scanning images. A variety of load case-material property combinations were simulated and conducted using FE analysis. The first principal stress distribution in the crown and luting agent was plotted and analyzed. The glass-ceramic crown had stress concentrations on the occlusal surface surrounding the area of loading and the cemented surface underneath the area of loading, while the PMC crown had only stress concentration on the occlusal surface. The PMC crown had lower maximum stress than the glass-ceramic crown in all load cases, but this difference was not substantial when the loading had a lateral component. Eccentric loading did not substantially increase the maximum stress in the prosthesis. Both materials are resistant to fracture with physiological occlusal load. The PMC crown had lower maximum stress than the glass-ceramic crown, but the effect of a lateral loading component was more pronounced for a PMC crown than for a glass-ceramic crown. Knowledge of the stress distribution in dental crowns with low modulus of elasticity will aid clinicians in planning treatments that include such restorations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Unified continuum damage model for matrix cracking in composite rotor blades

Energy Technology Data Exchange (ETDEWEB)

Pollayi, Hemaraju; Harursampath, Dineshkumar [Nonlinear Multifunctional Composites - Analysis and Design Lab (NMCAD Lab) Department of Aerospace Engineering Indian Institute of Science Bangalore - 560012, Karnataka (India)

2015-03-10

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic load.

Unified continuum damage model for matrix cracking in composite rotor blades

International Nuclear Information System (INIS)

Pollayi, Hemaraju; Harursampath, Dineshkumar

2015-01-01

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic load

The development of an algebraic multigrid algorithm for symmetric positive definite linear systems

Energy Technology Data Exchange (ETDEWEB)

Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)

1996-12-31

An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.

Elastic stiffnesses of an Nb-Ti/Cu-composite superconductive wire

Science.gov (United States)

Kim, Sudook; Ledbetter, Hassel; Ogi, Hirotsugu

2000-09-01

Elastic-stiffness coefficients were determined on a 1.4-mm-diameter wire consisting of superconducting Nb-Ti fibers in a copper matrix, with a polyvinyl-resin coating. The matrix contained 324 Nb-Ti fibers. An electromagnetic-acoustic-resonance method was used to obtain five independent elastic-stiffness coefficients assuming transverse-isotropic symmetry. From these we calculated Young moduli, bulk modulus, and principal Poisson ratios. As a check, we used a mechanical-impulse-excitation method to directly measure the Young modulus in the fiber direction. The three-phase composite wire showed a 10% anisotropy in the Young modulus.

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

Science.gov (United States)

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.

Prediction of elastic properties for polymer-particle nanocomposites exhibiting an interphase

International Nuclear Information System (INIS)

Deng Fei; Van Vliet, Krystyn J

2011-01-01

Particle-polymer nanocomposites often exhibit mechanical properties described poorly by micromechanical models that include only the particle and matrix phases. Existence of an interfacial region between the particle and matrix, or interphase, has been posited and indirectly demonstrated to account for this effect. Here, we present a straightforward analytical approach to estimate effective elastic properties of composites comprising particles encapsulated by an interphase of finite thickness and distinct elastic properties. This explicit solution can treat nanocomposites that comprise either physically isolated nanoparticles or agglomerates of such nanoparticles; the same framework can also treat physically isolated nanoparticle aggregates or agglomerates of such aggregates. We find that the predicted elastic moduli agree with experiments for three types of particle-polymer nanocomposites, and that the predicted interphase thickness and stiffness of carbon black-rubber nanocomposites are consistent with measured values. Finally, we discuss the relative influence of the particle-polymer interphase thickness and stiffness to identify maximum possible changes in the macroscale elastic properties of such materials.

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

Energy Technology Data Exchange (ETDEWEB)

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.

Non-linear waves in heterogeneous elastic rods via homogenization

KAUST Repository

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.

Elastic plastic fracture mechanics

International Nuclear Information System (INIS)

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)

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

NARCIS (Netherlands)

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

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

Energy Technology Data Exchange (ETDEWEB)

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.

Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede

2004-01-01

This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

vSmartMOM: A vector matrix operator method-based radiative transfer model linearized with respect to aerosol properties

International Nuclear Information System (INIS)

Sanghavi, Suniti; Davis, Anthony B.; Eldering, Annmarie

2014-01-01

In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions. We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (60°), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function. We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector [I,Q,U,V] as well as the more practical use of only [I,Q,U]. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes

Elastic limit and microplastic response of hardened steels

Energy Technology Data Exchange (ETDEWEB)

Zaccone, M.A. (McDonnell Douglas Aerospace Co., St. Louis, MO (United States)); Krauss, G. (Colorado School of Mines, Golden, CO (United States). Dept. of Metallurgical and Materials Engineering)

1993-10-01

Tempered martensite-retained austenite microstructures were produced by direct quenching a series of 41XX medium carbon steels, direct quenching and reheating a series of five 0.8C-Cr-Ni-Mo steels and intercritically austenitizing at various temperatures, and quenching a SAE 52100 steel. All specimens were tempered either at 150 C or at 200 C. Specimens were subjected to compression and tension testing in the microstrain regime to determine the elastic limits and microplastic response of the microstructures. The retained austenite and matrix carbon content of the intercritically austenized specimens were measured by X-ray diffraction and Mossbauer spectroscopy. The elastic limit of the microstructures decreases with increasing amounts of retained austenite. Refining of the austenite distribution increases the elastic limit. Low elastic limits are mainly due to low flow stresses in the austenite and not internal stresses. The elastic limit correlates with the largest austenite free-mean path by a Hall-Petch type equation. The elastic limit increases with decreasing intercritical austenitizing temperature in the SAE 52100 due to a lower carbon content in the matrix reducing the retained austenite levels and retained carbides that refine grain size and, therefore, the austenite distribution in quenched specimens. In the microplastic region, the strain is accommodated by successively smaller austenite regions until the flow strength matches that of the martensite. Reheating and quenching refines the microstructure and renders the austenite unstable in the microplastic regime, causing transformation of the austenite to martensite by a strain-induced mechanism. The transformation of austenite to martensite occurs by a stress-assisted mechanism in medium carbon steels. The low elastic limits in medium carbon steels were due to the inability of the strain from the stress-assisted transformation to balance the plastic strain accumulated in the austenite.

Laminin and biomimetic extracellular elasticity enhance functional differentiation in mammary epithelia

Energy Technology Data Exchange (ETDEWEB)

Alcaraz, Jordi; Xu, Ren; Mori, Hidetoshi; Nelson, Celeste M.; Mroue, Rana; Spencer, Virginia A.; Brownfield, Doug; Radisky, Derek C.; Bustamante, Carlos; Bissell, Mina J.

2008-10-20

In the mammary gland, epithelial cells are embedded in a 'soft' environment and become functionally differentiated in culture when exposed to a laminin-rich extracellular matrix gel. Here, we define the processes by which mammary epithelial cells integrate biochemical and mechanical extracellular cues to maintain their differentiated phenotype. We used single cells cultured on top of gels in conditions permissive for {beta}-casein expression using atomic force microscopy to measure the elasticity of the cells and their underlying substrata. We found that maintenance of {beta}-casein expression required both laminin signalling and a 'soft' extracellular matrix, as is the case in normal tissues in vivo, and biomimetic intracellular elasticity, as is the case in primary mammary epithelial organoids. Conversely, two hallmarks of breast cancer development, stiffening of the extracellular matrix and loss of laminin signalling, led to the loss of {beta}-casein expression and non-biomimetic intracellular elasticity. Our data indicate that tissue-specific gene expression is controlled by both the tissues unique biochemical milieu and mechanical properties, processes involved in maintenance of tissue integrity and protection against tumorigenesis.

Controlling elastic waves with small phononic crystals containing rigid inclusions

KAUST Repository

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.

Stressed-deformed state of mountain rocks in elastic stage and between elasticity

Directory of Open Access Journals (Sweden)

Samedov A.M.

2017-12-01

destroy as a plastic material. In the elastic stage, the link between stress and strain is linear.

Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation

Science.gov (United States)

Huebsch, Nathaniel; Lippens, Evi; Lee, Kangwon; Mehta, Manav; Koshy, Sandeep T.; Darnell, Max C.; Desai, Rajiv M.; Madl, Christopher M.; Xu, Maria; Zhao, Xuanhe; Chaudhuri, Ovijit; Verbeke, Catia; Kim, Woo Seob; Alim, Karen; Mammoto, Akiko; Ingber, Donald E.; Duda, Georg N.; Mooney, David J.

2015-12-01

The effectiveness of stem cell therapies has been hampered by cell death and limited control over fate. These problems can be partially circumvented by using macroporous biomaterials that improve the survival of transplanted stem cells and provide molecular cues to direct cell phenotype. Stem cell behaviour can also be controlled in vitro by manipulating the elasticity of both porous and non-porous materials, yet translation to therapeutic processes in vivo remains elusive. Here, by developing injectable, void-forming hydrogels that decouple pore formation from elasticity, we show that mesenchymal stem cell (MSC) osteogenesis in vitro, and cell deployment in vitro and in vivo, can be controlled by modifying, respectively, the hydrogel’s elastic modulus or its chemistry. When the hydrogels were used to transplant MSCs, the hydrogel’s elasticity regulated bone regeneration, with optimal bone formation at 60 kPa. Our findings show that biophysical cues can be harnessed to direct therapeutic stem cell behaviours in situ.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Science.gov (United States)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

International Nuclear Information System (INIS)

Qiu, S.; Clausen, B.; Padula, S.A.; Noebe, R.D.; Vaidyanathan, R.

2011-01-01

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

Structure of 14C via elastic and inelastic neutron scattering from 13C: Measurement, R-matrix analysis, and shell model calculations

International Nuclear Information System (INIS)

Resler, D.A.

1987-03-01

The specific purpose of this work is to provide a better understanding of the 14 C level structure; the general purpose is to provide the details for using shell model calculations in R-matrix analyses. Using the TOF facilities of the Ohio University Accelerator Laboratory, the elastic and first 3 inelastic differential scattering cross sections for 13 C + n were measured at 69 energies for 4.5 ≤ E/sub n/ ≤ 11 MeV. A multiple scattering code was developed which provided a simulation of the experimental scattering process allowing accurate corrections to the small inelastic data. The integrated 13 C(n,α) 10 Be cross section is estimated. The sequential 2n-decay of 14 C states populated by 13 C + n was observed. A shell model code was developed. Normal and nonnormal parity calculations were made for the lithium isotopes using a new two-body interaction. The results for 5 Li predict the 2s/sub 1/2/ and 1d/sub 5/2/ single-particle states to be located below the 3/2 + state. Similar calculations were made for 13 C, 13 N, and 14 C. Results for 13 C and 13 N show for E/sub x/ 7 Li and 14 C, 2 h-barω calculations were done. Shell model calculations generated the R-matrix parameters for the elastic and first 3 inelastic channels of 13 C + n. After adjusting some energies, the predicted structure generally agrees with experiment for E/sub n/ 13 C + n data were refit to replace R 0 background terms by more realistic broad states and to get better agreement with model calculations. R-matrix fitting of the full data set produced new 14 C level information. For E/sub n/ > 4 MeV (E/sub x/ > 12 MeV), 5 states are given definite J/sup π/ assignments; 3, tentative assignments. 122 refs., 91 figs., 30 tabs

Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

Science.gov (United States)

Pan, Guangming; Wang, Shaochen; Zhou, Wang

2017-10-01

In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.

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

International Nuclear Information System (INIS)

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)

Spatially patterned matrix elasticity directs stem cell fate

Science.gov (United States)

Yang, Chun; DelRio, Frank W.; Ma, Hao; Killaars, Anouk R.; Basta, Lena P.; Kyburz, Kyle A.; Anseth, Kristi S.

2016-08-01

There is a growing appreciation for the functional role of matrix mechanics in regulating stem cell self-renewal and differentiation processes. However, it is largely unknown how subcellular, spatial mechanical variations in the local extracellular environment mediate intracellular signal transduction and direct cell fate. Here, the effect of spatial distribution, magnitude, and organization of subcellular matrix mechanical properties on human mesenchymal stem cell (hMSCs) function was investigated. Exploiting a photodegradation reaction, a hydrogel cell culture substrate was fabricated with regions of spatially varied and distinct mechanical properties, which were subsequently mapped and quantified by atomic force microscopy (AFM). The variations in the underlying matrix mechanics were found to regulate cellular adhesion and transcriptional events. Highly spread, elongated morphologies and higher Yes-associated protein (YAP) activation were observed in hMSCs seeded on hydrogels with higher concentrations of stiff regions in a dose-dependent manner. However, when the spatial organization of the mechanically stiff regions was altered from a regular to randomized pattern, lower levels of YAP activation with smaller and more rounded cell morphologies were induced in hMSCs. We infer from these results that irregular, disorganized variations in matrix mechanics, compared with regular patterns, appear to disrupt actin organization, and lead to different cell fates; this was verified by observations of lower alkaline phosphatase (ALP) activity and higher expression of CD105, a stem cell marker, in hMSCs in random versus regular patterns of mechanical properties. Collectively, this material platform has allowed innovative experiments to elucidate a novel spatial mechanical dosing mechanism that correlates to both the magnitude and organization of spatial stiffness.

Perturbation analysis of nonlinear matrix population models

Directory of Open Access Journals (Sweden)

Hal Caswell

2008-03-01

Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

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

CERN Document Server

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...

Effect of interface/surface stress on the elastic wave band structure of two-dimensional phononic crystals

International Nuclear Information System (INIS)

Liu, Wei; Chen, Jiwei; Liu, Yongquan; Su, Xianyue

2012-01-01

In the present Letter, the multiple scattering theory (MST) for calculating the elastic wave band structure of two-dimensional phononic crystals (PCs) is extended to include the interface/surface stress effect at the nanoscale. The interface/surface elasticity theory is employed to describe the nonclassical boundary conditions at the interface/surface and the elastic Mie scattering matrix embodying the interface/surface stress effect is derived. Using this extended MST, the authors investigate the interface/surface stress effect on the elastic wave band structure of two-dimensional PCs, which is demonstrated to be significant when the characteristic size reduces to nanometers. -- Highlights: ► Multiple scattering theory including the interface/surface stress effect. ► Interface/surface elasticity theory to describe the nonclassical boundary conditions. ► Elastic Mie scattering matrix embodying the interface/surface stress effect. ► Interface/surface stress effect would be significant at the nanoscale.

A hyper elasticity method for interactive virtual design of hearing aids

DEFF Research Database (Denmark)

Darkner, Sune; Erleben, Kenny

2011-01-01

We present a computational efficient method for isotropic hyper elasticity based on functional analysis. By selecting a class of shape functions, we arrive at a computational scheme which yields very sparse tensors. This enables fast computations of the hyper elastic energy potential and its...... derivatives. We achieve efficiency and performance through the use of shape functions that are linear in their parameters and through rotation into the eigenspace of the right Cauchy–Green strain tensor. This makes near real time evaluation of hyper elasticity of complex meshes on CPU relatively easy...... to implement. The approach does not rely on a specific shape function or material model but offers a general framework for isotropic hyper elasticity. The method is aimed at interactive and accurate non-linear hyper elastic modeling for a wide range of industrial virtual design applications, which we exemplify...

An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

International Nuclear Information System (INIS)

Shao Hai-Jian; Cai Guo-Liang; Wang Hao-Xiang

2010-01-01

In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications

Morphology and linear-elastic moduli of random network solids.

Science.gov (United States)

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.

Linear algebra

CERN Document Server

Shilov, Georgi E

1977-01-01

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

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

Science.gov (United States)

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.

Efficient education policy: A second-order elasticity rule

OpenAIRE

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...

Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

Directory of Open Access Journals (Sweden)

Zhe Zhang

2010-09-01

Full Text Available With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.In the framework of mixed model equations, a new best linear unbiased prediction (BLUP method including a trait-specific relationship matrix (TA was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP and BLUP with realized relationship matrix (GBLUP. It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.

