Nonlinear constitutive relations for anisotropic elastic materials
Sokolova, Marina; Khristich, Dmitrii
2018-03-01
A general approach to constructing of nonlinear variants of connection between stresses and strains in anisotropic materials with different types of symmetry of properties is considered. This approach is based on the concept of elastic proper subspaces of anisotropic materials introduced in the mechanics of solids by J. Rychlewski and on the particular postulate of isotropy proposed by A. A. Il’yushin. The generalization of the particular postulate on the case of nonlinear anisotropic materials is formulated. Systems of invariants of deformations as lengths of projections of the strain vector into proper subspaces are developed. Some variants of nonlinear constitutive relations for anisotropic materials are offered. The analysis of these relations from the point of view of their satisfaction to general and limit forms of generalization of partial isotropy postulate on anisotropic materials is performed. The relations for particular cases of anisotropy are written.
International Nuclear Information System (INIS)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao
2015-01-01
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications
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.
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys
International Nuclear Information System (INIS)
Jin Ke; Kou Yong; Zheng Xiaojing
2012-01-01
This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops. - Highlights: ► A general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials is proposed. ► Model is thermodynamically motivated and the reversible magnetic domain rotation and irreversible domain wall motion are taken. ► The predictions are in good accordance with the experimental data including both rods and films. ► Magnetostrictive alloys are sensitive to environment temperature and pre-stress or residual stress.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-11-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Elasticity of Doped Semiconductors
2017-02-01
AFRL-RY-WP-TR-2016-0206 NONLINEAR ELASTICITY OF DOPED SEMICONDUCTORS Mark Dykman and Kirill Moskovtsev Michigan State University...2016 4. TITLE AND SUBTITLE NONLINEAR ELASTICITY OF DOPED SEMICONDUCTORS 5a. CONTRACT NUMBER FA8650-16-1-7600 5b. GRANT NUMBER 5c. PROGRAM...vibration amplitude. 15. SUBJECT TERMS semiconductors , microresonators, microelectromechanical 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF
Nonlinear theory of elastic shells
International Nuclear Information System (INIS)
Costa Junior, J.A.
1979-08-01
Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt
Constitutive relations for non-elastic deformation
International Nuclear Information System (INIS)
Hart, E.W.
1978-01-01
A new class of constitutive equations is described for non-elastic deformation of metals. The relations are embodied in a model that has had considerable experimental investigation. The model employs two deformation state variables of which one is a scalar hardness variable and the other is a stored anelastic strain. The description is entirely in terms of real time strain rates. The model and its experimental background is discussed. The relationship to mechanical calculations and a possible extension to radiation environment is also considered. (Auth.)
Teaching nonlinear dynamics through elastic cords
International Nuclear Information System (INIS)
Chacon, R; Galan, C A; Sanchez-Bajo, F
2011-01-01
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
Multiaxial probabilistic elastic-plastic constitutive simulations of soils
Sadrinezhad, Arezoo
Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to simulate elastic-plastic constitutive behaviors of materials with uncertain material properties. The FPK equation approach transforms the stochastic constitutive rate equation, which is a stochastic, nonlinear, ordinary differential equation (ODE) in the stress-pseudo time space into a second-order accurate, deterministic, linear FPK partial differential equation (PDE) in the probability density of stress-pseudo time space. This approach does not suffer from the drawbacks of the traditional approaches such as the Monte Carlo approach and the perturbation approach for solving nonlinear ODEs with random coefficients. In this study, the existing one dimensional FPK framework for probabilistic constitutive modeling of soils is extended to multi--dimension. However, the multivariate FPK PDEs cannot be solved using the traditional mathematical techniques such as finite difference techniques due to their high computational cost. Therefore, computationally efficient algorithms based on the Fourier spectral approach are developed for solving a class of FPK PDEs that arises in probabilistic elasto-plasticity. This class includes linear FPK PDEs in (stress) space and (pseudo) time - having space-independent but time-dependent, and both space- and time-dependent coefficients - with impulse initial conditions and reflecting boundary conditions. The solution algorithms, rely on first mapping the stress space of the governing PDE between 0 and 2pi using the change of coordinates rule, followed by approximating the solution of the PDE in the 2pi-periodic domain by a finite Fourier series in the stress space and unknown time-dependent solution coefficients. Finally, the time-dependent solution coefficients are obtained from the initial condition. The accuracy and efficiency of the developed algorithms are tested. The developed algorithms are used to simulate uniaxial and multiaxial, monotonic and cyclic
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.
New constitutive equations to describe infinitesimal elastic-plastic deformations
International Nuclear Information System (INIS)
Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.
1983-01-01
A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Elastic-plastic constitutive modeling of concrete
International Nuclear Information System (INIS)
Takahashi, Y.
1983-03-01
The need to understand concrete behavior under high temperatures in the nuclear industry has become rather accute. For this purpose, a constitutive model of concrete especially developed for this severe environment is indispensable. This report reviews the presently available constitutive models of concrete at standard-temperature conditions and considers their advantages and drawbacks. A rather simple but effective approach is selected to treat concrete behavior at high temperatures. Special emphasis is devoted to the modeling of concrete up to and including failure. The derived constitutive model is checked with biaxial and triaxial benchmark experimental results. Very good agreement is obtained
Dynamic nonlinear interaction of elastic plates on discrete supports
International Nuclear Information System (INIS)
Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.
1984-01-01
A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt
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
Nonlinear elasticity in resonance experiments
Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel
2018-04-01
Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....
Nonlinear surface elastic modes in crystals
Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.
1990-03-01
The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.
Beams on nonlinear elastic foundation
International Nuclear Information System (INIS)
Lukkassen, Dag; Meidell, Annette
2014-01-01
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction
Polynomial constitutive model for shape memory and pseudo elasticity
International Nuclear Information System (INIS)
Savi, M.A.; Kouzak, Z.
1995-01-01
This paper reports an one-dimensional phenomenological constitutive model for shape memory and pseudo elasticity using a polynomial expression for the free energy which is based on the classical Devonshire theory. This study identifies the main characteristics of the classical theory and introduces a simple modification to obtain better results. (author). 9 refs., 6 figs
Free-vibration acoustic resonance of a nonlinear elastic bar
Tarumi, Ryuichi; Oshita, Yoshihito
2011-02-01
Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.
Stability of non-linear constitutive formulations for viscoelastic fluids
Siginer, Dennis A
2014-01-01
Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.
Special discontinuities in nonlinearly elastic media
Chugainova, A. P.
2017-06-01
Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.
Nonlinear transverse vibrations of elastic beams under tension
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Konno, Kimiaki; Wadati, Miki.
1980-02-01
Nonlinear transverse vibrations of elastic beams under end-thrust have been examined with full account of the rigorous nonlinear relation of curvature and deformation of elastic beams. When the beams are subject to tension, the derived equation is shown to be reduced to one of the new integrable evolution equations discovered by us. (author)
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Constitutive relationships for elastic deformation of clay rock: Data Analysis
International Nuclear Information System (INIS)
Liu, H.H.; Rutqvist, J.; Birkholzer, J.T.
2011-01-01
Geological repositories have been considered a feasible option worldwide for storing high-level nuclear waste. Clay rock is one of the rock types under consideration for such purposes, because of its favorable features to prevent radionuclide transport from the repository. Coupled hydromechanical processes have an important impact on the performance of a clay repository, and establishing constitutive relationships for modeling such processes are essential. In this study, we propose several constitutive relationships for elastic deformation in indurated clay rocks based on three recently developed concepts. First, when applying Hooke's law in clay rocks, true strain (rock volume change divided by the current rock volume), rather than engineering strain (rock volume change divided by unstressed rock volume), should be used, except when the degree of deformation is very small. In the latter case, the two strains will be practically identical. Second, because of its inherent heterogeneity, clay rock can be divided into two parts, a hard part and a soft part, with the hard part subject to a relatively small degree of deformation compared with the soft part. Third, for swelling rock like clay, effective stress needs to be generalized to include an additional term resulting from the swelling process. To evaluate our theoretical development, we analyze uniaxial test data for core samples of Opalinus clay and laboratory measurements of single fractures within macro-cracked Callovo-Oxfordian argillite samples subject to both confinement and water reduced swelling. The results from this evaluation indicate that our constitutive relationships can adequately represent the data and explain the related observations.