On elastic moduli and elastic anisotropy in polycrystalline martensitic NiTi

Energy Technology Data Exchange (ETDEWEB)

Qiu, S. [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States); Clausen, B. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Padula, S.A.; Noebe, R.D. [NASA Glenn Research Center, Cleveland, OH 44135 (United States); Vaidyanathan, R., E-mail: raj@mail.ucf.edu [Advanced Materials Processing and Analysis Center (AMPAC), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL 32816 (United States)

2011-08-15

A combined experimental and computational effort was undertaken to provide insight into the elastic response of B19' martensitic NiTi variants as they exist in bulk, polycrystalline aggregate form during monotonic tensile and compressive loading. The experimental effort centered on using in situ neutron diffraction during loading to measure elastic moduli in several directions along with an average Young's modulus and a Poisson's ratio. The measurements were compared with predictions from a 30,000 variant, self-consistent polycrystalline deformation model that accounted for the elastic intergranular constraint, and also with predictions of single crystal behavior from previously published ab initio studies. Variant conversion and detwinning processes that influenced the intergranular constraint occurred even at stresses where the macroscopic stress-strain response appeared linear. Direct evidence of these processes was revealed in changes in texture, which were captured in inverse pole figures constructed from the neutron diffraction measurements.

Multivariate Matrix-Exponential Distributions

DEFF Research Database (Denmark)

Bladt, Mogens; Nielsen, Bo Friis

2010-01-01

be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...

Support minimized inversion of acoustic and elastic wave scattering

International Nuclear Information System (INIS)

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

Modeling elastic anisotropy in strained heteroepitaxy.

Science.gov (United States)

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy

Science.gov (United States)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to facets on the surface.

Equivalence between short-time biphasic and incompressible elastic material responses.

Science.gov (United States)

Ateshian, Gerard A; Ellis, Benjamin J; Weiss, Jeffrey A

2007-06-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltatelasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

H{sub 2}/H{infinity} control of flexible structures through linear matrix inequalities with pole placement

Energy Technology Data Exchange (ETDEWEB)

Lopes, Jean C. [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil)

2009-07-01

The objective of this work is to apply the H2/H{infinity} control technique using linear matrix inequalities and pole placement constraints to the flexible structures control problem. The H2/H{infinity}control is a technique to design a controller with mixed features of the H2 and H{infinity} control formulations, such as, optimal dynamical performance and robust performance. The Linear Matrix Inequalities allow formulating the problem as a convex optimization problem, and additional constraints can be included such as the pole placement. The pole placement requirement comes from the necessity of adjusting the transient response of the plant and ensuring a specific behavior in terms of speed and damping responses. The mathematical model used for this study is related to a flexible beam, with an applied disturbance and an actuator in different positions. The state-space matrices of the structure were obtained using the finite element method with the Euler-Bernoulli formulation of beams. The results showed that the pole placement constraints can improve the performance of the controller H2/H{infinity}. The Matlab was used for the computational implementation. (author)

Extreme non-linear elasticity and transformation optics

DEFF Research Database (Denmark)

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...

Microscopic cluster model analysis of 14O+p elastic scattering

International Nuclear Information System (INIS)

Baye, D.; Descouvemont, P.; Leo, F.

2005-01-01

The 14 O+p elastic scattering is discussed in detail in a fully microscopic cluster model. The 14 O cluster is described by a closed p shell for protons and a closed p3/2 subshell for neutrons in the translation-invariant harmonic-oscillator model. The exchange and spin-orbit parameters of the effective forces are tuned on the energy levels of the 15 C mirror system. With the generator-coordinate and microscopic R-matrix methods, phase shifts and cross sections are calculated for the 14 O+p elastic scattering. An excellent agreement is found with recent experimental data. A comparison is performed with phenomenological R-matrix fits. Resonances properties in 15 F are discussed

Elastic unitarity of direct channel and Froissart saturation

International Nuclear Information System (INIS)

Glushko, N.I.; Kobylinsky, N.A.

1982-01-01

The condition of elastic unitarity for direct channel continued analytically to high-energy range reveals a fast (upper the Froissart bound) rise of the amplitude between elastic and inelastic cuts in the case when the hadron scattering picture approaches the black disc limit. This fact is assumed as a basis for a new model of generating the Froissart saturation which describes well the main characteristics of NN, PIN and KN scattering. The model suggested is also compared witn the U-matrix approach

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

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....

Contributions to micromechanical model of the non linear behavior of the Callovo-Oxfordian argillite

International Nuclear Information System (INIS)

Abou-Chakra Guery, A.

2007-12-01

This work is performed in the general context of the project of underground disposal of radioactive waste, undertaken by the French National Radioactive Waste Management Agency (ANDRA). Due to its strong density and weak permeability, the formation of Callovo-Oxfordian argillite is chosen as one of possible geological barriers to radionuclides. The objective of the study to develop and validate a non linear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modelled as a composite constituted of an elasto(visco)plastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill. The derived model is first compared to Finite Element calculations on unit cell. It is then validated and applied for the prediction of the macroscopic stress-strain responses of the argillite at different geological depths. Finally, the micromechanical model is implemented in a commercial finite element code (Abaqus) for the simulation of a vertical shaft of the underground laboratory. This allows predicting the distribution of damage state and plastic strains and characterizing the excavation damage zone (EDZ). (author)

DFT calculation for elastic constants of orthorhombic structure within WIEN2K code: A new package (ortho-elastic)

International Nuclear Information System (INIS)

Reshak, Ali H.; Jamal, Morteza

2012-01-01

Highlights: ► A new package for calculating elastic constants of orthorhombic structure is released. ► The package called ortho-elastic. ► It is compatible with [FP-(L)APW+lo] method implemented in WIEN2k code. ► Several orthorhombic structure compounds were used to test the new package. ► Elastic constants calculated using this package show good agreement with experiment. - Abstract: A new package for calculating the elastic constants of orthorhombic structure is released. The package called ortho-elastic. The formalism of calculating the ortho-elastic constants is described in details. The package is compatible with the highly accurate all-electron full-potential (linearized) augmented plane-wave plus local orbital [FP-(L)APW+lo] method implemented in WIEN2k code. Several orthorhombic structure compounds were used to test the new package. We found that the calculated elastic constants using the new package show better agreement with the available experimental data than the previous theoretical results used different methods. In this package the second-order derivative E ″ (ε) of polynomial fit E=E(ε) of energy vs strains at zero strain (ε=0), used to calculate the orthorhombic elastic constants.

Geometric method for stability of non-linear elastic thin shells

CERN Document Server

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...

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

Science.gov (United States)

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

Two Propositions on the Application of Point Elasticities to Finite Price Changes.

Science.gov (United States)

Daskin, Alan J.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

Matrix effect study in the determination of linear alkylbenzene sulfonates in sewage sludge samples.

Science.gov (United States)

Cantarero, Samuel; Zafra-Gómez, Alberto; Ballesteros, Oscar; Navalón, Alberto; Vílchez, José L; Verge, Coral; De Ferrer, Juan A

2011-04-01

We propose a study of the matrix effect in the determination of linear alkylbenzene sulfonates (LAS) in sewage sludge samples. First, a rapid, selective and sensitive method is proposed. The method involves two stages: the extraction of the compound from the samples and analysis by liquid chromatography with fluorescence detection (LC-FLD). Three different techniques of extraction (microwave-assisted extraction, Soxhlet, and ultrasounds) were compared, and microwave-assisted extraction was selected as the best suited for our purpose. Microwave-assisted extraction allows reducing the extraction time (25 min compared with 12 h for conventional Soxhlet extraction) and solvent waste (25 ml of methanol compared with 200 ml for Soxhlet or more than 50 ml for the ultrasonic procedure). Absence of matrix effect was evaluated with two standards (2ØC(8:0) and 2ØC(16:0) ) that are not commercial; therefore, neither of them was detected in sewage sludge samples and they showed similar environmental behavior (adsorption and precipitation) to LAS (C(11:0) -C(13.0) ), which allow us to evaluate the matrix effect. Validation was carried out by a recovery assay, and the method was applied to samples from different sources; therefore, they had different compositions. Copyright © 2011 SETAC.

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

Science.gov (United States)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-07-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

Comparison of elastic and inelastic seismic response of high temperature piping systems

International Nuclear Information System (INIS)

Thomas, F.M.; McCabe, S.L.; Liu, Y.

1994-01-01

A study of high temperature power piping systems is presented. The response of the piping systems is determined when subjected to seismic disturbances. Two piping systems are presented, a main steam line, and a cold reheat line. Each of the piping systems are modeled using the ANSYS computer program and two analyses are performed on each piping system. First, each piping system is subjected to a seismic disturbance and the pipe material is assumed to remain linear and elastic. Next the analysis is repeated for each piping system when the pipe material is modeled as having elastic-plastic behavior. The results of the linear elastic analysis and elastic-plastic analysis are compared for each of the two pipe models. The pipe stresses, strains, and displacements, are compared. These comparisons are made so that the effect of the material yielding can be determined and to access what error is made when a linear analysis is performed on a system that yields

Software to compute elastostatic Green's functions for sources in 3D homogeneous elastic layers above a (visco)elastic halfspace

Science.gov (United States)

Bradley, A. M.; Segall, P.

2012-12-01

We describe software, in development, to calculate elastostatic displacement Green's functions and their derivatives for point and polygonal dislocations in three-dimensional homogeneous elastic layers above an elastic or a viscoelastic halfspace. The steps to calculate a Green's function for a point source at depth zs are as follows. 1. A grid in wavenumber space is chosen. 2. A six-element complex rotated stress-displacement vector x is obtained at each grid point by solving a two-point boundary value problem (2P-BVP). If the halfspace is viscoelastic, the solution is inverse Laplace transformed. 3. For each receiver, x is propagated to the receiver depth zr (often zr = 0) and then, 4, inverse Fourier transformed, with the Fourier component corresponding to the receiver's horizontal position. 5. The six elements are linearly combined into displacements and their derivatives. The dominant work is in step 2. The grid is chosen to represent the wavenumber-space solution with as few points as possible. First, the wavenumber space is transformed to increase sampling density near 0 wavenumber. Second, a tensor-product grid of Chebyshev points of the first kind is constructed in each quadrant of the transformed wavenumber space. Moment-tensor-dependent symmetries further reduce work. The numerical solution of the 2P-BVP problem in step 2 involves solving a linear equation A x = b. Half of the elements of x are of geophysical interest; the subset depends on whether zr ≤ zs. Denote these \\hat x. As wavenumber k increases, \\hat x can become inaccurate in finite precision arithmetic for two reasons: 1. The condition number of A becomes too large. 2. The norm-wise relative error (NWRE) in \\hat x is large even though it is small in x. To address this problem, a number of researchers have used determinants to obtain x. This may be the best approach for 6-dimensional or smaller 2P-BVP, where the combinatorial increase in work is still moderate. But there is an alternative

14O+p elastic scattering in a microscopic cluster model

International Nuclear Information System (INIS)

Descouvemont, P.; Baye, D.; Leo, F.

2006-01-01

The 14O+p elastic scattering is analyzed in a fully microscopic cluster model. With the Resonating Group Method associated with the microscopic R-matrix theory, phase shifts and cross sections are calculated. Data on 16O+p are used to test the precision of the model. For the 14O+p elastic scattering, an excellent agreement is found with recent experimental data. Resonances properties in 15F are discussed

Elastic properties of uniaxial-fiber reinforced composites - General features

Science.gov (United States)

Datta, Subhendu; Ledbetter, Hassel; Lei, Ming

The salient features of the elastic properties of uniaxial-fiber-reinforced composites are examined by considering the complete set of elastic constants of composites comprising isotropic uniaxial fibers in an isotropic matrix. Such materials exhibit transverse-isotropic symmetry and five independent elastic constants in Voigt notation: C(11), C(33), C(44), C(66), and C(13). These C(ij) constants are calculated over the entire fiber-volume-fraction range 0.0-1.0, using a scattered-plane-wave ensemple-average model. Some practical elastic constants such as the principal Young moduli and the principal Poisson ratios are considered, and the behavior of these constants is discussed. Also presented are the results for the four principal sound velocities used to study uniaxial-fiber-reinforced composites: v(11), v(33), v(12), and v(13).

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

Science.gov (United States)

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.

Elastic properties of rigid fiber-reinforced composites

Science.gov (United States)

Chen, J.; Thorpe, M. F.; Davis, L. C.

1995-05-01

We study the elastic properties of rigid fiber-reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson's ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital-image-based method and a finite element analysis to perform computer simulations which confirm our analytical predictions.

Zirconium elasticity modules

International Nuclear Information System (INIS)

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

Elastic Property Simulation of Nano-particle Reinforced Composites

Directory of Open Access Journals (Sweden)

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.

DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM

Directory of Open Access Journals (Sweden)

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.

Elasticities and the link between demographic and evolutionary dynamics

NARCIS (Netherlands)

Van Tienderen, P.H.

2000-01-01

Multivariate selection models and demographic matrix projections are closely related. The subtle differences among the parameters of both approaches (sensitivities, elasticities, selection differentials, and gradients) can be confusing. I suggest a hierarchical framework for analysis using

Homogenized Elastic Properties of Graphene for Small Deformations

Directory of Open Access Journals (Sweden)

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.

Elastic representation surfaces of unidirectional graphite/epoxy composites

International Nuclear Information System (INIS)

Kriz, R.D.; Ledbetter, H.M.

1985-01-01

Unidirectional graphite/epoxy composites exhibit high elastic anisotropy and unusual geometrical features in their elastic-property polar diagrams. From the five-component transverse-isotropic elastic-stiffness tensor we compute and display representation surfaces for Young's modulus, torsional modulus, linear compressibility, and Poisson's ratios. Based on Christoffel-equation solutions, we describe some unusual elastic-wave-surface topological features. Musgrave considered in detail the differences between phase-velocity and group-velocity surfaces arising from high elastic anisotropy. For these composites, we find effects similar to, but more dramatic than, Musgrave's. Some new, unexpected results for graphite/epoxy include: a shear-wave velocity that exceeds a longitudinal velocity in the plane transverse to the fiber; a wave that changes polarization character from longitudinal to transverse as the propagation direction sweeps from the fiber axis to the perpendicular axis

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

Science.gov (United States)

Wu, H. I.; Spence, R. D.; Sharpe, P. J.; Goeschl, J. D.

1985-01-01

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.

Elastic wave excitation in centrosymmetric strontium titanate crystals

International Nuclear Information System (INIS)

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

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

Calculation model of non-linear dynamic deformation of composite multiphase rods

Directory of Open Access Journals (Sweden)

Mishchenko Andrey Viktorovich

2014-05-01

Full Text Available The method of formulating non-linear physical equations for multiphase rods is suggested in the article. Composite multiphase rods possess various structures, include shear, polar, radial and axial inhomogeneity. The Timoshenko’s hypothesis with the large rotation angles is used. The method is based on the approximation of longitudinal normal stress low by basic functions expansions regarding the linear viscosity low. The shear stresses are calculated with the equilibrium equation using the subsidiary function of the longitudinal shift force. The system of differential equations connecting the internal forces and temperature with abstract deformations are offered by the basic functions. The application of power functions with arbitrary index allows presenting the compact form equations. The functional coefficients in this system are the highest order rigidity characteristics. The whole multiphase cross-section rigidity characteristics are offered the sums of the rigidity characteristics of the same phases individually. The obtained system allows formulating the well-known particular cases. Among them: hard plasticity and linear elastic deformation, different module deformation and quadratic Gerstner’s low elastic deformation. The reform of differential equations system to the quasilinear is suggested. This system contains the secant variable rigidity characteristics depending on abstract deformations. This system includes the sum of the same uniform blocks of different order. The rods phases defined the various set of uniform blocks phase materials. The integration of dynamic, kinematic and physical equations taking into account initial and edge condition defines the full dynamical multiphase rods problem. The quasilinear physical equations allow getting the variable flexibility matrix of multiphase rod and rods system.

Modeling Pseudo-elastic Behavior of Springback

International Nuclear Information System (INIS)

Xia, Z. Cedric

2005-01-01

One of the principal foundations of mathematical theory of conventional plasticity for rate-independent metals is that there exists a well-defined yield surface in stress space for any material point under deformation. A material point can undergo further plastic deformation if the applied stresses are beyond current yield surface which is generally referred as 'plastic loading'. On the other hand, if the applied stress state falls within or on the yield surface, the metal will deform elastically only and is said to be undergoing 'elastic unloading'. Although it has been always recognized throughout the history of development of plasticity theory that there is indeed inelastic deformation accompanying elastic unloading, which leads to metal's hysteresis behavior, its effects were thought to be negligible and were largely ignored in the mathematical treatment.Recently there have been renewed interests in the study of unloading behavior of sheet metals upon large plastic deformation and its implications on springback prediction. Springback is essentially an elastic recovery process of a formed sheet metal blank when it is released from the forming dies. Its magnitude depends on the stress states and compliances of the deformed sheet metal if no further plastic loading occurs during the relaxation process. Therefore the accurate determination of material compliances during springback and its effective incorporation into simulation software are important aspects for springback calculation. Some of the studies suggest that the unloading curve might deviate from linearity, and suggestions were made that a reduced elastic modulus be used for springback simulation.The aim of this study is NOT to take a position on the debate of whether elastic moduli are changed during sheet metal forming process. Instead we propose an approach of modeling observed psuedoelastic behavior within the context of mathematical theory of plasticity, where elastic moduli are treated to be

Equilibrium stability of a cylindrical body subject to the internal structure of the material and inelastic behaviour of the completely compressed matrix

Science.gov (United States)

Gotsev, D. V.; Perunov, N. S.; Sviridova, E. N.

2018-03-01

The mathematical model describing the stress-strain state of a cylindrical body under the uniform radial compression effect is constructed. The model of the material is the porous medium model. The compressed skeleton of the porous medium possesses hardening elastic-plastic properties. Deforming of the porous medium under the specified compressive loads is divided into two stages: elastic deforming of the porous medium and further elastic-plastic deforming of the material with completely compressed matrix. The analytical relations that define the fields of stress and displacement at each stage of the deforming are obtained. The influence of the porosity and other physical, mechanical and geometric parameters of the construction on the size of the plastic zone is evaluated. The question of the ground state equilibrium instability is investigated within the framework of the three-dimensional linearized relationships of the stability theory of deformed bodies.

The elastic response of composite materials

International Nuclear Information System (INIS)

Laws, N.

1980-01-01

The theory of linear elasticity is used to study the elastic response of composite materials. The main concern is the prediction of overall moduli. Some attention is paid to the problem of deciding upon when the idea of an overall modulus is meaningful. In addition it is shown how to calculate some rigorous bounds on the overall moduli, and some predictions of the self-consistent method are discussed. The paper mainly concentrates on isotropic dispersions of spheres, unidirectional fibre-reinforced materials and laminates. (author)

Factorizable S-matrix for SO(D)/SO(2) circle times SO(D - 2) non-linear σ models with fermions

International Nuclear Information System (INIS)

Abdalla, E.; Lima-Santos, A.

1988-01-01

The authors compute the exact S matrix for the non-linear sigma model with symmetry SO(D)/SO(2) circle times SO(D-2) coupled to fermions in a minimal or supersymmetric way. The model has some relevance in string theory with non-zero external curvature

Vascular elastic photoacoustic tomography in humans

Science.gov (United States)

Hai, Pengfei; Zhou, Yong; Liang, Jinyang; Li, Chiye; Wang, Lihong V.

2016-03-01

Quantification of vascular elasticity can help detect thrombosis and prevent life-threatening conditions such as acute myocardial infarction or stroke. Here, we propose vascular elastic photoacoustic tomography (VE-PAT) to measure vascular elasticity in humans. VE-PAT was developed by incorporating a linear-array-based photoacoustic computed tomography system with a customized compression stage. By measuring the deformation of blood vessels under uniaxial loading, VE-PAT was able to quantify the vascular compliance. We first demonstrated the feasibility of VE-PAT in blood vessel phantoms. In large vessel phantoms, VE-PAT detected a decrease in vascular compliance due to simulated thrombosis, which was validated by a standard compression test. In small blood vessel phantoms embedded 3 mm deep in gelatin, VE-PAT detected elasticity changes at depths that are difficult to image using other elasticity imaging techniques. We then applied VE-PAT to assess vascular compliance in a human subject and detected a decrease in vascular compliance when an occlusion occurred downstream from the measurement point, demonstrating the potential of VE-PAT in clinical applications such as detection of deep venous thrombosis.

Study of Wood Plastic Composites elastic behaviour using full field measurements

Science.gov (United States)

Ben Mbarek, T.; Robert, L.; Hugot, F.; Orteu, J. J.; Sammouda, H.; Graciaa, A.; Charrier, B.

2010-06-01

In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC) with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC). A non-linear behaviour is shown. The modulus of elasticity (MOE) is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM) is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE).

Mechanical confinement regulates cartilage matrix formation by chondrocytes

Science.gov (United States)

Lee, Hong-Pyo; Gu, Luo; Mooney, David J.; Levenston, Marc E.; Chaudhuri, Ovijit

2017-12-01

Cartilage tissue equivalents formed from hydrogels containing chondrocytes could provide a solution for replacing damaged cartilage. Previous approaches have often utilized elastic hydrogels. However, elastic stresses may restrict cartilage matrix formation and alter the chondrocyte phenotype. Here we investigated the use of viscoelastic hydrogels, in which stresses are relaxed over time and which exhibit creep, for three-dimensional (3D) culture of chondrocytes. We found that faster relaxation promoted a striking increase in the volume of interconnected cartilage matrix formed by chondrocytes. In slower relaxing gels, restriction of cell volume expansion by elastic stresses led to increased secretion of IL-1β, which in turn drove strong up-regulation of genes associated with cartilage degradation and cell death. As no cell-adhesion ligands are presented by the hydrogels, these results reveal cell sensing of cell volume confinement as an adhesion-independent mechanism of mechanotransduction in 3D culture, and highlight stress relaxation as a key design parameter for cartilage tissue engineering.

Plane strain problem in microstretch elastic solid

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

College, Patti 143 416, India. 3Department of Mathematics, Guru Nanak Dev University, Amritsar 143 005, ... lem in microstretch elastic solid by employing the eigenvalue approach. 975. Page 2. 976. Rajneesh Kumar et al. 2. Basic equations ..... of the matrix A are characteristic roots of (29) assuming that real parts of qs.

Residual stresses and mechanical properties of metal matrix composites

International Nuclear Information System (INIS)

Persson, Christer.

1993-01-01

The large difference in coefficient of thermal expansion of the matrix and particles in a metal matrix composite will introduce residual stresses during cooling from process temperature. These stresses are locally very high, and are known to influence the mechanical behaviour of the material. Changes in the stress state will occur during heat treatments and when the material is loaded due to different elastic, plastic, and creep properties of the constituents. The change of residual stresses in an Al-SiC particulate composite after different degree of plastic straining has been studied. The effect of plastic straining was modelled by an Eshelby model. The model and the measurements both show that the stress in the loading direction decreases for a tensile plastic strain and increases for a compressive plastic strain. By x-ray diffraction the stress response in the matrix and particles can be measured independently. This has been used to determine the stress state under and after heat treatments and under mechanical loading in two Al 15% SiC metal matrix composites. By analysing the line width from x-ray experiment the changes in the microstrains in the material were studied. A finite element model was used to model the generation of thermal residual stresses, stress relaxation during heat treatments, and load sharing during the first load cycle. Calculated stresses and microstrains were found to be in good agreement with the measured values. The elastic behaviour of the composite can be understood largely in terms of elastic load transfer between matrix and particles. However, at higher loads when the matrix becomes plastic residual stresses also become important. 21 refs

Creeping gaseous flows through elastic tube and annulus micro-configurations

Science.gov (United States)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

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

Science.gov (United States)

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.

Uniqueness in inverse elastic scattering with finitely many incident waves

International Nuclear Information System (INIS)

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.)

A Reevaluation of Price Elasticities for Irrigation Water

Science.gov (United States)

Howitt, Richard E.; Watson, William D.; Adams, Richard M.

1980-08-01

The effectiveness of pricing systems in the allocation of irrigation water is linked with the price elasticity of demand of farmers for water. Using microeconomic theory, it is shown that omission of the elasticity of demand for the crop produced leads to an inelastic bias in the demand for irrigated water. Linear programing approaches omit the product elasticity of demand and are consequently biased, whereas quadratic programing approaches to estimating derived demands for irrigation water include product demand functions. The difference between the resulting estimates are empirically demonstrated for regional derived demand functions estimated from a model of California's agricultural industry.

Negative stiffness honeycombs as tunable elastic metamaterials

Science.gov (United States)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Hydrogels preserve native phenotypes of valvular fibroblasts through an elasticity-regulated PI3K/AKT pathway.

Science.gov (United States)

Wang, Huan; Tibbitt, Mark W; Langer, Stephen J; Leinwand, Leslie A; Anseth, Kristi S

2013-11-26

Matrix elasticity regulates proliferation, apoptosis, and differentiation of many cell types across various tissues. In particular, stiffened matrix in fibrotic lesions has been shown to promote pathogenic myofibroblast activation. To better understand the underlying pathways by which fibroblasts mechano-sense matrix elasticity, we cultured primary valvular interstitial cells (VICs) isolated from porcine aortic valves on poly(ethylene glycol)-based hydrogels with physiologically relevant and tunable elasticities. We show that soft hydrogels preserve the quiescent fibroblast phenotype of VICs much better than stiff plastic plates. We demonstrate that the PI3K/AKT pathway is significantly up-regulated when VICs are cultured on stiff gels or tissue culture polystyrene compared with freshly isolated VICs. In contrast, myofibroblasts de-activate and pAKT/AKT decreases as early as 2 h after reducing the substrate modulus. When PI3K or AKT is inhibited on stiff substrates, myofibroblast activation is blocked. When constitutively active PI3K is overexpressed, the myofibroblast phenotype is promoted even on soft substrates. These data suggest that valvular fibroblasts are sensing the changes in matrix elasticity through the PI3K/AKT pathway. This mechanism may be used by other mechano-sensitive cells in response to substrate modulus, and this pathway may be a worthwhile target for treating matrix stiffness-associated diseases. Furthermore, hydrogels can be designed to recapitulate important mechanical cues in native tissues to preserve aspects of the native phenotype of primary cells for understanding basic cellular responses to biophysical and biochemical signals, and for tissue-engineering applications.

Density functional calculations of elastic properties of portlandite, Ca(OH)(2)

DEFF Research Database (Denmark)

Laugesen, Jakob Lund

2005-01-01

The elastic constants of portlandite, Ca(OH)(2), are calculated by use of density functional theory. A lattice optimization of an infinite (periodic boundary conditions) lattice is performed on which strains are applied. The elastic constants are extracted by minimizing Hooke's law of linear...

Mean Green operators of deformable fiber networks embedded in a compliant matrix and property estimates

Science.gov (United States)

Franciosi, Patrick; Spagnuolo, Mario; Salman, Oguz Umut

2018-04-01

Composites comprising included phases in a continuous matrix constitute a huge class of meta-materials, whose effective properties, whether they be mechanical, physical or coupled, can be selectively optimized by using appropriate phase arrangements and architectures. An important subclass is represented by "network-reinforced matrices," say those materials in which one or more of the embedded phases are co-continuous with the matrix in one or more directions. In this article, we present a method to study effective properties of simple such structures from which more complex ones can be accessible. Effective properties are shown, in the framework of linear elasticity, estimable by using the global mean Green operator for the entire embedded fiber network which is by definition through sample spanning. This network operator is obtained from one of infinite planar alignments of infinite fibers, which the network can be seen as an interpenetrated set of, with the fiber interactions being fully accounted for in the alignments. The mean operator of such alignments is given in exact closed form for isotropic elastic-like or dielectric-like matrices. We first exemplify how these operators relevantly provide, from classic homogenization frameworks, effective properties in the case of 1D fiber bundles embedded in an isotropic elastic-like medium. It is also shown that using infinite patterns with fully interacting elements over their whole influence range at any element concentration suppresses the dilute approximation limit of these frameworks. We finally present a construction method for a global operator of fiber networks described as interpenetrated such bundles.

Linear Algebraic Method for Non-Linear Map Analysis

International Nuclear Information System (INIS)

Yu, L.; Nash, B.

2009-01-01

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

Arterial elastic fiber structure. Function and potential roles in acute aortic dissection.

Science.gov (United States)

Pratt, B; Curci, J

2010-10-01

The lethality of acute aortic dissection is well recognized. Successful treatment and prevention of aortic dissection is going to be dependent upon an improved understanding of the molecular and physiologic events which predispose to dissection development and propagation. In this review, we will focus on the elastic fiber, one of the critical elements of the aortic wall matrix. Mechanical or functional failure of the elastin in the wall of the aorta likely predisposes to dissection as well as the post-dissection aortic degeneration with aneurysm formation. Insight into the role of the elastin and the elastic fiber in aortic dissection has recently been accelerated by research into the molecular mechanisms associated with hereditary propensity for aortic dissection, such as Marfan syndrome. These studies have implicated both structural and metabolic contributions of alterations in the scaffolding proteins in matrix elastic fibers. In particular, increased transforming growth factor-β (TGF-β) activity may play a prominent role in predisposing the aortic wall to dissection. The events which predispose to post-dissection aortic degeneration are somewhat less well defined. However, the loss of the structural integrity of the remaining elastic fibers leaves the wall weaker and prone to dilatation and rupture. It appears likely that the upregulation of several potent proteases, particularly those of the matrix metalloproteinase (MMP) family such as MMP-9, are participating in the subsequent matrix damage. Novel medical treatments based on this pathologic data have been proposed and in some cases have made it to clinical trials. The ongoing study evaluating whether therapeutic inhibition of TGF-β may be useful in reducing the risk of aortic dissection in patients at high risk represents one promising new strategy in the treatment of this deadly disease.

ITMETH, Iterative Routines for Linear System

International Nuclear Information System (INIS)

Greenbaum, A.

1989-01-01

1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

A numerical approximation to the elastic properties of sphere-reinforced composites

Science.gov (United States)

Segurado, J.; Llorca, J.

2002-10-01

Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the "exact" solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory

Directory of Open Access Journals (Sweden)

Qian Hong

2008-05-01

Full Text Available Abstract Background: Several approaches, including metabolic control analysis (MCA, flux balance analysis (FBA, correlation metric construction (CMC, and biochemical circuit theory (BCT, have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results: In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RT BS and ST BS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion: One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA.

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

Science.gov (United States)

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.

Determination of elastic modulus for hollow spherical shells via resonant ultrasound spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Ma, Xiaojun [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Xing; Wang, Zongwei [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Chen, Qian; Qian, Menglu [Institute of Acoustic, Tongji University, Shanghai 200092 (China); Meng, Jie [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Yongjian [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Shen, Hao [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Gao, Dangzhong, E-mail: dgaocn@163.com [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China)

2017-04-15

Highlights: • The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method. • The simulated results demonstrate that the natural frequencies of a hollow sphere are more strongly dependent on Young’s modulus than Poisson's ratio. • The Young’s moduli of polymer capsules with an sub-millimeter inner radius are measured accurately with an uncertainty of ∼10%. - Abstract: The elastic property of a capsule is one of the essential parameters both in engineering applications and scientific understanding of material nature in inertial confinement fusion (ICF) experiments. The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method, and a combined resonant ultrasound spectroscopy(RUS), which consists of a piezoelectric-based resonant ultrasound spectroscopy(PZT-RUS) and a laser-based resonant ultrasound spectroscopy(LRUS), is developed for determining the elastic modulus of capsule. To understand the behavior of natural frequencies varying with elastic properties, the dependence of natural frequencies on Young’s modulus and Poisson’s ratio are calculated numerically. Some representative polymer capsules are measured using PZT-RUS and LRUS. Based on the theoretical and experimental results, the Young’s moduli of these capsules are measured accurately with an uncertainty of ∼10%.