Constitutive relationships for elastic deformation of clay rock: Data Analysis
Energy Technology Data Exchange (ETDEWEB)
Liu, H.H.; Rutqvist, J.; Birkholzer, J.T.
2011-04-15
Geological repositories have been considered a feasible option worldwide for storing high-level nuclear waste. Clay rock is one of the rock types under consideration for such purposes, because of its favorable features to prevent radionuclide transport from the repository. Coupled hydromechanical processes have an important impact on the performance of a clay repository, and establishing constitutive relationships for modeling such processes are essential. In this study, we propose several constitutive relationships for elastic deformation in indurated clay rocks based on three recently developed concepts. First, when applying Hooke's law in clay rocks, true strain (rock volume change divided by the current rock volume), rather than engineering strain (rock volume change divided by unstressed rock volume), should be used, except when the degree of deformation is very small. In the latter case, the two strains will be practically identical. Second, because of its inherent heterogeneity, clay rock can be divided into two parts, a hard part and a soft part, with the hard part subject to a relatively small degree of deformation compared with the soft part. Third, for swelling rock like clay, effective stress needs to be generalized to include an additional term resulting from the swelling process. To evaluate our theoretical development, we analyze uniaxial test data for core samples of Opalinus clay and laboratory measurements of single fractures within macro-cracked Callovo-Oxfordian argillite samples subject to both confinement and water reduced swelling. The results from this evaluation indicate that our constitutive relationships can adequately represent the data and explain the related observations.
Nonlinear elastic inclusions in isotropic solids
Yavari, A.
2013-10-16
We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.
Sapphire: A kinking nonlinear elastic solid
Basu, S.; Barsoum, M. W.; Kalidindi, S. R.
2006-03-01
Kinking nonlinear elastic (KNE) solids are a recently identified large class of solids that deform fully reversibly by the formation of dislocation-based kink bands [Barsoum et al. Phys. Rev. Lett. 92, 255508 (2004)]. We further conjectured that a high c/a ratio-that ensures that only basal slip is operative-is a sufficient condition for a solid to be KNE. The c/a ratio of sapphire is 2.73 and thus, if our conjecture is correct, it should be a KNE solid. Herein by repeatedly loading-up to 30 times-the same location of sapphire single crystals of two orientations-A and C-with a 1 μm radius spherical nanoindenter, followed by atomic force microscopy, we showed that sapphire is indeed a KNE solid. After pop-ins of the order of 100 nm, the repeated loadings give rise to fully reversible, reproducible hysteresis loops wherein the energy dissipated per unit volume per cycle Wd is of the order of 0.5 GJ/m3. Wd is due to the back and fro motion of the dislocations making up the incipient kink bands that are fully reversible. The results presented here strongly suggest that-like in graphite and mica-kink bands play a more critical role in the room temperature constrained deformation of sapphire than had hitherto been appreciated. Our interpretation is also in agreement with, and can explain most, recent nanoindentation results on sapphire.
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks
Sebastian, Resmi; Sitharam, T. G.
2018-01-01
Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2017-04-15
The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.
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.
Nonlinear elastic inclusions in isotropic solids
Yavari, A.; Goriely, A.
2013-01-01
We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Nonlinear analysis of flexible plates lying on elastic foundation
Directory of Open Access Journals (Sweden)
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
Power laws and elastic nonlinearity in materials with complex microstructure
Energy Technology Data Exchange (ETDEWEB)
Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it
2016-01-28
Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.
Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints
Directory of Open Access Journals (Sweden)
Shaochong Yang
2017-01-01
Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.
Constitution-specific features of perspiration and skin visco-elasticity in SCM.
Kim, Young-Min; Ku, Boncho; Jung, Chang Jin; Kim, Jaeuk U; Jeon, Young Ju; Kim, Keun Ho; Kim, Jong Yeol
2014-01-15
Human skin properties have been used as an important diagnostic component in traditional medicine as they change with health conditions. Sasang constitutional medicine (SCM) puts emphasis on the recognition of the constitution-specific skin features prior to the diagnostic decision of health. In this work, in search of skin-characteristics effectively reflecting SCM features, we compared several skin properties such as perspiration, visco-elasticity, elasticity, and elasticity hysteresis, in several candidate body parts. We conducted a clinical study in which a total of 111 healthy females aged 50 - 70 years participated with their Sasang constitution (SC) types determined objectively by the Sasang constitutional analytic tool. Perspiration on the skin surface was estimated by using a capacitance sensor to measure the amount of moisture on the palm, forehead, and philtrum before and after a heating stimulus. We acquired the visco-elasticity, elasticity, and elasticity hysteresis at the forearm by Dermalab's elasticity sensing device. An analysis of covariance (ANCOVA) was conducted to evaluate the effect of SC on the nine skin features acquired. The visco-elasticity of the forearm of the Soeum-in (SE) group was significantly lower than that of the Taeeum-in (TE) group (F = 68.867, p elasticity hysteresis of the SE group was higher than that of the TE group (F = 10.364, p elasticity, elasticity hysteresis, perspiration on the forehead and philtrum. Our findings are based on a novel interpretation of the SCM literature and will contribute to developing the constitutional health status evaluation system in SCM.
Energy Technology Data Exchange (ETDEWEB)
Lester, Brian T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
Energy Technology Data Exchange (ETDEWEB)
Lester, Brian [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
On the dynamic buckling of a weakly damped nonlinear elastic ...
African Journals Online (AJOL)
In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular ...
On nonlinear thermo-electro-elasticity.
Mehnert, Markus; Hossain, Mokarram; Steinmann, Paul
2016-06-01
Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.
A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials
International Nuclear Information System (INIS)
Zhou Haomiao; Zhou Youhe; Zheng Xiaojing; Ye Qiang; Wei Jing
2009-01-01
In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang; Alkhalifah, Tariq Ali
2017-01-01
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang
2017-08-16
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity
Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.
2012-12-01
In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang
2016-09-06
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang; Alkhalifah, Tariq Ali
2016-01-01
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.
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.)
DYNAMICS OF VIBRATION FEEDERS WITH A NONLINEAR ELASTIC CHARACTERISTIC
Directory of Open Access Journals (Sweden)
V. I. Dyrda
2017-04-01
Full Text Available Purpose. Subject to the smooth and efficient operation of each production line, is the use of vehicles transporting high specification. It worked well in practice for transporting construction machines, which are used during the vibration. The use of vibration machines requires optimization of their operation modes. In the form of elastic link in them are increasingly using rubber-metallic elements, which are characterized by nonlinear damping properties. So it is necessary to search for new, more modern, methods of calculation of dynamic characteristics of the vibration machines on the properties of rubber as a cushioning material. Methodology. The dynamics of vibration machine that is as elastic rubber block units and buffer shock absorbers limiting the amplitude of the vibrations of the working body. The method of determining amplitude-frequency characteristics of the vibrating feeder is based on the principle of Voltaire, who in the calculations of the damping properties of the dampers will allow for elastic-hereditary properties of rubber. When adjusting the basic dynamic stiffness of the elastic ties and vibratory buffers, using the principle of heredity rubber properties, determine the dependence of the amplitude of the working body of the machine vibrations. This method is called integro-operator using the fractional-exponential kernels of relaxation. Findings. Using the derived formula for determining the amplitude of the resonance curve is constructed one-mass nonlinear system. It is established that the use of the proposed method of calculation will provide a sufficiently complete description of the damping parameters of rubber-metallic elements and at the same time be an effective means of calculating the amplitude-frequency characteristics of nonlinear vibration systems. Originality. The authors improved method of determining damping characteristics of rubber-metallic elements and the amplitude-frequency characteristics of nonlinear
Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity
2015-08-13
sufficient conditions for the compatibility of displacement gradient and the existence of stress functions on non-contractible bodies. The main...conditions. 15. SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...complex allows one to readily derive the necessary and sufficient conditions for the compatibility of displacement gradient and the existence of stress
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
2017-01-01
The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.