Ground states of linear rotor chains via the density matrix renormalization group

Science.gov (United States)

Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

Green's matrix for a second-order self-adjoint matrix differential operator

International Nuclear Information System (INIS)

Sisman, Tahsin Cagri; Tekin, Bayram

2010-01-01

A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

Mechanics of Fluctuating Elastic Plates and Fiber Networks

Science.gov (United States)

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

The R-matrix theory

International Nuclear Information System (INIS)

Descouvemont, P; Baye, D

2010-01-01

The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schroedinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.

NONLINEAR SPECTRAL IMAGING OF ELASTIC CARTILAGE IN RABBIT EARS

Directory of Open Access Journals (Sweden)

JING CHEN

2013-07-01

Full Text Available Elastic cartilage in the rabbit external ear is an important animal model with attractive potential value for researching the physiological and pathological states of cartilages especially during wound healing. In this work, nonlinear optical microscopy based on two-photon excited fluorescence and second harmonic generation were employed for imaging and quantifying the intact elastic cartilage. The morphology and distribution of main components in elastic cartilage including cartilage cells, collagen and elastic fibers were clearly observed from the high-resolution two-dimensional nonlinear optical images. The areas of cell nuclei, a parameter related to the pathological changes of normal or abnormal elastic cartilage, can be easily quantified. Moreover, the three-dimensional structure of chondrocytes and matrix were displayed by constructing three-dimensional image of cartilage tissue. At last, the emission spectra from cartilage were obtained and analyzed. We found that the different ratio of collagen over elastic fibers can be used to locate the observed position in the elastic cartilage. The redox ratio based on the ratio of nicotinamide adenine dinucleotide (NADH over flavin adenine dinucleotide (FAD fluorescence can also be calculated to analyze the metabolic state of chondrocytes in different regions. Our results demonstrated that this technique has the potential to provide more accurate and comprehensive information for the physiological states of elastic cartilage.

H{infinity} Filtering for Dynamic Compensation of Self-Powered Neutron Detectors - A Linear Matrix Inequality Based Method -

Energy Technology Data Exchange (ETDEWEB)

Park, M.G.; Kim, Y.H.; Cha, K.H.; Kim, M.K. [Korea Electric Power Research Institute, Taejon (Korea)

1999-07-01

A method is described to develop and H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for both continuous- and discrete-time models. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency. (author). 15 refs., 4 figs., 3 tabs.

Analysis of elastic-plastic dynamic response of reinforced concrete frame structure

International Nuclear Information System (INIS)

Li Zhongcheng

2009-01-01

Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)

Are rapid changes in brain elasticity possible?

Science.gov (United States)

Parker, K. J.

2017-09-01

Elastography of the brain is a topic of clinical and preclinical research, motivated by the potential for viscoelastic measures of the brain to provide sensitive indicators of pathological processes, and to assist in early diagnosis. To date, studies of the normal brain and of those with confirmed neurological disorders have reported a wide range of shear stiffness and shear wave speeds, even within similar categories. A range of factors including the shear wave frequency, and the age of the individual are thought to have a possible influence. However, it may be that short term dynamics within the brain may have an influence on the measured stiffness. This hypothesis is addressed quantitatively using the framework of the microchannel flow model, which derives the tissue stiffness, complex modulus, and shear wave speed as a function of the vascular and fluid network in combination with the elastic matrix that comprise the brain. Transformation rules are applied so that any changes in the fluid channels or the elastic matrix can be mapped to changes in observed elastic properties on a macroscopic scale. The results are preliminary but demonstrate that measureable, time varying changes in brain stiffness are possible simply by accounting for vasodynamic or electrochemical changes in the state of any region of the brain. The value of this preliminary exploration is to identify possible mechanisms and order-of-magnitude changes that may be testable in vivo by specialized protocols.

LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

International Nuclear Information System (INIS)

Dongarra, J.J.

1979-01-01

1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

Multi-scale imaging and elastic simulation of carbonates

Science.gov (United States)

Faisal, Titly Farhana; Awedalkarim, Ahmed; Jouini, Mohamed Soufiane; Jouiad, Mustapha; Chevalier, Sylvie; Sassi, Mohamed

2016-05-01

Digital Rock Physics (DRP) is an emerging technology that can be used to generate high quality, fast and cost effective special core analysis (SCAL) properties compared to conventional experimental techniques and modeling techniques. The primary workflow of DRP conssits of three elements: 1) image the rock sample using high resolution 3D scanning techniques (e.g. micro CT, FIB/SEM), 2) process and digitize the images by segmenting the pore and matrix phases 3) simulate the desired physical properties of the rocks such as elastic moduli and velocities of wave propagation. A Finite Element Method based algorithm, that discretizes the basic Hooke's Law equation of linear elasticity and solves it numerically using a fast conjugate gradient solver, developed by Garboczi and Day [1] is used for mechanical and elastic property simulations. This elastic algorithm works directly on the digital images by treating each pixel as an element. The images are assumed to have periodic constant-strain boundary condition. The bulk and shear moduli of the different phases are required inputs. For standard 1.5" diameter cores however the Micro-CT scanning reoslution (around 40 μm) does not reveal smaller micro- and nano- pores beyond the resolution. This results in an unresolved "microporous" phase, the moduli of which is uncertain. Knackstedt et al. [2] assigned effective elastic moduli to the microporous phase based on self-consistent theory (which gives good estimation of velocities for well cemented granular media). Jouini et al. [3] segmented the core plug CT scan image into three phases and assumed that micro porous phase is represented by a sub-extracted micro plug (which too was scanned using Micro-CT). Currently the elastic numerical simulations based on CT-images alone largely overpredict the bulk, shear and Young's modulus when compared to laboratory acoustic tests of the same rocks. For greater accuracy of numerical simulation prediction, better estimates of moduli inputs

Study of Wood Plastic Composites elastic behaviour using full field measurements

Directory of Open Access Journals (Sweden)

Graciaa A.

2010-06-01

Full Text Available In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC. A non-linear behaviour is shown. The modulus of elasticity (MOE is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE.

Fully coupled heat conduction and deformation analyses of visco-elastic solids

KAUST Repository

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.

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Science.gov (United States)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

Micromechanical analysis on anisotropy of structured magneto-rheological elastomer

International Nuclear Information System (INIS)

Li, R; Zhang, Z; Wang, X J; Chen, S W

2015-01-01

This paper investigates the equivalent elastic modulus of structured magneto-rheological elastomer (MRE) in the absence of magnetic field. We assume that both matrix and ferromagnetic particles are linear elastic materials, and ferromagnetic particles are embedded in matrix with layer-like structure. The structured composite could be divided into matrix layer and reinforced layer, in which the reinforced layer is composed of matrix and the homogenously distributed ferromagnetic particles in matrix. The equivalent elastic modulus of reinforced layer is analysed by the Mori-Tanaka method. Finite Element Method (FEM) is also carried out to illustrate the relationship between the elastic modulus and the volume fraction of ferromagnetic particles. The results show that the anisotropy of elastic modulus becomes noticeable, as the volume fraction of particles increases. (paper)

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

International Nuclear Information System (INIS)

Yeheskel, O.

2008-01-01

The elastic moduli of γ-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a tool for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals

Introduction to computational linear algebra

CERN Document Server

Nassif, Nabil; Erhel, Jocelyne

2015-01-01

Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

Elastic properties of gamma-Pu by resonant ultrasound spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Migliori, Albert [Los Alamos National Laboratory; Betts, J [Los Alamos National Laboratory; Trugman, A [Los Alamos National Laboratory; Mielke, C H [Los Alamos National Laboratory; Mitchell, J N [Los Alamos National Laboratory; Ramos, M [Los Alamos National Laboratory; Stroe, I [WORXESTER, MA

2009-01-01

Despite intense experimental and theoretical work on Pu, there is still little understanding of the strange properties of this metal. We used resonant ultrasound spectroscopy method to investigate the elastic properties of pure polycrystalline Pu at high temperatures. Shear and longitudinal elastic moduli of the {gamma}-phase of Pu were determined simultaneously and the bulk modulus was computed from them. A smooth linear and large decrease of all elastic moduli with increasing temperature was observed. We calculated the Poisson ratio and found that it increases from 0.242 at 519K to 0.252 at 571K.

On the hyperbolicity condition in linear elasticity

Directory of Open Access Journals (Sweden)

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.

Matrix with Prescribed Eigenvectors

Science.gov (United States)

Ahmad, Faiz

2011-01-01

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

The study of Widmanstätten ferrite in Fe–C alloys by a phase field model coupled with anisotropic elasticity

Energy Technology Data Exchange (ETDEWEB)

Zhang, Li [China State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Shen, Yao, E-mail: yaoshen@sjtu.edu.cn [China State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Wan, Haibo [China State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Shanghai Power Equipment Research Institute, Shanghai 200240 (China); Xiong, Xiaochuan [General Motors Global Research & Development, China Science Laboratory, Shanghai 201206 (China); Zhang, Lanting [China State Key Lab of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China)

2015-11-25

A phase field model accounting for anisotropic elastic energy has been formulated to investigate the morphology and growth kinetics of a Widmanstätten microstructure during the isothermal austenite to ferrite transformation in binary Fe–C. Physically realistic parameters are employed, for which the thermodynamic functions and the diffusional mobilities are from the literatures that were assessed via the Calphad technique and from experimental results respectively. The simulation results suggest that the anisotropy of elastic energy, resulting from the lattice distortion between the ferrite precipitate and the austenite matrix in the phase transformation, is sufficient to generate a plate-like Widmanstätten structure. The growth of the ferrite precipitate follows completely different dynamic laws in different directions, i.e., parabolic thickening in the direction of the plate thickness and linear lengthening in the direction toward the plate tip. The chief reason for the former is that the moving of the plate broad sides may be regarded as a migration of straight interfaces in the diffusion-controlled phase transformation; the latter is because that the plate tip can maintain a constant radius of curvature during the phase transition after a transient initial stage. Furthermore, the aspect ratio and the lengthening rate of the Widmanstätten ferrite plate simulated by our analyses are in good agreement with the experimental observations. - Highlights: • A model assuming elastic anisotropy for the growth of ferrites is formulated. • The elastic anisotropy is sufficient to generate acicular Widmanstätten ferrites. • The direction of the plate thickness features a parabolic thickening. • The direction of the plate tip characterizes a linear lengthening. • The calculated aspect ratio and growth rate are in good agreement with experiments.

Postbuckling of magneto-electro-elastic CNT-MT composite nanotubes resting on a nonlinear elastic medium in a non-uniform thermal environment

Science.gov (United States)

Kamali, M.; Shamsi, M.; Saidi, A. R.

2018-03-01

As a first endeavor, the effect of nonlinear elastic foundation on the postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanotubes is investigated. The composite nanotube is affected by a non-uniform thermal environment. A typical MEE composite nanotube consists of microtubules (MTs) and carbon nanotubes (CNTs) with a MEE cylindrical nanoshell for smart control. It is assumed that the nanoscale layers of the system are coupled by a polymer matrix or filament network depending on the application. In addition to thermal loads, magneto-electro-mechanical loads are applied to the composite nanostructure. Length scale effects are taken into account using the nonlocal elasticity theory. The principle of virtual work and von Karman's relations are used to derive the nonlinear governing differential equations of MEE CNT-MT nanotubes. Using Galerkin's method, nonlinear critical buckling loads are determined. Various types of non-uniform temperature distribution in the radial direction are considered. Finally, the effects of various parameters such as the nonlinear constant of elastic medium, thermal loading factor and small scale coefficient on the postbuckling of MEE CNT-MT nanotubes are studied.

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

Science.gov (United States)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

Effect of reinforcement volume fraction on the density & elastic ...

African Journals Online (AJOL)

Effect of reinforcement volume fraction on the density & elastic parameters of BMG's matrix composites. Wahiba Metiri 1, Fatiha Hadjoub1, 2 and Leila Touati Tliba 1. 1 Laboratoire des Semi-Conducteurs, Département de Physique, Faculté des Sciences, Université Badji-. Mokhtar, BP 12, Annaba -23000, Algeria.

Solution of the scattering T matrix equation in discrete complex momentum space

International Nuclear Information System (INIS)

Rawitscher, G.H.; Delic, G.

1984-01-01

The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Science.gov (United States)

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Directory of Open Access Journals (Sweden)

Xiaobin Guo

2013-01-01

Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

Elasticity in Elastics-An in-vitro study.

Science.gov (United States)

Kamisetty, Supradeep Kumar; Nimagadda, Chakrapani; Begam, Madhoom Ponnachi; Nalamotu, Raghuveer; Srivastav, Trilok; Gs, Shwetha

2014-04-01

Orthodontic tooth movement results from application of forces to teeth. Elastics in orthodontics have been used both intra-orally and extra- orally to a great effect. Their use, combined with good patient co-operation provides the clinician with the ability to correct both anteroposterior and vertical discrepancies. Force decay over a period of time is a major problem in the clinical usage of latex elastics and synthetic elastomers. This loss of force makes it difficult for the clinician to determine the actual force transmitted to the dentition. It's the intent of the clinician to maintain optimal force values over desired period of time. The majority of the orthodontic elastics on the market are latex elastics. Since the early 1990s, synthetic products have been offered in the market for latex-sensitive patients and are sold as nonlatex elastics. There is limited information on the risk that latex elastics may pose to patients. Some have estimated that 0.12-6% of the general population and 6.2% of dental professionals have hypersensitivity to latex protein. There are some reported cases of adverse reactions to latex in the orthodontic population but these are very limited to date. Although the risk is not yet clear, it would still be inadvisable to prescribe latex elastics to a patient with a known latex allergy. To compare the in-vitro performance of latex and non latex elastics. Samples of 0.25 inch, latex and non latex elastics (light, medium, heavy elastics) were obtained from three manufacturers (Forestadent, GAC, Glenroe) and a sample size of ten elastics per group was tested. The properties tested included cross sectional area, internal diameter, initial force generated by the elastics, breaking force and the force relaxation for the different types of elastics. Force relaxation testing involved stretching the elastics to three times marketed internal diameter (19.05 mm) and measuring force level at intervals over a period of 48 hours. The data were

Extremal Overall Elastic Response of Polycrystalline Materials

DEFF Research Database (Denmark)

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...

Elastic scattering of positronium: Application of the confined variational method

KAUST Repository

Zhang, Junyi

2012-08-01

We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.

Elastic scattering of positronium: Application of the confined variational method

KAUST Repository

Zhang, Junyi; Yan, Zong-Chao; Schwingenschlö gl, Udo

2012-01-01

We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

International Nuclear Information System (INIS)

Wu, J.-X.; Li, X.-F.; Tang, G.-J.

2012-01-01

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

Energy Technology Data Exchange (ETDEWEB)

Wu, J.-X. [School of Civil Engineering, Central South University, Changsha, Hunan 410075 (China); Li, X.-F., E-mail: xfli25@yahoo.com.cn [School of Civil Engineering, Central South University, Changsha, Hunan 410075 (China); Tang, G.-J. [College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha 410073 (China)

2012-02-15

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.

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

Science.gov (United States)

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.

Application of elasticity theory at Sandia Labortories

International Nuclear Information System (INIS)

Davison, L.

1975-01-01

Examples are given of the application of linear elasticity theory to the solution of practical problems encountered at Sandia Laboratories. It is being applied to a very broad range of problems: those in one, two, and three spatial dimensions, some involving static and some dynamic response, to materials having isotropic and anisotropic symmetry, to homogeneous and inhomogeneous bodies, etc. Various extensions of the theory to include electric, magnetic and thermal effects, to account for material microstructure, for radiation and spall damage, chemical reactions, and other phenomena have been developed and/or applied. In some applications linear elasticity represents the physics of a problem well and is the theory of choice. In others the theory was used because it lent insight into a larger problem that was also attacked by means of other theories and/or experiment, and in some cases it serves as a part of a more encompassing theory

Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2015-01-01

the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Modern Nondestructive Test Methods for Army Ceramic Matrix Composites

National Research Council Canada - National Science Library

Strand, Douglas J

2008-01-01

.... Ceramic matrix composites (CMC) are potentially good high-temperature structural materials because of their low density, high elastic moduli, high strength, and for those with weak interfaces, surprisingly good damage tolerance...

Free vibration analysis of elastically supported Timoshenko columns ...

Indian Academy of Sciences (India)

, concen- trated mass ... linear equations of motion for transverse vibrations of a simply supported beam carrying con- centrated ... a cantilever Timoshenko beam with a rigid tip mass. Ferreira .... Figure 3. Free body diagram of elastic support.

Synchrotron X-ray diffraction measurements of internal stresses during loading of steel-based metal matrix composites reinforced with TiB2 particles

International Nuclear Information System (INIS)

Bacon, D.H.; Edwards, L.; Moffatt, J.E.; Fitzpatrick, M.E.

2011-01-01

Highlights: → Synchrotron X-ray diffraction was used to measure internal stresses in Fe-TiB 2 MMCs. → Samples of the MMCs were loaded to failure in situ in the X-ray beam. → The results show good elastic load transfer from the matrix to the reinforcement. → There is good agreement with the predicted elastic stresses from Eshelby modeling. → During plastic deformation there is increasing load transfer to the reinforcement. - Abstract: High-energy synchrotron X-ray diffraction was used to measure the internal strain evolution in the matrix and reinforcement of steel-based metal matrix composites reinforced with particulate titanium diboride (TiB 2 ). Two systems were studied: a 316L matrix with 25% TiB 2 by volume and a W1.4418 matrix with 10% reinforcement. In situ loading experiments were performed, where the materials were loaded uniaxially in the X-ray beam. The results show the strain partitioning between the phases in the elastic regime, and the evolution of the strain partitioning once plasticity occurs. The results are compared with results from Eshelby modelling, and very good agreement is seen between the measured and modelled response for elastic loading of the material. Heat treatment of the 316-based material did not affect the elastic internal strain response.

Thermodynamics and elastic properties of Ir from first-principle calculations

International Nuclear Information System (INIS)

Li Qiang; Huang Duohui; Cao Qilong; Wang Fanhou

2013-01-01

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties, including phonon dispersion curves, equation of state, linear thermal expansion coefficient and temperature-dependent entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young's modulus of Ir have been studied using first-principles projector-augmented wave method. The results revealed that the predicted phonon dispersion curves of Ir are in agreement with the experimental measurements by neutron diffractions. Considering the thermal electronic contribution to Helmholtz free energy, the calculated entropy, enthalpy, heat capacity and linear thermal expansion co- efficient from the first-principle are consistent well with the experimental data. At 2600 K, the electronic heat capacity accounts for 17% of the total heat capacity at constant pressure, thus the thermal electronic contribution to Helmholtz free energy is very important. The predicted elastic constants, bulk modulus, shear modulus and Young's modulus at room temperature are also in agreement with the available measurements and increase with the increasing temperature. (authors)

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

KAUST Repository

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.

Basic components of connective tissues and extracellular matrix: elastin, fibrillin, fibulins, fibrinogen, fibronectin, laminin, tenascins and thrombospondins.

Science.gov (United States)

Halper, Jaroslava; Kjaer, Michael

2014-01-01

Collagens are the most abundant components of the extracellular matrix and many types of soft tissues. Elastin is another major component of certain soft tissues, such as arterial walls and ligaments. Many other molecules, though lower in quantity, function as essential components of the extracellular matrix in soft tissues. Some of these are reviewed in this chapter. Besides their basic structure, biochemistry and physiology, their roles in disorders of soft tissues are discussed only briefly as most chapters in this volume deal with relevant individual compounds. Fibronectin with its muldomain structure plays a role of "master organizer" in matrix assembly as it forms a bridge between cell surface receptors, e.g., integrins, and compounds such collagen, proteoglycans and other focal adhesion molecules. It also plays an essential role in the assembly of fibrillin-1 into a structured network. Laminins contribute to the structure of the extracellular matrix (ECM) and modulate cellular functions such as adhesion, differentiation, migration, stability of phenotype, and resistance towards apoptosis. Though the primary role of fibrinogen is in clot formation, after conversion to fibrin by thrombin, it also binds to a variety of compounds, particularly to various growth factors, and as such fibrinogen is a player in cardiovascular and extracellular matrix physiology. Elastin, an insoluble polymer of the monomeric soluble precursor tropoelastin, is the main component of elastic fibers in matrix tissue where it provides elastic recoil and resilience to a variety of connective tissues, e.g., aorta and ligaments. Elastic fibers regulate activity of TGFβs through their association with fibrillin microfibrils. Elastin also plays a role in cell adhesion, cell migration, and has the ability to participate in cell signaling. Mutations in the elastin gene lead to cutis laxa. Fibrillins represent the predominant core of the microfibrils in elastic as well as non-elastic

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

Science.gov (United States)

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.

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Mathematically Simulated Elastic Characteristics of the Composite Reinforced by Spherical Inclusions

Directory of Open Access Journals (Sweden)

E. S. Sergeeva

2017-01-01

Full Text Available Composite materials are widely used in engineering, especially in constructions working under simultaneous intensive mechanical and thermal loads. In the industry the main requirements for materials are restrictions on the elastic characteristics, such as bulk modulus and shear modulus.Composite materials consist of a base material, a so-called binder (matrix, and reinforcing inclusions. The composite matrix defines a method for the composite manufacturing and must meet a set of operational and technological requirements. The most commonly used types are a metal matrix and a polymer one, because of the relative ease of manufacture, good wettability, and chemical resistance.Reinforcing inclusions can be of different nature (boron, crystalline, etc. and shape (spherical, lamellar, fiber. Lately, active researches have been conducted with the nanostructural elements (fullerenes, single-walled and multi-walled carbon nanotubes (SWCNTs and MWCNTs plates, nanoclusters used as the filler.There are various ways of modeling the elastic properties of the composites. The most common are numerical methods using a finite element method and analytical methods.In simulation of composite characteristics, in addition to the properties of its components, a reinforcing structure plays an important role.The paper considers an obtained isotropic composite with a metal matrix reinforced by the spherical nanoclusters of randomly oriented SWNTs with a reinforcement scheme similar to the cubic crystal lattice. Numerical modeling and analytical methods were used.For the numerical solution two types of periodic structure of the material were obtained: a cube with eight parts of the ball in the corners of a cube and a sphere in the center. For each of the periodic cells a representative volume is selected in which, using the kinematic and force boundary conditions, have been implemented two types of stress-strain state, namely stretching along one axis and shear. For

Contact instabilities of anisotropic and inhomogeneous soft elastic films

Science.gov (United States)

Tomar, Gaurav; Sharma, Ashutosh

2012-02-01

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

International Nuclear Information System (INIS)

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)

The price elasticity of electricity demand in South Australia

International Nuclear Information System (INIS)

Fan Shu; Hyndman, Rob J.

2011-01-01

In this paper, the price elasticity of electricity demand, representing the sensitivity of customer demand to the price of electricity, has been estimated for South Australia. We first undertake a review of the scholarly literature regarding electricity price elasticity for different regions and systems. Then we perform an empirical evaluation of the historic South Australian price elasticity, focussing on the relationship between price and demand quantiles at each half-hour of the day. This work attempts to determine whether there is any variation in price sensitivity with the time of day or quantile, and to estimate the form of any relationships that might exist in South Australia. - Highlights: → We review the scholarly literature on electricity own-price elasticity for different regions and systems. → We use annual log-linear econometric models of the electricity demand to estimate the historic South Australian price elasticity. → We focus on the relationship between price and demand quantiles at each half-hour of the day. → The overall price elasticity in South Australia ranges from -0.363 to -0.428.

A linear programming manual

Science.gov (United States)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Triangularization of a Matrix

Indian Academy of Sciences (India)

Much of linear algebra is devoted to reducing a matrix (via similarity or unitary similarity) to another that has lots of zeros. The simplest such theorem is the Schur triangularization theorem. This says that every matrix is unitarily similar to an upper triangular matrix. Our aim here is to show that though it is very easy to prove it ...

Dynamic elasticity measurement for prosthetic socket design.

Science.gov (United States)

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.

Semidefinite linear complementarity problems

International Nuclear Information System (INIS)

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

Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2

International Nuclear Information System (INIS)

Ravindran, P.; Fast, L.; Korzhavyi, P.A.; Johansson, B.; Wills, J.; Eriksson, O.

1998-01-01

A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi 2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young's modulus, and Poisson's ratio for ideal polycrystalline TiSi 2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young's modulus for single crystal TiSi 2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi 2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximation is used for the exchange and correlation potential. copyright 1998 American Institute of Physics

Fatigue crack growth from a cracked elastic particle into a ductile matrix

NARCIS (Netherlands)

Groh, S.; Olarnrithinun, S.; Curtin, W. A.; Needleman, A.; Deshpande, V. S.; Van der Giessen, E.

2008-01-01

The monotonic and cyclic crack growth rate of cracks is strongly influenced by the microstructure. Here, the growth of cracks emanating from pre-cracked micron-scale elastic particles and growing into single crystals is investigated, with a focus on the effects of (i) plastic confinement due to the

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

Science.gov (United States)

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.

A meta-analysis of the price elasticity of gasoline demand. A SUR approach

NARCIS (Netherlands)

Brons, M.R.E.; Nijkamp, P.; Pels, E.; Rietveld, P.

2008-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

Science.gov (United States)

Giersch, C; Cornish-Bowden, A

1996-10-07

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

Interface effects on effective elastic moduli of nanocrystalline materials

International Nuclear Information System (INIS)

Wang Gangfeng; Feng Xiqiao; Yu Shouwen; Nan Cewen

2003-01-01

Interfaces often play a significant role in many physical properties and phenomena of nanocrystalline materials (NcMs). In the present paper, the interface effects on the effective elastic property of NcMs are investigated. First, an atomic potential method is suggested for estimating the effective elastic modulus of an interface phase. Then, the Mori-Tanaka effective field method is employed to determine the overall effective elastic moduli of a nanocrystalline material, which is regarded as a binary composite consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. Finally, the stiffening effects of strain gradients are examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Our analysis shows two physical mechanisms of interfaces that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and another is the baffling effect due to the existence of boundary layers between the interface phase and the crystalline phase

Radii of Solvability and Unsolvability of Linear Systems

Czech Academy of Sciences Publication Activity Database

Hladík, M.; Rohn, Jiří

2016-01-01

Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

Science.gov (United States)

Wu, Wei; Cui, Bao-Tong

2007-07-01

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

Strain evolution after fiber failure in a single-fiber metal matrix composite under cyclic loading

Energy Technology Data Exchange (ETDEWEB)

Hanan, Jay C. [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States)]. E-mail: jay.hanan@okstate.edu; Mahesh, Sivasambu [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Uestuendag, Ersan [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States)]. E-mail: ersan@caltech.edu; Beyerlein, Irene J. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Swift, Geoffrey A. [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States); Clausen, Bjorn [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States); Brown, Donald W. [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Bourke, Mark A.M. [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

2005-06-15

The evolution of in situ elastic strain with cyclic tensile loading in each phase of a single Al{sub 2}O{sub 3}-fiber/aluminum-matrix composite was studied using neutron diffraction (ND). An analytical model appropriate for metal matrix composites (MMCs) was developed to connect the measured axial strain evolution in each phase with the possible micromechanical events that could occur during loading at room temperature: fiber fracture, interfacial slipping, and matrix plastic deformation. Model interpretation showed that the elastic strain evolution in the fiber and matrix was governed by fiber fracture and interface slipping and not by plastic deformation of the matrix, whereas the macroscopic stress-strain response of the composite was influenced by all three. The combined single-fiber composite model and ND experiment introduces a new and quick engineering approach for qualifying the micromechanical response in MMCs due to cyclic loading and fiber fracture.

Strain evolution after fiber failure in a single-fiber metal matrix composite under cyclic loading

International Nuclear Information System (INIS)

Hanan, Jay C.; Mahesh, Sivasambu; Uestuendag, Ersan; Beyerlein, Irene J.; Swift, Geoffrey A.; Clausen, Bjorn; Brown, Donald W.; Bourke, Mark A.M.

2005-01-01

The evolution of in situ elastic strain with cyclic tensile loading in each phase of a single Al 2 O 3 -fiber/aluminum-matrix composite was studied using neutron diffraction (ND). An analytical model appropriate for metal matrix composites (MMCs) was developed to connect the measured axial strain evolution in each phase with the possible micromechanical events that could occur during loading at room temperature: fiber fracture, interfacial slipping, and matrix plastic deformation. Model interpretation showed that the elastic strain evolution in the fiber and matrix was governed by fiber fracture and interface slipping and not by plastic deformation of the matrix, whereas the macroscopic stress-strain response of the composite was influenced by all three. The combined single-fiber composite model and ND experiment introduces a new and quick engineering approach for qualifying the micromechanical response in MMCs due to cyclic loading and fiber fracture

Rayleigh wave effects in an elastic half-space.

Science.gov (United States)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry.

Science.gov (United States)

Patty, C H Lucas; Luo, David A; Snik, Frans; Ariese, Freek; Buma, Wybren Jan; Ten Kate, Inge Loes; van Spanning, Rob J M; Sparks, William B; Germer, Thomas A; Garab, Győző; Kudenov, Michael W

2018-06-01

Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650 nm to 710 nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization. Copyright © 2018 The Author(s). Published by Elsevier B.V. All rights reserved.

Response of orthotropic micropolar elastic medium due to time ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

namic response of anisotropic continuum has received the attention of ... linear theory of micropolar elasticity and bending of orthotropic micropolar ... medium due to time harmonic concentrated load, the continuum is divided into two half-.

Diffraction by an immersed elastic wedge

CERN Document Server

Croisille, Jean-Pierre

1999-01-01

This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.

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

Czech Academy of Sciences Publication Activity Database

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

Porting of the DBCSR library for Sparse Matrix-Matrix Multiplications to Intel Xeon Phi systems

OpenAIRE

Bethune, Iain; Gloess, Andeas; Hutter, Juerg; Lazzaro, Alfio; Pabst, Hans; Reid, Fiona

2017-01-01

Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block Compressed Sparse Row) has been specifically designed to efficiently perform such sparse matrix-matrix multiplications. This library is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. It is para...

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

OpenAIRE

Zuidwijk, Rob

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

Science.gov (United States)

Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

2017-11-01

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

Purely elastic scattering theories and their ultraviolet limits

International Nuclear Information System (INIS)

Klassen, T.R.; Chicago Univ., IL; Melzer, E.

1990-01-01

We use the thermodynamic Bethe ansatz to find the finite-size corrections to the ground-state energy in an arbitrary (1+1)-dimensional purely elastic scattering theory. The leading finite-size effects are characterized by tilde c=c-12d 0 , where c and d 0 are the central charge and the lowest scaling dimension, respectively, of the (possibly nonunitary) CFT describing the ultraviolet limit of the massive scattering theory. After presenting the purely elastic S-matrix theories that emerged in recent discussions of perturbed CFTs, we calculate their finite-size scaling coefficient tilde c. Our results show that the UV limits of the 'minimal' S-matrix theories are the unperturbed CFTs in question. On the other hand, the S-matrices which have been suggested to describe affine Toda field theories, differing from the minimal S-matrices by coupling-dependent factors, are seen to have free bosonic CFTs as their UV limits. We also discuss some interesting properties of tilde c. In particular, we suggest that tilde c is a measure of the number of degrees of freedom of an arbitrary two-dimensional CFT. (orig.)