Lewiński, Paweł M.; Dudziak, Sławomir
2018-01-01
In the paper, two kinds of constitutive models for ground and structure were adopted for the nonlinear interaction analysis of the RC cylindrical tank with subsoil. The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Moreover, a non-linear elastic-brittle-plastic analysis of RC axisymmetric structures using finite element iterative techniques is presented. The constitutive laws for concrete and subsoil are developed in compliance with the deformational and plastic flow theories of plasticity. Two examples of an FE analysis of soil-structure interaction were performed and the results were analysed.
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
Elastic Nonlinear Response in Granular Media Under Resonance Conditions
Jia, X.; Johnson, P. A.
2004-12-01
We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass
Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.
Ciampa, Francesco; Mankar, Akash; Marini, Andrea
2017-11-07
Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
International Nuclear Information System (INIS)
Anderson, C.A.; Smith, P.D.
1979-01-01
Numerical prediction of the behavior of prestressed concrete reactor vessels (PCRVs) under static, dynamic and long term loadings is complicated by the currently ill-defined behavior of concrete under stress and the three-dimensional nature of PCRVs. Which constitutive model most closely approximates the behavior of concrete in PCRVs under load has not yet been decided. Many equations for accurately modeling the three-dimensional behavior of PCRVs tax the capability of a most up-to-date computing system. The main purpose of this paper is to compare the characteristics of two constitutive models which have been proposed for concrete, variable modulus cracking model and elastic-plastic model. Moreover, the behavior of typical concrete structures was compared, the materials of which obey these constitutive laws. The response to internal pressure of PCRV structure, the constitutive models for concrete, the test problems using a thick-walled concrete ring and a rectangular concrete plate, and the analysis of an axisymmetric concrete pressure vessel PV-26 using the variable modulus cracking model of the ADINA code are explained. The variable modulus cracking model can predict the behavior of reinforced concrete structures well into the range of nonlinear behavior. (Kako, I.)
On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms
Directory of Open Access Journals (Sweden)
Ida Mascolo
2018-03-01
Full Text Available The present work studies the geometrically nonlinear response of class θ = 1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables or compression (bars, under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either “standard” or “expanded” configurations. An experimental validation of the predicted constitutive response is conducted with reference to a “thick” and a “slender” model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.
On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms
Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando
2018-03-01
The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.
Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.
2018-01-01
Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.
Khan, Kamran
2012-11-10
We formulate a variational constitutive framework that accounts for nonlinear viscous behavior of electrically sensitive polymers, specifically Dielectric Elastomers (DEs), under large deformation. DEs are highly viscoelastic and their actuation response is greatly affected in dynamic applications. We used the generalized Maxwell model to represent the viscoelastic response of DE allowing the material to relax with multiple mechanisms. The constitutive updates at each load increment are obtained by minimizing an objective function formulated using the free energy and electrostatic energy of the elastomer, in addition to the viscous dissipation potential of the dashpots in each Maxwell branch. The model is then used to predict the electromechanical instability (EMI) of DE. The electro-elastic response of the DE is verified with available analytical solutions in the literature and then the material parameters are calibrated using experimental data. The model is integrated with finite element software to perform a variety of simulations on different types of electrically driven actuators under various electromechanical loadings. The electromechanical response of the DE and the critical conditions at which EMI occurs were found to be greatly affected by the viscoelasticity. Our model predicts that under a dead load EMI can be avoided if the DE operates at a high voltage rate. Subjected to constant, ramp and cyclic voltage, our model qualitatively predicts responses similar to the ones obtained from the analytical solutions and experimental data available in the literature. © 2012 Springer-Verlag Berlin Heidelberg.
Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage
International Nuclear Information System (INIS)
Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu
2007-01-01
Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material
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.
Khan, Kamran; El Sayed, Tamer S.
2012-01-01
We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer
Homogenized global nonlinear constitutive model for RC panels under cyclic loadings
International Nuclear Information System (INIS)
Huguet, Miquel; Voldoire, Francois; Kotronis, Panagiotis; Erlicher, Silvano
2014-01-01
A new nonlinear stress resultant global constitutive model for RC panels is presented. Concrete damage, concrete stress transfer at cracks and bond-slip stress are the main nonlinear effects identified at the local scale that constitute the basis for the construction of the stress resultant global model through an analytical homogenization technique. The closed form solution is obtained using general functions for the previous phenomena. (authors)
Georgievskii, D. V.
2017-07-01
The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.
Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach
International Nuclear Information System (INIS)
Sporykhin, A.N.
1995-01-01
The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle
A new type of surface acoustic waves in solids due to nonlinear elasticity
International Nuclear Information System (INIS)
Mozhaev, V.G.
1988-12-01
It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs
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...
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.
Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions
Khajehtourian, Romik
Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The
Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene
Sfyris, D.; Sfyris, G. I.; Bustamante, R.
2016-04-01
Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.
Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems
International Nuclear Information System (INIS)
Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E
2012-01-01
Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.
Florentin, Éric
2011-08-09
The constitutive equation gap method (CEGM) is a well-known concept which, until now, has been used mainly for the verification of finite element simulations. Recently, CEGM-based functional has been proposed to identify local elastic parameters based on experimental full-field measurement. From a technical point of view, this approach requires to quickly describe a space of statically admissible stress fields. We present here the technical insights, inspired from previous works in verification, that leads to the construction of such a space. Then, the identification strategy is implemented and the obtained results are compared with the actual material parameters for numerically generated benchmarks. The quality of the identification technique is demonstrated that makes it a valuable tool for interactive design as a way to validate local material properties. © 2011 Springer-Verlag.
Florentin, Éric
2010-04-23
Today, the identification ofmaterialmodel parameters is based more and more on full-field measurements. This article explains how an appropriate use of the constitutive equation gap method (CEGM) can help in this context. The CEGM is a well-known concept which, until now, has been used mainly for the verification of finite element simulations. This has led to many developments, especially concerning the techniques for constructing statically admissible stress fields. The originality of the present study resides in the application of these recent developments to the identification problem. The proposed CEGM is described in detail, then evaluated through the identification of heterogeneous isotropic elastic properties. The results obtained are systematically compared with those of the equilibrium gap method, which is a well-known technique for the resolution of such identification problems. We prove that the use of the enhanced CEGM significantly improves the quality of the results. © Springer-Verlag 2010.
Bulk nonlinear elastic strain waves in a bar with nanosize inclusions
DEFF Research Database (Denmark)
Gula, Igor A.; Samsonov (†), Alexander M.
2018-01-01
We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...
On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation
Zarubinskaya, M.A.; Van Horssen, W.T.
2003-01-01
In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is
Variational problems arising in classical mechanics and nonlinear elasticity
International Nuclear Information System (INIS)
Spencer, P.
1999-01-01
In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in
Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data
Schmitt, François G.
2007-10-01
Several nonlinear constitutive equations have been proposed to overcome the limitations of the linear eddy-viscosity models to describe complex turbulent flows. These nonlinear equations have often been compared to experimental data through the outputs of numerical models. Here we perform a priori analysis of nonlinear eddy-viscosity models using direct numerical simulation (DNS) of simple shear flows. In this paper, the constitutive equation is directly checked using a tensor projection which involves several invariants of the flow. This provides a 3 terms development which is exact for 2D flows, and a best approximation for 3D flows. We provide the quadratic nonlinear constitutive equation for the near-wall region of simple shear flows using DNS data, and estimate their coefficients. We show that these coefficients have several common properties for the different simple shear flow databases considered. We also show that in the central region of pipe flows, where the shear rate is very small, the coefficients of the constitutive equation diverge, indicating the failure of this representation for vanishing shears.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns...... with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions. The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions...
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.
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)
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
Energy Technology Data Exchange (ETDEWEB)
Chen, Ming-Song; Li, Kuo-Kuo [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Lin, Y.C. [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Central South University, Light Alloy Research Institute, Changsha (China); Chen, Jian [Changsha University of Science and Technology, School of Energy and Power Engineering, Key Laboratory of Efficient and Clean Energy Utilization, Changsha (China)
2016-09-15
The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)
International Nuclear Information System (INIS)
Chen, Ming-Song; Li, Kuo-Kuo; Lin, Y.C.; Chen, Jian
2016-01-01
The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)
The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation
Directory of Open Access Journals (Sweden)
Eitzinger B
2014-12-01
Full Text Available This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.