A companion matrix for 2-D polynomials

International Nuclear Information System (INIS)

Boudellioua, M.S.

1995-08-01

In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

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

Science.gov (United States)

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.

The elastic modulus of alumina-zirconia composite using through transmission ultrasonics

International Nuclear Information System (INIS)

Tan, K.S.; Hing, P.

1996-01-01

The elastic modulus of unstabilized Al 2 O 3 -ZrO 2 composites is determined from ultrasonic velocities and density measurements. The dynamic elastic modulus and the density of the green unstabilized Al 2 O 3 -ZrO 2 follow the rule of mixture. However, the elastic modulus and density of the sintered Al 2 O 3 -ZrO 2 do not follow the rule of mixture. The elastic modulus and diametrical compressive fracture stress of the Al 2 O 3 can be enhanced by (1) a high green (before sintering) compacting pressure and (2) addition of about 3wt% unstabilized ZrO 2 at a sintering time of two hours at 1550 degC. The ZrO 2 is found to improve the bulk density of the composite by a reduction in the porosity. This improves the elastic modulus and the diametrical compressive fracture stress. The thermal expansion on cooling with > 25wt% ZrO 2 in the Al 2 O 3 matrix has also been established. (author)

Morphological and ultrastructural characteristics of extracellular matrix changes in oral squamous cell carcinoma

Directory of Open Access Journals (Sweden)

Usha Agrawal

2011-01-01

Full Text Available Background: The biology of oral squamous cell carcinoma (OSCC, including its progression from dysplasia to carcinoma, "field effects", genetic changes in tumor associated mucosa (TAM and effect of matrix metalloproteinases in breaking down of matrix proteins to facilitate invasion, has been well documented. However, what remains to be done is to extrapolate this knowledge to improve patient care. Aim: The aim of this study was to observe the extracellular matrix (ECM changes with the routine histochemical stains available to most histopathologists. Materials and Methods: The study includes 72 cases of OSCC in which the tumor and adjacent normal appearing areas were sampled to study the ECM changes with hematoxylin and eosin (H and E and Verhoeff′s-Van Gieson elastic stain (VVG. Results: Basophilic fragmentation of collagen (H and E and clumped short elastic fibers (VVG were seen in 12 (16.7% cases. Of the remaining cases, 18 (25% had a dense lymphocytic infiltrate and had no demonstrable elastic fibers. Those cases with H and E changes were further studied and compared with normal mucosa for ultrastructural changes. The ultrastructural study demonstrated an increase in oxytalan, elaunin and elastic fibers and decrease in collagen fibers with some transformation changes associated with OSCCs and lymph node metastasis. Conclusion: Changes in transformation of collagen to elastic fibers and also the loss of both the fibers in areas of lymphocytic infiltration possibly indicate degradation of ECM fibers by factors released from the lymphocytes or tumor cells and the limiting effect on the tumor by ECM remodeling.

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

Science.gov (United States)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results

Handbook of linear algebra

CERN Document Server

Hogben, Leslie

2013-01-01

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

KAUST Repository

Contreras, Andres A.; Le Maî tre, Olivier P.; Aquino, Wilkins; Knio, Omar

2016-01-01

of stiff inclusions embedded in a soft matrix, mimicking tumors in soft tissues. We rely on a polynomial chaos (PC) surrogate to accelerate the inference process. The PC surrogate predicts the dependence of the displacements field with the random elastic

Linear data mining the Wichita clinical matrix suggests sleep and allostatic load involvement in chronic fatigue syndrome.

Science.gov (United States)

Gurbaxani, Brian M; Jones, James F; Goertzel, Benjamin N; Maloney, Elizabeth M

2006-04-01

To provide a mathematical introduction to the Wichita (KS, USA) clinical dataset, which is all of the nongenetic data (no microarray or single nucleotide polymorphism data) from the 2-day clinical evaluation, and show the preliminary findings and limitations, of popular, matrix algebra-based data mining techniques. An initial matrix of 440 variables by 227 human subjects was reduced to 183 variables by 164 subjects. Variables were excluded that strongly correlated with chronic fatigue syndrome (CFS) case classification by design (for example, the multidimensional fatigue inventory [MFI] data), that were otherwise self reporting in nature and also tended to correlate strongly with CFS classification, or were sparse or nonvarying between case and control. Subjects were excluded if they did not clearly fall into well-defined CFS classifications, had comorbid depression with melancholic features, or other medical or psychiatric exclusions. The popular data mining techniques, principle components analysis (PCA) and linear discriminant analysis (LDA), were used to determine how well the data separated into groups. Two different feature selection methods helped identify the most discriminating parameters. Although purely biological features (variables) were found to separate CFS cases from controls, including many allostatic load and sleep-related variables, most parameters were not statistically significant individually. However, biological correlates of CFS, such as heart rate and heart rate variability, require further investigation. Feature selection of a limited number of variables from the purely biological dataset produced better separation between groups than a PCA of the entire dataset. Feature selection highlighted the importance of many of the allostatic load variables studied in more detail by Maloney and colleagues in this issue [1] , as well as some sleep-related variables. Nonetheless, matrix linear algebra-based data mining approaches appeared to be of

H-/H∞ structural damage detection filter design using an iterative linear matrix inequality approach

International Nuclear Information System (INIS)

Chen, B; Nagarajaiah, S

2008-01-01

The existence of damage in different members of a structure can be posed as a fault detection problem. It is also necessary to isolate structural members in which damage exists, which can be posed as a fault isolation problem. It is also important to detect the time instants of occurrence of the faults/damage. The structural damage detection filter developed in this paper is a model-based fault detection and isolation (FDI) observer suitable for detecting and isolating structural damage. In systems, possible faults, disturbances and noise are coupled together. When system disturbances and sensor noise cannot be decoupled from faults/damage, the detection filter needs to be designed to be robust to disturbances as well as sensitive to faults/damage. In this paper, a new H - /H ∞ and iterative linear matrix inequality (LMI) technique is developed and a new stabilizing FDI filter is proposed, which bounds the H ∞ norm of the transfer function from disturbances to the output residual and simultaneously does not degrade the component of the output residual due to damage. The reduced-order error dynamic system is adopted to form bilinear matrix inequalities (BMIs), then an iterative LMI algorithm is developed to solve the BMIs. The numerical example and experimental verification demonstrate that the proposed algorithm can successfully detect and isolate structural damage in the presence of measurement noise

Mini-lecture course: Introduction into hierarchical matrix technique

KAUST Repository

Litvinenko, Alexander

2017-12-14

The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations (mesh points). The H-matrix technique allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

Linear Models

CERN Document Server

Searle, Shayle R

2012-01-01

This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

Extra-fibrillar matrix mechanics of annulus fibrosus in tension and compression.

Science.gov (United States)

Cortes, Daniel H; Elliott, Dawn M

2012-07-01

The annulus fibrosus (AF) of the disk is a highly nonlinear and anisotropic material that undergoes a complex combination of loads in multiple orientations. The tensile mechanical behavior of AF in the lamellar plane is dominated by collagen fibers and has been accurately modeled using exponential functions. On the other hand, AF mechanics perpendicular to the lamella, in the radial direction, depend on the properties of the ground matrix with little to no fiber contribution. The ground matrix is mainly composed of proteoglycans (PG), which are negatively charged macromolecules that maintain the tissue hydration via osmotic pressure. The mechanical response of the ground matrix can be divided in the contribution of osmotic pressure and an elastic solid part known as extra-fibrillar matrix (EFM). Mechanical properties of the ground matrix have been measured using tensile and confined compression tests. However, EFM mechanics have not been measured directly. The objective of this study was to measure AF nonlinear mechanics of the EFM in tension and compression. To accomplish this, a combination of osmotic swelling and confined compression in disk radial direction, perpendicular to the lamella, was used. For this type of analysis, it was necessary to define a stress-free reference configuration. Thus, a brief analysis on residual stress in the disk and a procedure to estimate the reference configuration are presented. The proposed method was able to predict similar swelling deformations when using different loading protocols and models for the EFM, demonstrating its robustness. The stress-stretch curve of the EFM was linear in the range 0.9 disk and can be applied to differentiate between functional degeneration effects such as PG loss and stiffening due to cross-linking.

Substrate-dependent cell elasticity measured by optical tweezers indentation

Science.gov (United States)

Yousafzai, Muhammad S.; Ndoye, Fatou; Coceano, Giovanna; Niemela, Joseph; Bonin, Serena; Scoles, Giacinto; Cojoc, Dan

2016-01-01

In the last decade, cell elasticity has been widely investigated as a potential label free indicator for cellular alteration in different diseases, cancer included. Cell elasticity can be locally measured by pulling membrane tethers, stretching or indenting the cell using optical tweezers. In this paper, we propose a simple approach to perform cell indentation at pN forces by axially moving the cell against a trapped microbead. The elastic modulus is calculated using the Hertz-model. Besides the axial component, the setup also allows us to examine the lateral cell-bead interaction. This technique has been applied to measure the local elasticity of HBL-100 cells, an immortalized human cell line, originally derived from the milk of a woman with no evidence of breast cancer lesions. In addition, we have studied the influence of substrate stiffness on cell elasticity by performing experiments on cells cultured on two substrates, bare and collagen-coated, having different stiffness. The mean value of the cell elastic modulus measured during indentation was 26±9 Pa for the bare substrate, while for the collagen-coated substrate it diminished to 19±7 Pa. The same trend was obtained for the elastic modulus measured during the retraction of the cell: 23±10 Pa and 13±7 Pa, respectively. These results show the cells adapt their stiffness to that of the substrate and demonstrate the potential of this setup for low-force probing of modifications to cell mechanics induced by the surrounding environment (e.g. extracellular matrix or other cells).

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

Science.gov (United States)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

Two-velocity elasticity theory and facet growth

OpenAIRE

Andreev, A. F.; Melnikovsky, L. A.

2002-01-01

We explain the linear growth of smooth solid helium facets by the presence of lattice point defects. To implement this task, the framework of very general two-velocity elasticity theory equations is developed. Boundary conditions for these equations for various surface types are derived. We also suggest additional experiments to justify the concept.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

Science.gov (United States)

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

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

OpenAIRE

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...

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

Science.gov (United States)

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.

Matrix density effects on the mechanical properties of SiC fiber-reinforced silicon nitride matrix properties

Science.gov (United States)

Bhatt, Ramakrishna T.; Kiser, Lames D.

1990-01-01

The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.

Homogenization of linear viscoelastic three phase media: internal variable formulation versus full-field computation

International Nuclear Information System (INIS)

Blanc, V.; Barbie, L.; Masson, R.

2011-01-01

Homogenization of linear viscoelastic heterogeneous media is here extended from two phase inclusion-matrix media to three phase inclusion-matrix media. Each phase obeying to a compressible Maxwellian behaviour, this analytic method leads to an equivalent elastic homogenization problem in the Laplace-Carson space. For some particular microstructures, such as the Hashin composite sphere assemblage, an exact solution is obtained. The inversion of the Laplace-Carson transforms of the overall stress-strain behaviour gives in such cases an internal variable formulation. As expected, the number of these internal variables and their evolution laws are modified to take into account the third phase. Moreover, evolution laws of averaged stresses and strains per phase can still be derived for three phase media. Results of this model are compared to full fields computations of representative volume elements using finite element method, for various concentrations and sizes of inclusion. Relaxation and creep test cases are performed in order to compare predictions of the effective response. The internal variable formulation is shown to yield accurate prediction in both cases. (authors)

Using an elastic magnifier to increase power output and performance of heart-beat harvesters

Science.gov (United States)

Galbier, Antonio C.; Karami, M. Amin

2017-09-01

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been a growing and innovative research area. The goal of these systems, at present, is to remove the pacemaker battery, which makes up 60%-80% of the unit, and replace it with a sustainable power source. This requires that energy harvesting systems provide sufficient power, 1-3 μW, for operating a pacemaker. The goal of this work is to develop, test, and simulate cantilevered energy harvesters with a linear elastic magnifier (LEM). This research hopes to provide insight into the interaction between pacemaker energy harvesters and the heart. By introducing the elastic magnifier into linear and nonlinear systems oscillations of the tip are encouraged into high energy orbits and large tip deflections. A continuous nonlinear model is presented for the bistable piezoelectric energy harvesting (BPEH) system and a one-degree-of-freedom linear mass-spring-damper model is presented for the elastic magnifier. The elastic magnifier will not consider the damping negligible, unlike most models. A physical model was created for the bistable structure and formed to an elastic magnifier. A hydrogel was designed for the experimental model for the LEM. Experimental results show that the BPEH coupled with a LEM (BPEH + LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH + LEM). Numerical simulations are consistent with these results. It was observed that the system enters high-energy and high orbit oscillations and that, ultimately, BPEH systems implemented in medical pacemakers can, if designed properly, have enhanced performance if positioned over the heart.

A micromechanics model of the elastic properties of human dentine

Energy Technology Data Exchange (ETDEWEB)

Kinney, J. H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Balooch, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Marshall, G. W. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry; Marshall, S. J. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry

1999-10-01

A generalized self-consistent model of cylindrical inclusions in a homogeneous and isotropic matrix phase was used to study the effects of tubule orientation on the elastic properties of dentin. Closed form expressions for the five independent elastic constants of dentin were derived in terms of tubule concentration, and the Young's moduli and Poisson ratios of peri- and intertubular dentin. An atomic force microscope (AFM) indentation technique determined the Young's moduli of the peri- and intertubular dentin as approximately 30 GPa and 15 GPa, respectively. Over the natural variation in tubule density found in dentin, there was only a slight variation in the axial and transverse shear moduli with position in the tooth, and there was no measurable effect of tubule orientation. We conclude that tubule orientation has no appreciable effect on the elastic behavior of normal dentin, and that the elastic properties of healthy dentin can be modeled as an isotropic continuum with a Young's modulus of approximately 16 GPa and a shear modulus of 6.2 GPa.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

Science.gov (United States)

Burr, P. A.; Cooper, M. W. D.

2017-09-01

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Thermodynamic analysis of elastic-plastic deformation

International Nuclear Information System (INIS)

Lubarda, V.

1981-01-01

The complete set of constitutive equations which fully describes the behaviour of material in elastic-plastic deformation is derived on the basis of thermodynamic analysis of the deformation process. The analysis is done after the matrix decomposition of the deformation gradient is introduced into the structure of thermodynamics with internal state variables. The free energy function, is decomposed. Derive the expressions for the stress response, entropy and heat flux, and establish the evolution equation. Finally, we establish the thermodynamic restrictions of the deformation process. (Author) [pt

Inelastic behaviour of collagen networks in cell–matrix interactions and mechanosensation

Science.gov (United States)

Mohammadi, Hamid; Arora, Pamma D.; Simmons, Craig A.; Janmey, Paul A.; McCulloch, Christopher A.