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)
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Non-linear waves in heterogeneous elastic rods via homogenization
Quezada de Luna, Manuel
2012-03-01
We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.
The propagation of nonlinear rayleigh waves in layered elastic half-space
International Nuclear Information System (INIS)
Ahmetolan, S.
2004-01-01
In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
Hocking, Erica G.; Wereley, Norman M.
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30-80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible.
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
International Nuclear Information System (INIS)
Hocking, Erica G; Wereley, Norman M
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30–80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible. (paper)
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)
1993-11-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.
International Nuclear Information System (INIS)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.
1993-01-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime
Equations of motion for anisotropic nonlinear elastic continuum in gravitational field
International Nuclear Information System (INIS)
Sokolov, S.N.
1994-01-01
Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs
Directory of Open Access Journals (Sweden)
Alain Mignot
2005-09-01
Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Thomsen, Jon Juel; Snaeland, Sveinn Orri
2008-01-01
The aim of this article is to investigate how highfrequency (HF) excitation, combined with strong nonlinear elastic material behavior, influences the effective material or structural properties for low-frequency excitation and wave propagation. The HF effects are demonstrated on discrete linear s...
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity
Directory of Open Access Journals (Sweden)
Dae Woo Park
2016-01-01
Full Text Available Shear wave elasticity imaging (SWEI can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE- based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard tumor and surrounding tissue (soft. The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.
Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity.
Park, Dae Woo
2015-01-01
Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.
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.
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...
Elastic-Plastic Endochronic Constitutive Model of 0Crl7Ni4Cu4Nb Stainless Steels
Directory of Open Access Journals (Sweden)
Jinquan Guo
2016-01-01
Full Text Available We presented an elastic-plastic endochronic constitutive model of 0Crl7Ni4Cu4Nb stainless steel based on the plastic endochronic theory (which does not need the yield surface and experimental stress-strain curves. The key feature of the model is that it can precisely describe the relation of stress and strain under various loading histories, including uniaxial tension, cyclic loading-unloading, cyclic asymmetric-stress axial tension and compression, and cyclic asymmetric-stress axial tension and compression. The effects of both mean stress and amplitude of stress on hysteresis loop based on the elastic-plastic endochronic constitutive model were investigated. Compared with the experimental and calculated results, it is demonstrated that there was a good agreement between the model and the experiments. Therefore, the elastic-plastic endochronic constitutive model provides a method for the accurate prediction of mechanical behaviors of 0Crl7Ni4Cu4Nb stainless steel subjected to various loadings.
Song, Han Wook; Lee, SungJun; Park, Yon Kyu; Woo, Sam Yong
2009-01-01
The usefulness of constitutional diagnoses based on skin measurements has been established in oriental medicine. However, it is very difficult to standardize traditional diagnosis methods. According to Sasang constitutional medicine, humans can be distinguished based on properties of the skin, including its texture, roughness, hardness and elasticity. The elasticity of the skin was previously used to distinguish between people with Tae-eumin (TE) and Soeumin (SE) constitutions. The present st...
Florentin, É ric; Lubineau, Gilles
2010-01-01
study resides in the application of these recent developments to the identification problem. The proposed CEGM is described in detail, then evaluated through the identification of heterogeneous isotropic elastic properties. The results obtained
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-03-12
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Lefèvre, Victor; Lopez-Pamies, Oscar
2017-02-01
This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi
Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.
Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames
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Jaroon Rungamornrat
2014-01-01
Full Text Available This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior. An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations. This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics. Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship. The global force-displacement relation for each element can be derived subsequently using corotational formulations. A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm. A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.
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.
International Nuclear Information System (INIS)
Baltacioglu, A.K.; Civalek, O.; Akgoez, B.; Demir, F.
2011-01-01
This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature. - Highlights: → Large deflection analysis of laminated composite plates are investigated. → As foundation, nonlinear elastic models have been used firstly. → The effects of three-parameter foundation are investigated in detail.
International Nuclear Information System (INIS)
Ruas, V.
1982-09-01
A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk
2009-01-01
Roč. 19, č. 2 (2009), s. 14-14 ISSN 1213-3825. [NDT in PROGRESS. 12.11.2009-14.11.2009, Praha] R&D Projects: GA ČR GA106/07/1393; GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear elastic wave spectroscopy (NEWS) * ESAM * time reversal (TR) * TR-NEWS imaging * tomography * DORT Subject RIV: BI - Acoustics
Song, Han Wook; Lee, Sungjun; Park, Yon Kyu; Woo, Sam Yong
2009-09-01
The usefulness of constitutional diagnoses based on skin measurements has been established in oriental medicine. However, it is very difficult to standardize traditional diagnosis methods. According to Sasang constitutional medicine, humans can be distinguished based on properties of the skin, including its texture, roughness, hardness and elasticity. The elasticity of the skin was previously used to distinguish between people with Tae-eumin (TE) and Soeumin (SE) constitutions. The present study designed a system that uses a compression method to measure the elasticity of hand skin and evaluated its measurement repeatability. The proposed system was used to compare the skin elasticity between SE and TE subjects, which produced a measurement repeatability error of <3%. The proposed system is suitable for use as a quantitative constitution diagnosis method for distinguishing between TE and SE subjects with an acceptable level of uncertainty.
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.
Cox, B. S.; Groh, R. M. J.; Avitabile, D.; Pirrera, A.
2018-07-01
The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to "nudge" the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging
Khan, Kamran
2012-11-09
We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material\\'s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions. © 2012 Springer-Verlag Wien.
Yu, Chao; Kang, Guozheng; Kan, Qianhua
2015-09-01
Based on the experimental observations on the anisotropic cyclic deformation of super-elastic NiTi shape memory alloy single crystals done by Gall and Maier (2002), a crystal plasticity based micromechanical constitutive model is constructed to describe such anisotropic cyclic deformation. To model the internal stress caused by the unmatched inelastic deformation between the austenite and martensite phases on the plastic deformation of austenite phase, 24 induced martensite variants are assumed to be ellipsoidal inclusions with anisotropic elasticity and embedded in the austenite matrix. The homogeneous stress fields in the austenite matrix and each induced martensite variant are obtained by using the Mori-Tanaka homogenization method. Two different inelastic mechanisms, i.e., martensite transformation and transformation-induced plasticity, and their interactions are considered in the proposed model. Following the assumption of instantaneous domain growth (Cherkaoui et al., 1998), the Helmholtz free energy of a representative volume element of a NiTi shape memory single crystal is established and the thermodynamic driving forces of the internal variables are obtained from the dissipative inequalities. The capability of the proposed model to describe the anisotropic cyclic deformation of super-elastic NiTi single crystals is first verified by comparing the predicted results with the experimental ones. It is concluded that the proposed model can capture the main quantitative features observed in the experiments. And then, the proposed model is further used to predict the uniaxial and multiaxial transformation ratchetting of a NiTi single crystal.
Directory of Open Access Journals (Sweden)
Larissa Carvalho Trojan Serpe
Full Text Available Introduction : This study aims to evaluate the influence of the biomechanical behavior of the midpalatal suture (MPS during the rapid maxillary expansion (RME when modeled by the Finite Element Method. Methods Four simulation alternatives are discussed and, for each analysis, the suture is considered as a functional unit with a different mechanical behavior: (i without MPS elements, (ii MPS with Young's modulus (E equal to 1 MPa, (ii MPS with E equal to 0.01 MPa and (iv MPS with bilinear elastic behavior. Results The stress analysis showed that, when MPS is not considered in the model, stress peaks are reduced in magnitude and their distribution is restricted to a smaller area when compared to the model with the inclusion of MPS (E=1 MPa. The increased suture stiffness also has a direct influence on MPS displacements after 30 expander activations. Conclusion The consideration of the MPS in RME computer models influences greatly the calculated displacements between the suture bone ends, even as the stress levels in maxillary structures. Furthermore, as proposed for the described model, the elastic bilinear behavior assigned to MPS allows coherent prediction of stresses and displacements results, being a good representation for this suture overall behavior.
A 2D nonlinear multiring model for blood flow in large elastic arteries
Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves
2017-12-01
In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.
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.
Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies
Sozio, Fabio; Yavari, Arash
2017-01-01
In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.
Elastic-plastic mechanical constitutive description for rock salt triaxial compression
International Nuclear Information System (INIS)
Butcher, B.M.
1981-06-01
A model for the time-independent part of the mechanical deformation of rock salt from the Waste Isolation Pilot Plant Site in southeastern New Mexico is presented. A recently published creep model was first used to correct conventional triaxial compression data for time-dependent deformation. The experimental data was from tests at a loading rate of approximately 11.9 N/s, 23 0 C, and confining pressures from 0 to -20.7 MPa. The corrected time-independent curves were then used to determine material constants for the model. Generalization to a three-dimensional plasticity-failure theory using a general constitutive relation proposed by Rudnicki and Rice was also performed. 7 figures, 3 tables
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.
Metamaterials-based sensor to detect and locate nonlinear elastic sources
Energy Technology Data Exchange (ETDEWEB)
Gliozzi, Antonio S.; Scalerandi, Marco [Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Miniaci, Marco; Bosia, Federico [Department of Physics, University of Torino, Via Pietro Giuria 1, 10125 Torino (Italy); Pugno, Nicola M. [Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Center for Materials and Microsystems, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (Trento) (Italy); School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)
2015-10-19
In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations.
Metamaterials-based sensor to detect and locate nonlinear elastic sources
International Nuclear Information System (INIS)
Gliozzi, Antonio S.; Scalerandi, Marco; Miniaci, Marco; Bosia, Federico; Pugno, Nicola M.
2015-01-01
In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations
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.
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.
van Kempen, Thomas H S; Donders, Wouter P; van de Vosse, Frans N; Peters, Gerrit W M
2016-04-01
The mechanical properties determine to a large extent the functioning of a blood clot. These properties depend on the composition of the clot and have been related to many diseases. However, the various involved components and their complex interactions make it difficult at this stage to fully understand and predict properties as a function of the components. Therefore, in this study, a constitutive model is developed that describes the viscoelastic behavior of blood clots with various compositions. Hereto, clots are formed from whole blood, platelet-rich plasma and platelet-poor plasma to study the influence of red blood cells, platelets and fibrin, respectively. Rheological experiments are performed to probe the mechanical behavior of the clots during their formation. The nonlinear viscoelastic behavior of the mature clots is characterized using a large amplitude oscillatory shear deformation. The model is based on a generalized Maxwell model that accurately describes the results for the different rheological experiments by making the moduli and viscosities a function of time and the past and current deformation. Using the same model with different parameter values enables a description of clots with different compositions. A sensitivity analysis is applied to study the influence of parameter variations on the model output. The relative simplicity and flexibility make the model suitable for numerical simulations of blood clots and other materials showing similar behavior.
International Nuclear Information System (INIS)
Anderson, C.A.; Smith, P.D.
1978-01-01
The variable modulus-cracking model is capable of predicting the behavior of reinforced concrete structures (such as the reinforced plate under transverse pressure described previously) well into the range of nonlinear behavior including the prediction of the ultimate load. For unreinforced thick-walled concrete vessels under internal pressure the use of elastic--plastic concrete models in finite element codes enhances the apparent ductility of the vessels in contrast to variable modulus-cracking models that predict nearly instantaneous rupture whenever the tensile strength at the inner wall is exceeded. For unreinforced thick-walled end slabs representative of PCRV heads, the behavior predicted by finite element codes using variable modulus-cracking models is much stiffer in the nonlinear range than that observed experimentally. Although the shear type failures and crack patterns that are observed experimentally are predicted by such concrete models, the ultimate load carrying capacity and vessel-ductility are significantly underestimated. It appears that such models do not adequately model such features as aggregate interlock that could lead to an enhanced vessel reserve strength and ductility
Detecting Damage in Composite Material Using Nonlinear Elastic Wave Spectroscopy Methods
Meo, Michele; Polimeno, Umberto; Zumpano, Giuseppe
2008-05-01
Modern aerospace structures make increasing use of fibre reinforced plastic composites, due to their high specific mechanical properties. However, due to their brittleness, low velocity impact can cause delaminations beneath the surface, while the surface may appear to be undamaged upon visual inspection. Such damage is called barely visible impact damage (BVID). Such internal damages lead to significant reduction in local strengths and ultimately could lead to catastrophic failures. It is therefore important to detect and monitor damages in high loaded composite components to receive an early warning for a well timed maintenance of the aircraft. Non-linear ultrasonic spectroscopy methods are promising damage detection and material characterization tools. In this paper, two different non-linear elastic wave spectroscopy (NEWS) methods are presented: single mode nonlinear resonance ultrasound (NRUS) and nonlinear wave modulation technique (NWMS). The NEWS methods were applied to detect delamination damage due to low velocity impact (<12 J) on various composite plates. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future NDT and structural health monitoring applications.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Carvalho, Gabriel D.
2013-11-11
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Carvalho, Gabriel D.; Miranda, José A.; Gadê lha, Hermes
2013-01-01
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Directory of Open Access Journals (Sweden)
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.
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee
In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
Compatible-strain mixed finite element methods for incompressible nonlinear elasticity
Faghih Shojaei, Mostafa; Yavari, Arash
2018-05-01
We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.
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.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current
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Ping Wang
2017-01-01
Full Text Available Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM, consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.
Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud
2016-09-01
The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.
Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.
Morlock, Merlin B; Kim, Jin-Yeon; Jacobs, Laurence J; Qu, Jianmin
2015-01-01
The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.
Liu, Lili
2014-05-22
We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.
Liu, Lili; Wu, Xiaozhi; Wang, Rui; Gan, Liyong; Wei, Qunyi
2014-01-01
We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.
Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining
2018-05-01
The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.
Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin
2017-02-01
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
Differential behavior of amino-imino constitutional isomers in nonlinear optical processes.
Latorre, Sonia; Moreira, Ibério de P R; Villacampa, Belén; Julià, Lluís; Velasco, Dolores; Bofill, Josep Maria; López-Calahorra, Francisco
2010-03-15
A detailed study of the "blocked" amino-imino tautomers derived from N-acridine-substituted 2-aminobenzothiazole--and their effect on the nonlinear optical response--is presented. The synthesis, characterization, and nonlinear optical properties of these frozen tautomers, namely, N-methyl-N-(2-nitroacridin-6-yl)-2-aminobenzothia-zole and 3-methyl-N-(7-nitroacridin-3-yl)-2-iminobenzothiazole, are reported. A theoretical model based on valence-bond theory is also proposed and used to analyze the effects of the nuclear configuration corresponding to each frozen tautomer structure. In the present case, the aromatic form and the allylic-anion-like system of the -N-C-N- group inherent to each isomer are crucial for understanding and analyzing the different responses of each "blocked" tautomer.
Directory of Open Access Journals (Sweden)
Yurii M. Streliaiev
2016-06-01
Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.
International Nuclear Information System (INIS)
Mirzade, Fikret Kh.
2005-01-01
The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined
Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady
2008-02-01
We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald
Gorb, Yuliya; Walton, Jay R.
2010-01-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging
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
Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).
Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P
2014-01-01
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Civalek, Ö.
2014-01-01
In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied
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.