2015-01-01

The mechanical properties of extracellular matrix proteins strongly influence cell-induced tension in the matrix, which in turn influences cell function. Despite progress on the impact of elastic behaviour of matrix proteins on cell–matrix interactions, little is known about the influence of inelastic behaviour, especially at the large and slow deformations that characterize cell-induced matrix remodelling. We found that collagen matrices exhibit deformation rate-dependent behaviour, which leads to a transition from pronounced elastic behaviour at fast deformations to substantially inelastic behaviour at slow deformations (1 μm min−1, similar to cell-mediated deformation). With slow deformations, the inelastic behaviour of floating gels was sensitive to collagen concentration, whereas attached gels exhibited similar inelastic behaviour independent of collagen concentration. The presence of an underlying rigid support had a similar effect on cell–matrix interactions: cell-induced deformation and remodelling were similar on 1 or 3 mg ml−1 attached collagen gels while deformations were two- to fourfold smaller in floating gels of high compared with low collagen concentration. In cross-linked collagen matrices, which did not exhibit inelastic behaviour, cells did not respond to the presence of the underlying rigid foundation. These data indicate that at the slow rates of collagen compaction generated by fibroblasts, the inelastic responses of collagen gels, which are influenced by collagen concentration and the presence of an underlying rigid foundation, are important determinants of cell–matrix interactions and mechanosensation. PMID:25392399

Robust Model Predictive Control Using Linear Matrix Inequalities for the Treatment of Asymmetric Output Constraints

Directory of Open Access Journals (Sweden)

Mariana Santos Matos Cavalca

2012-01-01

Full Text Available One of the main advantages of predictive control approaches is the capability of dealing explicitly with constraints on the manipulated and output variables. However, if the predictive control formulation does not consider model uncertainties, then the constraint satisfaction may be compromised. A solution for this inconvenience is to use robust model predictive control (RMPC strategies based on linear matrix inequalities (LMIs. However, LMI-based RMPC formulations typically consider only symmetric constraints. This paper proposes a method based on pseudoreferences to treat asymmetric output constraints in integrating SISO systems. Such technique guarantees robust constraint satisfaction and convergence of the state to the desired equilibrium point. A case study using numerical simulation indicates that satisfactory results can be achieved.

Data-Driven Problems in Elasticity

Science.gov (United States)

Conti, S.; Müller, S.; Ortiz, M.

2018-01-01

We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.

How tall can gelatin towers be? An introduction to elasticity and buckling

Science.gov (United States)

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.

Consequences of elastic anisotropy in patterned substrate heteroepitaxy.

Science.gov (United States)

Dixit, Gopal Krishna; Ranganathan, Madhav

2018-06-13

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi--infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film--substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro--Tiller--Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time--scale for this inversion as function of height is analyzed. © 2018 IOP Publishing Ltd.

Linear reversible second-order cellular automata and their first-order matrix equivalents

International Nuclear Information System (INIS)

Macfarlane, A J

2004-01-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..

Effect of price elasticity of demand in monopolies with gradient adjustment

International Nuclear Information System (INIS)

Cavalli, Fausto; Naimzada, Ahmad

2015-01-01

Highlights: •A monopoly with isoelastic demand function is studied. •Reduced rationality monopolist uses gradient adjustment. •If marginal cost is small, increasing elasticity leads to stable dynamics. •For large marginal cost, dynamic can be unstable for both small and large elasticity. -- Abstract: We study a monopolistic market characterized by a constant elasticity demand function, in which the firm technology is described by a linear total cost function. The firm is assumed to be boundedly rational and to follow a gradient rule to adjust the production level in order to optimize its profit. We focus on what happens on varying the price elasticity of demand, studying the effect on the equilibrium stability. We prove that, depending on the relation between the market size and the marginal cost, two different scenarios are possible, in which elasticity has either a stabilizing or a mixed stabilizing/destabilizing effect

A Smoothed Finite Element-Based Elasticity Model for Soft Bodies

Directory of Open Access Journals (Sweden)

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.

A comparative study of Kalman filter and Linear Matrix Inequality based H infinity filter for SPND delay compensation

International Nuclear Information System (INIS)

Tamboli, P.K.; Duttagupta, Siddhartha P.; Roy, Kallol

2016-01-01

Highlights: • Derivation for delay compensation algorithm using recursive Kalman filter. • Derivation for delay compensation algorithm using Linear Matrix Inequality based H infinity filter. • Process modeling suitable for delay compensation. • Dynamic tuning of the delay compensation algorithm for both Kalman and H infinity filter. • Simulations and trade-off curve for Kalman and H infinity filter. - Abstract: This paper deals with delay compensation of vanadium Self Powered Neutron Detectors (SPNDs) using Linear Matrix Inequality (LMI) based H-infinity filtering method and compares the results with Kalman filtering method. The entire study is established upon the framework of neutron flux estimation in large core Pressurized Heavy Water Reactor (PHWR) in which delayed SPNDs such as vanadium SPNDs are used as in-core flux monitoring detectors. The use of vanadium SPNDs are limited to 3-D flux mapping despite of providing better Signal to Noise Ratio as compared to other prompt SPNDs, due to their small prompt component in the signal. The use of an appropriate delay compensation technique has been always considered to be an effective strategy to build a prompt and accurate estimate of the neutron flux. We also indicate the noise-response trade-off curve for both the techniques. Since all the delay compensation algorithms always suffer from noise amplification, we propose an efficient adaptive parameter tuning technique for improving performance of the filtering algorithm against noise in the measurement.

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

Science.gov (United States)

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.

Variational linear algebraic equations method

International Nuclear Information System (INIS)

Moiseiwitsch, B.L.

1982-01-01

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

Passive and active ventricular elastances of the left ventricle

Directory of Open Access Journals (Sweden)

Ng Eddie YK

2005-02-01

Full Text Available Abstract Background Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep and active (Ea elastance. By incorporating this concept in left ventricular (LV models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. Methods and Results Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as: ; Epis represented as: . Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. Conclusions Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea can be used to characterize the ventricle's contractile state, while passive elastance (Ep can represent a measure of resistance-to-filling.

Analysis of elastic interactions of hadrons at high energies

International Nuclear Information System (INIS)

Yuldashev, B.S.; Fazilova, Z.F.; Ismatov, E.I.; Kurmanbai, M.S.; Ajniyazova, G.T.; Tskhay, K.V.; Medeuova, A.B.

2004-01-01

Study of elastic interactions of hadrons at high energies if of great interest due to the fact that the amplitude of this process is the simplest, and at the same time, it is a fundamental object for theoretical and experimental researches. Study of this process allows one to have a quantitative check of various theories and models, and to make a critical selection. By using of fundamental property of theory - unitarity condition of scattering matrix - elastic scattering can be connected with inelastic reaction. Based on S-channel unitarity condition expressing elastic amplitude via inelastic overlapping function, to study the latter, as well as to describe the experimentally measured characteristics of hadron-nucleon interactions at high-energies, as well as for results prediction. By using experimental data on differential cross-section of elastic scattering of hadrons at various energies and by theoretical information on ratio of a real part and an imaginary part of scattering amplitude δ(t) the t-dependence of inelastic and elastic overlapping functions is studied. Influence of a zigzag form of differential cross-section of elastic pp(p) scattering on profile function and inelastic overlapping function to violation of geometric scaling was studied. In frames of the scaling the general expressions for s- and t-dependences of inelastic overlapping function are derived. Comparison of this function in three elastic scattering models was carried out. It was demonstrated that one would need to assume that hadrons become blacker at central part in order to correctly describe experimental angular distribution data. Dependence of differential cross-section on transfer momentum square for elastic hadrons scattering at energies of ISR and SPS in the model of inelastic overlapping function is studied. (author)

Analysis of elastic interactions of hadrons at high energies

International Nuclear Information System (INIS)

Fazylov, M.I.; Yuldashev, B.S.; Azhniyazova, G.T.; Ismatov, E.I.; Sartbay, T.; Kurmanbay, M.S.; Tskhay, K.V.

2004-01-01

Full text: Study of elastic interactions of hadrons at high energies if of great interest due to the fact that the amplitude of this process is the simplest, and at the same time, it is a fundamental object for theoretical and experimental researches. Study of this process allows one to have a quantitative check of various theories and models, and to make a critical selection. By using of fundamental property of theory - unitarity condition of scattering matrix - elastic scattering can be connected with inelastic reaction. Based on S-channel unitarity condition expressing elastic amplitude via inelastic overlapping function, to study the latter, as well as to describe the experimentally measured characteristics of hadron-nucleon interactions at high-energies, as well as for results prediction. By using experimental data on differential cross-section of elastic scattering of hadrons at various energies and by theoretical information on ratio of a real part and an imaginary part of scattering amplitude δ(t) the t-dependence of inelastic and elastic overlapping functions is studied. Influence of a zigzag form of differential cross-section of elastic pp(p) scattering on profile function and inelastic overlapping function to violation of geometric scaling was studied. In frames of the scaling the general expressions for s- and t-dependences of inelastic overlapping function are derived. Comparison of this function in three elastic scattering models was carried out. It was demonstrated that one would need to assume that hadrons become blacker at central part in order to correctly describe experimental angular distribution data. Dependence of differential cross-section on transfer momentum square for elastic hadrons scattering at energies of ISR and SPS in the model of inelastic overlapping function is studied

Micromechanical Analyses of Debonding and Matrix Cracking in Dual-Phase Materials

DEFF Research Database (Denmark)

Legarth, Brian Nyvang; Yang, Qingda

2016-01-01

Failure in elastic dual-phase materials under transverse tension is studied numerically. Cohesive zones represent failure along the interface and the augmented finite element method (A-FEM) is used for matrix cracking. Matrix cracks are formed at an angle of 55 deg - 60 deg relative to the loading...... direction, which is in good agreement with experiments. Matrix cracks initiate at the tip of the debond, and for equi-biaxial loading cracks are formed at both tips. For elliptical reinforcement the matrix cracks initiate at the narrow end of the ellipse. The load carrying capacity is highest for ligaments...

A Meta-analysis of the Price Elasticity of Gasoline Demand. A System of Equations Approach

NARCIS (Netherlands)

Brons, Martijn; Nijkamp, Peter; Pels, Eric; Rietveld, Piet

2006-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In

Rotational covariance and light-front current matrix elements

International Nuclear Information System (INIS)

Keister, B.D.

1994-01-01

Light-front current matrix elements for elastic scattering from hadrons with spin 1 or greater must satisfy a nontrivial constraint associated with the requirement of rotational covariance for the current operator. Using a model ρ meson as a prototype for hadronic quark models, this constraint and its implications are studied at both low and high momentum transfers. In the kinematic region appropriate for asymptotic QCD, helicity rules, together with the rotational covariance condition, yield an additional relation between the light-front current matrix elements

Elastic cartilage reconstruction by transplantation of cultured hyaline cartilage-derived chondrocytes.

Science.gov (United States)

Mizuno, M; Takebe, T; Kobayashi, S; Kimura, S; Masutani, M; Lee, S; Jo, Y H; Lee, J I; Taniguchi, H

2014-05-01

Current surgical intervention of craniofacial defects caused by injuries or abnormalities uses reconstructive materials, such as autologous cartilage grafts. Transplantation of autologous tissues, however, places a significant invasiveness on patients, and many efforts have been made for establishing an alternative graft. Recently, we and others have shown the potential use of reconstructed elastic cartilage from ear-derived chondrocytes or progenitors with the unique elastic properties. Here, we examined the differentiation potential of canine joint cartilage-derived chondrocytes into elastic cartilage for expanding the cell sources, such as hyaline cartilage. Articular chondrocytes are isolated from canine joint, cultivated, and compared regarding characteristic differences with auricular chondrocytes, including proliferation rates, gene expression, extracellular matrix production, and cartilage reconstruction capability after transplantation. Canine articular chondrocytes proliferated less robustly than auricular chondrocytes, but there was no significant difference in the amount of sulfated glycosaminoglycan produced from redifferentiated chondrocytes. Furthermore, in vitro expanded and redifferentiated articular chondrocytes have been shown to reconstruct elastic cartilage on transplantation that has histologic characteristics distinct from hyaline cartilage. Taken together, cultured hyaline cartilage-derived chondrocytes are a possible cell source for elastic cartilage reconstruction. Crown Copyright © 2014. Published by Elsevier Inc. All rights reserved.

Two linearization methods for atmospheric remote sensing

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions

International Nuclear Information System (INIS)

Zamolodchikov, A.B.

1981-01-01

The quantum S-matrix theory of straight-strings (infinite one-dimensioanl objects like straight domain walls) in 2 + 1-dimensions is considered. The S-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-string S-matrix, which apparently satisfies this tetrahedron equation, is proposed. (orig.)

Three Interpretations of the Matrix Equation Ax = b

Science.gov (United States)

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

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

CSIR Research Space (South Africa)

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...

Optimizing Thermal-Elastic Properties of C/C–SiC Composites Using a Hybrid Approach and PSO Algorithm

Science.gov (United States)

Xu, Yingjie; Gao, Tian

2016-01-01

Carbon fiber-reinforced multi-layered pyrocarbon–silicon carbide matrix (C/C–SiC) composites are widely used in aerospace structures. The complicated spatial architecture and material heterogeneity of C/C–SiC composites constitute the challenge for tailoring their properties. Thus, discovering the intrinsic relations between the properties and the microstructures and sequentially optimizing the microstructures to obtain composites with the best performances becomes the key for practical applications. The objective of this work is to optimize the thermal-elastic properties of unidirectional C/C–SiC composites by controlling the multi-layered matrix thicknesses. A hybrid approach based on micromechanical modeling and back propagation (BP) neural network is proposed to predict the thermal-elastic properties of composites. Then, a particle swarm optimization (PSO) algorithm is interfaced with this hybrid model to achieve the optimal design for minimizing the coefficient of thermal expansion (CTE) of composites with the constraint of elastic modulus. Numerical examples demonstrate the effectiveness of the proposed hybrid model and optimization method. PMID:28773343

Approximate formulas for elasticity of the Tornquist functions and some their advantages

Science.gov (United States)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

Science.gov (United States)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-05-01

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT=1 , the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998), 10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Metric elasticity in a collapsing star: Gravitational radiation coupled to torsional motion

International Nuclear Information System (INIS)

Gerlach, U.H.; Scott, J.F.

1986-01-01

Torsional oscillatory matter motion as well as differential rotation couple via the linearized Einstein field equations to the gravitational degrees of freedom. For an arbitrary spherically symmetric background, such as that of a wildly pulsating or a catastrophically collapsing star, we exhibit (a) the strain tensor and (b) the corresponding stress-energy tensor. It is found that in the star there are two elasticity tensors. One expresses the familiar elasticity of matter, the other expresses the elasticity of the geometry. This metric elasticity is responsible for coupling the gravitational and matter degrees of freedom. The two coupled scalar wave equations for these degrees of freedom are exhibited. Also exhibited are their characteristics as well as the junction conditions for their solutions across any spherical surface of discontinuity

EVALUATION OF EFFECTIVE PROPERTIES OF BASALT TEXTILE REINFORCED CERAMIC MATRIX COMPOSITES

Directory of Open Access Journals (Sweden)

Soňa Valentová

2017-11-01

Full Text Available The present paper is concerned with the analysis of a ceramic matrix composite, more specifically the plain weave textile fabric composite made of basalt fibers embedded into the pyrolyzed polysiloxane matrix. Attention is paid to the determination of effective elastic properties of the yarn via homogenization based on the Mori-Tanaka averaging scheme and the 1st order numerical homogenization method adopting a suitable representative computational model. The latter approach is then employed to simulate the response of the yarn when loaded beyond the elastic limits. The required mechanical properties of individual material phases are directly measured using nanoindentation with in-build scanning probe microscopy. Applicability of the proposed computational methodology is supported by the analysis of a unidirectional fibrous composite, representing the yarn, subjected to a macroscopically uniform strain.

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Algebraic Theory of Linear Viscoelastic Nematodynamics

International Nuclear Information System (INIS)

Leonov, Arkady I.