International Nuclear Information System (INIS)
Zhou, Hao-Miao; Li, Chao; Xuan, Li-Ming; Zhao, Ji-Xiang; Wei, Jing
2011-01-01
This paper analyzes the magnetoelectric (ME) response around the resonance frequency in the magnetostrictive/piezoelectric/magnetostrictive (MPM) magnetoelectric laminate composites. Following the equivalent circuit method and considering the mechanical loss, we select the nonlinear magnetostrictive constitutive model to present a novel explicit nonlinear expression for the resonant magnetoelectric (ME) coefficient of the magnetoelectric laminate composites. Compared with the experimental results, the predicted resonant ME coefficient of the explicit expression shows a good agreement both qualitatively and quantitatively. Also, when the electromechanical coupling factor of the piezoelectric material, k 31 p , is small, this explicit expression can be reduced to the existing model. On this basis, this paper considers and predicts the magnetoelectric conversion characteristics of the magnetoelectric laminate composites, calculates and analyzes the influences of the thickness ratio of magnetostrictive layer and piezoelectric material, bias magnetic field, and saturation magnetostrictive coefficient on the resonant ME coefficient. This research can provide a theoretical basis for the preparation of magnetoelectric devices with good magnetoelectric conversion characteristics, such as magnetoelectric sensors, energy harvesting transducers, microwave devices etc
Nonlinear Elasticity of Borocarbide Superconductor YNi2B2C: A First-Principles Study
Directory of Open Access Journals (Sweden)
Lili Liu
2017-01-01
Full Text Available First-principles calculations combined with homogeneous deformation methods are used to investigate the second- and third-order elastic constants of YNi2B2C with tetragonal structure. The predicted lattice constants and second-order elastic constants of YNi2B2C agree well with the available data. The effective second-order elastic constants are obtained from the second- and third-order elastic constants for YNi2B2C. Based on the effective second-order elastic constants, Pugh’s modulus ratio, Poisson’s ratio, and Vickers hardness of YNi2B2C under high pressure are further investigated. It is shown that the ductility of YNi2B2C increases with increasing pressure.
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Byers, Loren W. [Los Alamos National Laboratory; Ten Cate, James A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-06-28
Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately, nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.
Czech Academy of Sciences Publication Activity Database
Kosík, Adam; Feistauer, M.; Hadrava, Martin; Horáček, Jaromír
2015-01-01
Roč. 267, September (2015), s. 382-396 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : discontinuous Galerkin method * nonlinear elasticity * compressible viscous flow * fluid–structure interaction Subject RIV: BI - Acoustics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf
Huang, Yonghui; Yang, Zhicheng; Liu, Airong; Fu, Jiyang
2018-05-28
The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL's dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.
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.
Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P
2006-04-01
The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.
International Nuclear Information System (INIS)
Ruffino, E.; Scalerandi, M.
2000-01-01
As discovered by recent quasi-static and dynamic resonance experiments, the classical nonlinear theory fails in describing the hysteretic behaviour of nonlinear mesoscopic materials like rocks, concrete, etc. The paper applies the local interaction simulation approach (LISA) for studying such kind of nonclassical nonlinearity. To this purpose, in the LISA treatment of ultrasonic wave propagation has been included a phenomenological model, based on the PM space approach, of the local mesoscopic features of rocks and other materials with localized damages. A quantitative comparison of simulation and experimental results in quasi-static experiments is also presented
Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.
2015-10-01
We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...
Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul
2011-08-22
We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.
Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall
Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A.
2018-05-01
Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Energy Technology Data Exchange (ETDEWEB)
Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Analysis of elastic nonlinearity for impact damage detection in composite laminates
International Nuclear Information System (INIS)
Frau, A; Porcu, M C; Aymerich, F; Pieczonka, L; Staszewski, W J
2015-01-01
This paper concerns the experimental analysis of nonlinear response features of a composite laminate plate for impact damage detection. The measurement procedure is based on the Scaling Subtraction Method (SSM) and consists in exciting the damaged specimen with two sinusoidal signals at different amplitude. The linearly rescaled response signal at low amplitude excitation is subtracted from the response at large amplitude excitation to extract the nonlinear signatures. The latter are analysed in the time domain to infer the presence of damage. Results are compared with frequency domain analyses using the nonlinear vibro-acoustic modulation technique (NWMS). Changes in amplitude and phase as well as modulation effects of the acquired responses are also monitored. Surface-bonded, low profile piezoceramic transducers are used for excitation and sensing. Both measurements techniques are applied to detect barely visible impact damage in laminate composite plate. Non-destructive penetrant-enhanced X-ray inspections are carried out to characterize the extent of internal damage. The behavior of the nonlinear features and the sensitivity of each technique are also investigated in the paper. (paper)
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.
2012-01-01
Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.
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.
International Nuclear Information System (INIS)
Walter, H.; Mang, H.A.
1991-01-01
A procedure for combining nonlinear short-time behavior of concrete with nonlinear creep compliance functions is presented. It is an important ingredient of a computer code for nonlinear finite element (FE) analysis of prestressed concrete shells, considering creep, shrinkage and ageing of concrete, and relaxation of the prestressing steel. The program was developed at the Institute for Strength of Materials of Technical University of Vienna, Austria. The procedure has resulted from efforts to extend the range of application of a Finite Element program, abbreviated as FESIA, which originally was capable of modeling reinforeced concrete in the context of thin-shell analysis, using nonlinear constitutive relations for both, conrete and steel. The extension encompasses the time-dependent behavior of concrete: Creep, shrinkage and ageing. Creep is modeled with the help of creep compliance functions which may be nonlinear to conform with the short-time constitutive relations. Ageing causes an interdependence between long-time and short-time deformations. The paper contains a description of the physical background of the procedure and hints on the implementation of the algorithm. The focus is on general aspects. Details of the aforementioned computer program are considered only where this is inevitable. (orig.)
Connolly, Joe; Carlson, Jan-Renee; Kopasakis, George; Woolwine, Kyle
2015-01-01
This paper covers the development of an integrated nonlinear dynamic model for a variable cycle turbofan engine, supersonic inlet, and convergent-divergent nozzle that can be integrated with an aeroelastic vehicle model to create an overall Aero-Propulso-Servo-Elastic (APSE) modeling tool. The primary focus of this study is to provide a means to capture relevant thrust dynamics of a full supersonic propulsion system by using relatively simple quasi-one dimensional computational fluid dynamics (CFD) methods that will allow for accurate control algorithm development and capture the key aspects of the thrust to feed into an APSE model. Previously, propulsion system component models have been developed and are used for this study of the fully integrated propulsion system. An overview of the methodology is presented for the modeling of each propulsion component, with a focus on its associated coupling for the overall model. To conduct APSE studies the described dynamic propulsion system model is integrated into a high fidelity CFD model of the full vehicle capable of conducting aero-elastic studies. Dynamic thrust analysis for the quasi-one dimensional dynamic propulsion system model is presented along with an initial three dimensional flow field model of the engine integrated into a supersonic commercial transport.
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.
Erler, Norbert; Groß, Michael
2015-05-01
Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.
Brands, D.W.A.; Peters, G.W.M.; Bovendeerd, P.H.M.
2004-01-01
Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. CurrentFE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model
Nonlinear analysis of the inflation of an initially flat, circular, elastic disk
International Nuclear Information System (INIS)
Christensen, R.M.; Feng, W.W.
1986-01-01
An approximate analysis is given for the inflation of a thin, flat circular disk of elastomeric material. The analysis results in a closed-form analytical solution for the maximum displacement as a function of pressure. The method is illustrated through the use of a Mooney-Rivlin material model. The results are compared with the exact solution, obtained by numerical means, and they are satisfactory, up into the range of several hundred percent strain. The method greatly simplifies the procedure for reducing test data, from this type of test, to nonlinear range mechanical properties
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.
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.
Basafa, Ehsan; Farahmand, Farzam
2011-05-01
Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.
International Nuclear Information System (INIS)
Chen, Ming-Song; Lin, Y.C.; Li, Kuo-Kuo; Chen, Jian
2016-01-01
In authors' previous work (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0371-6, 2016), the nonlinear unloading behavior of a typical Ni-based superalloy was investigated by hot compressive experiments with intermediate unloading-reloading cycles. The characters of unloading curves were discussed in detail, and a new elasto-viscoplastic constitutive model was proposed to describe the nonlinear unloading behavior of the studied Ni-based superalloy. Still, the functional relationships between the deformation temperature, strain rate, pre-strain and the parameters of the proposed constitutive model need to be established. In this study, the effects of deformation temperature, strain rate and pre-strain on the parameters of the new constitutive model proposed in authors' previous work (Chen et al. 2016) are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate and pre-strain. (orig.)
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Chenji Wei
2018-02-01
Full Text Available Gas transport in shale gas reservoirs is largely affected by rock properties such as permeability. These properties are often sensitive to the in-situ stress state changes. Accurate modeling of shale gas transport in shale reservoir rocks considering the stress sensitive effects on rock petrophysical properties is important for successful shale gas extraction. Nonlinear elasticity in stress sensitive reservoir rocks depicts the nonlinear stress-strain relationship, yet it is not thoroughly studied in previous reservoir modeling works. In this study, an improved coupled flow and geomechanics model that considers nonlinear elasticity is proposed. The model is based on finite element methods, and the nonlinear elasticity in the model is validated with experimental data on shale samples selected from the Longmaxi Formation in Sichuan Basin China. Numerical results indicate that, in stress sensitive shale rocks, nonlinear elasticity affects shale permeability, shale porosity, and distributions of effective stress and pore pressure. Elastic modulus change is dependent on not only in-situ stress state but also stress history path. Without considering nonlinear elasticity, the modeling of shale rock permeability in Longmaxi Formation can overestimate permeability values by 1.6 to 53 times.
Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong
2013-02-21
It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.
International Nuclear Information System (INIS)
Li Qian; Tu Juan; Guo Xiasheng; Zhang Dong; Matula, Thomas J
2013-01-01
It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius–time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity. (paper)
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.
Xu, Jingping; Tripathy, Sakya; Rubin, Jonathan M; Stidham, Ryan W; Johnson, Laura A; Higgins, Peter D R; Kim, Kang
2012-03-01
Strain developed under quasi-static deformation has been mostly used in ultrasound elasticity imaging (UEI) to determine the stiffness change of tissues. However, the strain measure in UEI is often less sensitive to a subtle change of stiffness. This is particularly true for Crohn's disease where we have applied strain imaging to the differentiation of acutely inflamed bowel from chronically fibrotic bowel. In this study, a new nonlinear elastic parameter of the soft tissues is proposed to overcome this limit. The purpose of this study is to evaluate the newly proposed method and demonstrate its feasibility in the UEI. A nonlinear characteristic of soft tissues over a relatively large dynamic range of strain was investigated. A simplified tissue model based on a finite element (FE) analysis was integrated with a laboratory developed ultrasound radio-frequency (RF) signal synthesis program. Two-dimensional speckle tracking was applied to this model to simulate the nonlinear behavior of the strain developed in a target inclusion over the applied average strain to the surrounding tissues. A nonlinear empirical equation was formulated and optimized to best match the developed strain-to-applied strain relation obtained from the FE simulation. The proposed nonlinear equation was applied to in vivo measurements and nonlinear parameters were further empirically optimized. For an animal model, acute and chronic inflammatory bowel disease was induced in Lewis rats with trinitrobenzene sulfonic acid (TNBS)-ethanol treatments. After UEI, histopathology and direct mechanical measurements were performed on the excised tissues. The extracted nonlinear parameter from the developed strain-to-applied strain relation differentiated the three different tissue types with 1.96 ± 0.12 for normal, 1.50 ± 0.09 for the acutely inflamed and 1.03 ± 0.08 for the chronically fibrotic tissue. T-tests determined that the nonlinear parameters between normal, acutely inflamed and fibrotic tissue
International Nuclear Information System (INIS)
Singh, B.N.; Lal, Achchhe
2010-01-01
This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.
National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...
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Shahriar Dastjerdi
2016-06-01
Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.
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Chaudhari Virendra Kumar
2017-01-01
Full Text Available This paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT,Second order perturbation technique (SOPT and Monte Carlo simulation (MCS methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV and probability density function (PDF for various aforementioned parameters.
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2016-01-01
The response of an offshore wind turbine tower and its monopile foundation has been investigated when exposed to linear and fully nonlinear irregular waves on four different water depths. The investigation focuses on the consequences of including full nonlinearity in the wave kinematics. The line...
International Nuclear Information System (INIS)
Batou, A.; Soize, C.; Brie, N.
2013-01-01
Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading
Energy Technology Data Exchange (ETDEWEB)
Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)
2013-09-15
Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.
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Mustapha Lahmar
2015-04-01
Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.
Lucchetti, Liana; Fraccia, Tommaso P.; Ciciulla, Fabrizio; Bellini, Tommaso
2017-01-01
Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced bi...
Gorb, Yuliya
2010-11-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.
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.
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Allam M. N. M.
2017-12-01
Full Text Available Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.
Continuum mechanics elasticity, plasticity, viscoelasticity
Dill, Ellis H
2006-01-01
FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.
2009-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.
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
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Jaroszewicz Jerzy
2018-01-01
Full Text Available The work is devoted to methods of analysis of vibrations and stability of discrete-continuous, multi-parameter models of beams, shafts, rotors, vanes, converting to homogeneous and one-dimensional. The properties of Cauchy's influence function and the characteristic series method were used to solve the boundary problem. It has been shown that the methods are an effective tool for solving boundary problems described by ordinary fourth-and second-order differential equations with variable parameters. Particular attention should be paid to the solution of the border problem of two-parameter elastic systems with variable distribution of parameters. Universal beam-specific equations with typical support conditions including vertical support, which do not depend on beam shape and axial load type, are recorded. The shape and type of load are considered in the form of an impact function that corresponds to any change in cross-section of the support and continuous axial load, so that the functions describing the stiffness, the mass and the continuous load are complete. As a result of the solution of the boundary vibration problem of freely bent support and any change in its cross-section, loaded with any longitudinal load, arranged on the resilient substrate, strict relations between the own frequency parameters and the load parameters were derived. Using the methods, simple calculations were made, easy to use in engineering practice and conditions of use were given. Experimental studies have confirmed the high accuracy of theoretical calculations using the proposed methods and formulas.
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V. Y. Zaitsev
2017-09-01
Full Text Available Results of examination of experimental data on non-linear elasticity of rocks using experimentally determined pressure dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects with explicitly introduced shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance (∼ 80 % of cracks with the normal-to-shear compliance ratios that significantly exceed the values typical of conventionally used crack models (such as penny-shaped cuts or thin ellipsoidal cracks. Correspondingly, rocks with such cracks demonstrate a strongly decreased Poisson ratio including a significant (∼ 45 % portion of rocks exhibiting negative Poisson ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity for further development of crack models to account for the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast to the conventional viewpoint that occurrence of a negative Poisson ratio is an exotic fact that is mostly discussed for artificial structures.
Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G
2006-01-28
A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.
Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo
2014-10-07
The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.
International Nuclear Information System (INIS)
Deb Nath, S.K.; Deb Nath, S.K.; Wong, C.H.; Deb Nath, S.K.
2014-01-01
Perfluoro polyethers (PFPEs) are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds) are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenon affects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multi dented functional lubricants such as Ar-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
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S. K. Deb Nath
2014-01-01
Full Text Available Perfluoropolyethers (PFPEs are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenonaffects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multidented functional lubricants such as ARJ-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.
Elastic properties of Gum Metal
International Nuclear Information System (INIS)
Kuramoto, Shigeru; Furuta, Tadahiko; Hwang, Junghwan; Nishino, Kazuaki; Saito, Takashi
2006-01-01
In situ X-ray diffraction measurements under tensile loading and dynamic mechanical analysis were performed to investigate the mechanisms of elastic deformation in Gum Metal. Tensile stress-strain curves for Gum Metal indicate that cold working substantially decreases the elastic modulus while increasing the yield strength, thereby confirming nonlinearity in the elastic range. The gradient of each curve decreased continuously to about one-third its original value near the elastic limit. As a result of this decrease in elastic modulus and nonlinearity, elastic deformability reaches 2.5% after cold working. Superelasticity is attributed to stress-induced martensitic transformations, although the large elastic deformation in Gum Metal is not accompanied by a phase transformation
International Nuclear Information System (INIS)
Yang, D.S.; Nguyen Minh, D.; Chanchole, S.; Gharbi, H.; Valli, P.; Bornert, M.