2008-01-01

This paper consists of two parts. The first one develops algebraic theory of linear anisotropic nematic 'N-operators' build up on the additive group of traceless second rank 3D tensors. These operators have been implicitly used in continual theories of nematic liquid crystals and weakly elastic nematic elastomers. It is shown that there exists a non-commutative, multiplicative group N 6 of N-operators build up on a manifold in 6D space of parameters. Positive N-operators, which in physical applications hold thermodynamic stability constraints, do not generally form a subgroup of group N 6 . A three-parametric, commutative transversal-isotropic subgroup S 3 subset of N 6 of positive symmetric nematic operators is also briefly discussed. The special case of singular, non-negative symmetric N-operators reveals the algebraic structure of nematic soft deformation modes. The second part of the paper develops a theory of linear viscoelastic nematodynamics applicable to liquid crystalline polymer. The viscous and elastic nematic components in theory are described by using the Leslie-Ericksen-Parodi (LEP) approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi-(10) parametric character of the theory, the use of nematic operators presents it in a transparent form. When the magnetic field is absent, the theory is simplified for symmetric case with six parameters, and takes an extremely simple, two-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reducible to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

. The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Influence of elastic strain on the thermodynamics and kinetics of lithium vacancy in bulk LiCoO2

Science.gov (United States)

Moradabadi, Ashkan; Kaghazchi, Payam; Rohrer, Jochen; Albe, Karsten

2018-01-01

The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gi j) for ground state and saddle point configurations. We analyze finite size effects in the calculation of Gi j, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain, and discuss the differences. Based on our data, we calculate the variations in vacancy concentration and mobility due to the presence of external strain in bulk LiCoO2 cathodes. Our results reveal that elastic in-plane and out-of-plane strains can significantly change the ionic conductivity of bulk LiCoO2 by up to several orders of magnitude and thus strongly affect the performance of Li-secondary batteries.

Universal composition-structure-property maps for natural and biomimetic platelet-matrix composites and stacked heterostructures.

Science.gov (United States)

Sakhavand, Navid; Shahsavari, Rouzbeh

2015-03-16

Many natural and biomimetic platelet-matrix composites--such as nacre, silk, and clay-polymer-exhibit a remarkable balance of strength, toughness and/or stiffness, which call for a universal measure to quantify this outstanding feature given the structure and material characteristics of the constituents. Analogously, there is an urgent need to quantify the mechanics of emerging electronic and photonic systems such as stacked heterostructures. Here we report the development of a unified framework to construct universal composition-structure-property diagrams that decode the interplay between various geometries and inherent material features in both platelet-matrix composites and stacked heterostructures. We study the effects of elastic and elastic-perfectly plastic matrices, overlap offset ratio and the competing mechanisms of platelet versus matrix failures. Validated by several 3D-printed specimens and a wide range of natural and synthetic materials across scales, the proposed universally valid diagrams have important implications for science-based engineering of numerous platelet-matrix composites and stacked heterostructures.

Elastin overexpression by cell-based gene therapy preserves matrix and prevents cardiac dilation

Science.gov (United States)

Li, Shu-Hong; Sun, Zhuo; Guo, Lily; Han, Mihan; Wood, Michael F G; Ghosh, Nirmalya; Alex Vitkin, I; Weisel, Richard D; Li, Ren-Ke

2012-01-01

After a myocardial infarction, thinning and expansion of the fibrotic scar contribute to progressive heart failure. The loss of elastin is a major contributor to adverse extracellular matrix remodelling of the infarcted heart, and restoration of the elastic properties of the infarct region can prevent ventricular dysfunction. We implanted cells genetically modified to overexpress elastin to re-establish the elastic properties of the infarcted myocardium and prevent cardiac failure. A full-length human elastin cDNA was cloned, subcloned into an adenoviral vector and then transduced into rat bone marrow stromal cells (BMSCs). In vitro studies showed that BMSCs expressed the elastin protein, which was deposited into the extracellular matrix. Transduced BMSCs were injected into the infarcted myocardium of adult rats. Control groups received either BMSCs transduced with the green fluorescent protein gene or medium alone. Elastin deposition in the infarcted myocardium was associated with preservation of myocardial tissue structural integrity (by birefringence of polarized light; P elastin showed the greatest functional improvement (P elastin in the infarcted heart preserved the elastic structure of the extracellular matrix, which, in turn, preserved diastolic function, prevented ventricular dilation and preserved cardiac function. This cell-based gene therapy provides a new approach to cardiac regeneration. PMID:22435995

On Love's approximation for fluid-filled elastic tubes

International Nuclear Information System (INIS)

Caroli, E.; Mainardi, F.

1980-01-01

A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)

The theory of elastic waves and waveguides

CERN Document Server

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.

A meta-analysis of the price elasticity of gasoline demand. A SUR approach

Energy Technology Data Exchange (ETDEWEB)

Brons, Martijn; Rietveld, Piet [Department of Spatial Economics, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam (Netherlands); Tinbergen Institute Amsterdam (TIA), Roetersstraat 31, 1018 WB Amsterdam (Netherlands); Nijkamp, Peter [Department of Spatial Economics, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam (Netherlands); Tinbergen Institute Amsterdam (TIA), Roetersstraat 31, 1018 WB Amsterdam (Netherlands); The Netherlands Organisation of Scientific Research (NWO), postbus 93138 - 2509 AC Den Haag (Netherlands); Pels, Eric [Department of Spatial Economics, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam (Netherlands)

2008-09-15

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In this meta-analytical study we aim to investigate and explain the variation in empirical estimates of the price elasticity of gasoline demand. A methodological novelty is that we use the linear relationship between the elasticities to develop a meta-analytical estimation approach based on a Seemingly Unrelated Regression (SUR) model with Cross Equation Restrictions. This approach enables us to combine observations of different elasticities and thus increase our sample size. Furthermore, it allows for a more detailed interpretation of our meta-regression results. The empirical results of the study demonstrate that the SUR approach leads to more precise results (i.e., lower standard errors) than a standard meta-analytical approach. We find that, with mean short run and long run price elasticities of - 0.34 and - 0.84, respectively, the demand for gasoline is not very price sensitive. Both in the short and the long run, the impact of a change in the gasoline price on demand is mainly driven by responses in fuel efficiency and mileage per car and to a slightly lesser degree by changes in car ownership. Furthermore, we find that study characteristics relating to the geographic area studied, the year of the study, the type of data used, the time horizon and the functional specification of the demand equation have a significant impact on the estimated value of the price elasticity of gasoline demand. (author)

A meta-analysis of the price elasticity of gasoline demand. A SUR approach

International Nuclear Information System (INIS)

Brons, Martijn; Rietveld, Piet; Nijkamp, Peter; Pels, Eric

2008-01-01

Automobile gasoline demand can be expressed as a multiplicative function of fuel efficiency, mileage per car and car ownership. This implies a linear relationship between the price elasticity of total fuel demand and the price elasticities of fuel efficiency, mileage per car and car ownership. In this meta-analytical study we aim to investigate and explain the variation in empirical estimates of the price elasticity of gasoline demand. A methodological novelty is that we use the linear relationship between the elasticities to develop a meta-analytical estimation approach based on a Seemingly Unrelated Regression (SUR) model with Cross Equation Restrictions. This approach enables us to combine observations of different elasticities and thus increase our sample size. Furthermore, it allows for a more detailed interpretation of our meta-regression results. The empirical results of the study demonstrate that the SUR approach leads to more precise results (i.e., lower standard errors) than a standard meta-analytical approach. We find that, with mean short run and long run price elasticities of - 0.34 and - 0.84, respectively, the demand for gasoline is not very price sensitive. Both in the short and the long run, the impact of a change in the gasoline price on demand is mainly driven by responses in fuel efficiency and mileage per car and to a slightly lesser degree by changes in car ownership. Furthermore, we find that study characteristics relating to the geographic area studied, the year of the study, the type of data used, the time horizon and the functional specification of the demand equation have a significant impact on the estimated value of the price elasticity of gasoline demand. (author)

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections. Part 1; Electron-Hydrogen Elastic Scattering

Science.gov (United States)

Bhatia, A. K.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2001-01-01

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

The indentation of pressurized elastic shells: from polymeric capsules to yeast cells

KAUST Repository

Vella, D.

2011-08-10

Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here, we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker\\'s yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

Science.gov (United States)

Bienvenu, François; Akçay, Erol; Legendre, Stéphane; McCandlish, David M

2017-06-01

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units. Copyright © 2017 Elsevier Inc. All rights reserved.

Fundamental topics for thermo-elastic stress analyses

International Nuclear Information System (INIS)

Biermann, M.

1989-01-01

This paper delivers a consistent collection of theoretical fundamentals needed to perform rather sound experimental stress analyses on thermo-elastic materials. An exposition of important concepts of symmetry and so-called peer groups, yielding the very base for a rational description of materials, goes ahead and is followed by an introduction to the constitutive theory of simple materials. Neat distinction is made between stress contributions determined by deformational and thermal impressions, on the one part, and stress constraints not accessible to strain gauging, on the other part. The mathematical formalism required for establishing constitutive equations is coherently developed from scratch and aided, albeit not subrogated, by intuition. The main intention goes to turning some of the recent advances in the nonlinear field theories of thermomechanics to practical account. A full success therein, obviously, results under the restriction to thermo-elasticity. In adverting to more particular subjects, the elementary static effects of nonlinear isotropic elasticity are pointed out. Due allowance is made for thermal effects likely to occur in heat conducting materials also beyond the isothermal or isentropic limit cases. Linearization of the constitutive equations for anisotropic thermo-elastic materials is then shown to entail the formulas of the classical theory. (orig./MM) [de

Probing hysteretic elasticity in weakly nonlinear materials

Energy Technology Data Exchange (ETDEWEB)

Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS

2010-12-07

Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.

Matrix transformations and sequence spaces

International Nuclear Information System (INIS)

Nanda, S.

1983-06-01

In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems.

Science.gov (United States)

Langenbucher, Frieder

2005-01-01

A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

Finite element evaluation of elasto-plastic accommodation energies during solid state transformations: Coherent, spherical precipitate in finite matrix

International Nuclear Information System (INIS)

Sen, S.; Balasubramaniam, R.; Sethuraman, R.

1996-01-01

The molar volume difference between the matrix and the precipitate phases in the case of solid state phase transformations results in the creation of stain energy in the system due to the misfit strains. A finite element model based on the initial strain approach is proposed to evaluate elasto-plastic accommodation energies during solid state transformation. The three-dimensional axisymmetric model has been used to evaluate energies as a function of transformation for α-β hydrogen transformations in the Nb-H system. The transformation has been analyzed for the cases of transformation progressing both from the center to surface and from the surface to center of the system. The effect of plastic deformation has been introduced to make the model realistic, specifically to the Nb-NbH phase transformation which involves a 4% linear misfit strain. It has been observed that plastic deformation reduces the strain energies compared to the linear elastic analysis

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

Science.gov (United States)

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Two-step algorithm of generalized PAPA method applied to linear programming solution of dynamic matrix control

International Nuclear Information System (INIS)

Shimizu, Yoshiaki

1991-01-01

In recent complicated nuclear systems, there are increasing demands for developing highly advanced procedures for various problems-solvings. Among them keen interests have been paid on man-machine communications to improve both safety and economy factors. Many optimization methods have been good enough to elaborate on these points. In this preliminary note, we will concern with application of linear programming (LP) for this purpose. First we will present a new superior version of the generalized PAPA method (GEPAPA) to solve LP problems. We will then examine its effectiveness when applied to derive dynamic matrix control (DMC) as the LP solution. The approach is to aim at the above goal through a quality control of process that will appear in the system. (author)

Matrix groups for undergraduates

CERN Document Server

Tapp, Kristopher

2005-01-01

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.

A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete

International Nuclear Information System (INIS)

Pasa Dutra, V.F.; Maghous, S.; Campos Filho, A.; Pacheco, A.R.

2010-01-01

Some aspects of the constitutive behavior of fiber reinforced concrete (FRC) are investigated within a micromechanical framework. Special emphasis is put on the prediction of creep of such materials. The linear elastic behavior is first examined by implementation of a Mori-Tanaka homogenization scheme. The micromechanical predictions for the overall stiffness prove to be very close to finite element solutions obtained from the numerical analysis of a representative elementary volume of FRC modeled as a randomly heterogeneous medium. The validation of the micromechanical concepts based on comparison with a set of experiments, shows remarkable predictive capabilities of the micromechanical representation. The second part of the paper is devoted to non-ageing viscoelasticity of FRC. Adopting a Zener model for the behavior of the concrete matrix and making use of the correspondence principle, the homogenized relaxation moduli are derived analytically. The validity of the model is established by mean of comparison with available experiment measurements of creep strain of steel fiber reinforced concrete under compressive load. Finally, the model predictions are compared to those derived from analytical models formulated within a one-dimensional setting.

International Conference on Matrix Analysis and its Applications 2015

CERN Document Server

2017-01-01

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

Treatise on classical elasticity theory and related problems

CERN Document Server

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...

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

Science.gov (United States)

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.

Nonlinear elasticity in wurtzite GaN/AlN planar superlattices and quantum dots

International Nuclear Information System (INIS)

Lepkowski, S.P.; Majewski, J.A.; Jurczak, G.

2005-01-01

The elastic stiffness tensor for wurtzite GaN and AlN show a significant hydrostatic pressure dependence, which id the evidence of nonlinear elasticity of these compounds. We have examined how the pressure dependence of elastic constants for wurtzite nitrides influences elastic and piezoelectric properties of GaN/AlN planar superlattices and quantum dots. Particularly we show that built-in hydrostatic pressure, present in both quantum wells of the GaN/AlN superlattices and GaN/AlN quantum dots, increases significantly by 0.3-0.7 GPa when nonlinear elasticity is used. Consequently, the compressive volumetric strain in quantum wells and quantum dots decreases in comparison to the case of the linear elastic theory, However, the-component of the built-in electric field in the quantum wells and quantum dots increases considerably when nonlinear elasticity is taken into account. Both effects, i.e., a decrease in the compressive volumetric strain as well as an increase in the built-in electric field, decrease the band-to-band transition energies in the quantum wells and quantum dots. (author)

Elastic-plastic fracture mechanics of compact bone

Science.gov (United States)

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

Elastic and inelastic form factors of the Ne20 in the Hartree-Fock approximation

International Nuclear Information System (INIS)

Oliveira, S.A.C. de.

1977-01-01

Properties of Ne 20 fundamental band are studied such as particle densities and elastic and inelastic form factors. A two body interaction is used and its matrix elements involve only the independent particle states of the 1s-0d shell [pt

Linear methods in band theory

DEFF Research Database (Denmark)

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

Performance evaluation of matrix gradient coils.

Science.gov (United States)

Jia, Feng; Schultz, Gerrit; Testud, Frederik; Welz, Anna Masako; Weber, Hans; Littin, Sebastian; Yu, Huijun; Hennig, Jürgen; Zaitsev, Maxim

2016-02-01

In this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields. An optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils. A cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter. The assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.

Generalised Assignment Matrix Methodology in Linear Programming

Science.gov (United States)

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Towards an Aero-Propulso-Servo-Elasticity Analysis of a Commercial Supersonic Transport

Science.gov (United States)

Connolly, Joseph W.; Kopasakis, George; Chwalowski, Pawel; Sanetrik, Mark D.; Carlson, Jan-Renee; Silva, Walt A.; McNamara, Jack

2016-01-01

This paper covers the development of an aero-propulso-servo-elastic (APSE) model using computational fluid dynamics (CFD) and linear structural deformations. The APSE model provides the integration of the following two previously developed nonlinear dynamic simulations: a variable cycle turbofan engine and an elastic supersonic commercial transport vehicle. The primary focus of this study is to provide a means to include relevant dynamics of a turbomachinery propulsion system into the aeroelastic studies conducted during a vehicle design, which have historically neglected propulsion effects. A high fidelity CFD tool is used here for the integration platform. The elastic vehicle neglecting the propulsion system serves as a comparison of traditional approaches to the APSE results. An overview of the methodology is presented for integrating the propulsion system and elastic vehicle. Static aeroelastic analysis comparisons between the traditional and developed APSE models for a wing tip detection indicate that the propulsion system impact on the vehicle elastic response could increase the detection by approximately ten percent.

Exploring linear algebra labs and projects with Mathematica

CERN Document Server

Arangala, Crista

2014-01-01