2010-01-01
Document available in extended abstract form only. The construction of underground nuclear waste repositories will strongly disturb the initial thermo-hydro-chemo-mechanical equilibrium of the site. In addition to direct mechanical perturbations during excavation, which induce redistribution of the stresses and possible damage of the surrounding rock mass, the ventilation of the galleries will also modify the moisture content of the rock, resulting in shrinking or swelling, and more generally modifying the physical-chemical properties of the material. Safety concerns about preservation of confining properties of rock mass at short and long time scales require a deep understanding of the hydro-mechanical behavior of the host rock. In particular the dependence of elastic, possibly anisotropic, moduli and nonlinear properties (plasticity, damage, creep...) as a function of the moisture level, need to be quantified. In addition, in order to construct physically based micromechanical models of these dependencies, the various micro-mechanisms at their origin and their characteristic scales need to be identified. Various independent studies agree on the decrease of overall rigidity and failure stress of argillite with increasing humidity. A recent study making use of optical full-field strain measurement techniques on centi-metric samples under uniaxial compression suggests that this apparent decrease of elastic properties on wet samples can be essentially explained by the presence of a millimetric network of 'meso-cracks', induced by the preliminary unconfined hydration process. Indeed, thanks to the full-field measurement technique, it was possible to show that the mechanical response of undamaged areas, in-between cracks, was very similar at all moisture contents, both in terms of average strains and strain fluctuations at the micrometric scale of the composite structure of the rock (matrix clay + other mineral inclusions). The preliminary hydro
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Berkowitz, Peter
2009-01-01
After their dismal performance in election 2008, conservatives are taking stock. As they examine the causes that have driven them into the political wilderness and as they explore paths out, they should also take heart. After all, election 2008 shows that America's constitutional order is working as designed. Indeed, while sorting out their errors…
International Nuclear Information System (INIS)
Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.
1990-01-01
This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)
Energy Technology Data Exchange (ETDEWEB)
Hammerand, Daniel Carl; Scherzinger, William Mark
2007-09-01
The Library of Advanced Materials for Engineering (LAME) provides a common repository for constitutive models that can be used in computational solid mechanics codes. A number of models including both hypoelastic (rate) and hyperelastic (total strain) constitutive forms have been implemented in LAME. The structure and testing of LAME is described in Scherzinger and Hammerand ([3] and [4]). The purpose of the present report is to describe the material models which have already been implemented into LAME. The descriptions are designed to give useful information to both analysts and code developers. Thus far, 33 non-ITAR/non-CRADA protected material models have been incorporated. These include everything from the simple isotropic linear elastic models to a number of elastic-plastic models for metals to models for honeycomb, foams, potting epoxies and rubber. A complete description of each model is outside the scope of the current report. Rather, the aim here is to delineate the properties, state variables, functions, and methods for each model. However, a brief description of some of the constitutive details is provided for a number of the material models. Where appropriate, the SAND reports available for each model have been cited. Many models have state variable aliases for some or all of their state variables. These alias names can be used for outputting desired quantities. The state variable aliases available for results output have been listed in this report. However, not all models use these aliases. For those models, no state variable names are listed. Nevertheless, the number of state variables employed by each model is always given. Currently, there are four possible functions for a material model. This report lists which of these four methods are employed in each material model. As far as analysts are concerned, this information is included only for the awareness purposes. The analyst can take confidence in the fact that model has been properly implemented
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Crushed Salt Constitutive Model
International Nuclear Information System (INIS)
Callahan, G.D.
1999-01-01
The constitutive model used to describe the deformation of crushed salt is presented in this report. Two mechanisms -- dislocation creep and grain boundary diffusional pressure solution -- are combined to form the basis for the constitutive model governing the deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. Upon complete consolidation, the crushed-salt model reproduces the Multimechanism Deformation (M-D) model typically used for the Waste Isolation Pilot Plant (WIPP) host geological formation salt. New shear consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on WIPP and southeastern New Mexico salt. Nonlinear least-squares model fitting to the database produced two sets of material parameter values for the model -- one for the shear consolidation tests and one for a combination of the shear and hydrostatic consolidation tests. Using the parameter values determined from the fitted database, the constitutive model is validated against constant strain-rate tests. Shaft seal problems are analyzed to demonstrate model-predicted consolidation of the shaft seal crushed-salt component. Based on the fitting statistics, the ability of the model to predict the test data, and the ability of the model to predict load paths and test data outside of the fitted database, the model appears to capture the creep consolidation behavior of crushed salt reasonably well
International Nuclear Information System (INIS)
Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P
2007-01-01
In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures
Institute of Scientific and Technical Information of China (English)
Wei LIU; Zhenyuan JIA; Fuji WANG; Yongshun ZHANG; Dongming GUO
2008-01-01
The geometrical nonlinearity of a giant magne-tostrictive thin film (GMF) can be clearly detected under the magnetostriction effect. Thus, using geometrical linear elastic theory to describe the strain, stress, and constitutive relationship of GMF is inaccurate. According to nonlinear elastic theory, a nonlinear deformation model of the bimorph GMF is established based on assumptions that the magnetostriction effect is equivalent to the effect of body force loaded on the GMF. With Taylor series method, the numerical solution is deduced. Experiments on TbDyFe/Polyimide (PI)/SmFe and TbDyFe/Cu/SmFe are then conducted to verify the proposed model, respectively. Results indicate that the nonlinear deflection curve model is in good conformity with the experimental data.
Yokoyama, Naoto; Takaoka, Masanori
2014-12-01
A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.
Fully coupled heat conduction and deformation analyses of visco-elastic solids
Khan, Kamran
2012-04-21
Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a viscoelastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly viscoelastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969,Mech. Time-Depend. Mater. 1:209-240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209-240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored. © Springer Science+Business Media, B. V. 2012.
International Nuclear Information System (INIS)
Ledbetter, H.M.
1983-01-01
This chapter investigates the following five aspects of engineering-material solid-state elastic constants: general properties, interrelationships, relationships to other physical properties, changes during cooling from ambient to near-zero temperature, and near-zero-temperature behavior. Topics considered include compressibility, bulk modulus, Young's modulus, shear modulus, Poisson's ratio, Hooke's law, elastic-constant measuring methods, thermodynamic potentials, higher-order energy terms, specific heat, thermal expansivity, magnetic materials, structural phase transitions, polymers, composites, textured aggregates, and other-phenomena correlations. Some of the conclusions concerning polycrystalline elastic properties and their temperature dependence are: elastic constants are physical, not mechanical, properties which relate thermodynamically to other physical properties such as specific heat and thermal expansivity; elastic constants at low temperatures are nearly temperature independent, as required by the third law of thermodynamics; and elastic constants can be used to study directional properties of materials, such as textured aggregates and composites
CONCERNING THE ELASTIC ORTHOTROPIC MODEL APPLIED TO WOOD ELASTIC PROPERTIES
Tadeu Mascia,Nilson
2003-01-01
Among the construction materials, wood reveals an orthotropic pattern, because of unique characteristics in its internal structure with three axes of wood biological directions (longitudinal, tangential and radial). elastic symmetry: longitudinal, tangential and radial, reveals an orthotropic pattern. The effect of grain angle orientation onin the elastic modulus constitutes the fundamental cause forof wood anisotropy. It is responsible for the greatest changes in the values of the constituti...
On the steady-state structure of shock waves in elastic media and dielectrics
International Nuclear Information System (INIS)
Kulikovskii, A. G.; Chugainova, A. P.
2010-01-01
A simplified system of equations describing small-amplitude nonlinear quasi-transverse waves in an elastic weakly anisotropic medium with complicated dissipation and dispersion is considered. A simplified system of equations derived for describing the propagation and evolution of one-dimensional weakly nonlinear electromagnetic waves in a weakly anisotropic dielectric is found to be of the same type as the system of equations for quasi-transverse waves in an elastic medium. The steady-state structure of small-amplitude quasi-transverse discontinuities and a large number of admissible discontinuity types is studied using this system of equations. Viscous dissipation is traditionally assumed to be described in terms of the next differentiation order as compared to those constituting the hyperbolic system describing long waves, while the terms responsible for dispersion have an even higher differentiation order.
Integrodifferential relations in linear elasticity
Kostin, Georgy V
2012-01-01
This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.
International Nuclear Information System (INIS)
Yang, J H; Yang, J; Kitipornchai, S
2012-01-01
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)
Sun, C. T.; Yoon, K. J.
1990-01-01
A one-parameter plasticity model was shown to adequately describe the orthotropic plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The nonlinear stress-strain relations were measured and compared with those predicted by the finite element analysis using the one-parameter elastic-plastic constitutive model. The results show that the one-parameter orthotropic plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.
Nonlinear dynamics between linear and impact limits
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.
Experimental determination of third-order elastic constants of diamond.
Lang, J M; Gupta, Y M
2011-03-25
To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Constitutive properties of salt from four sites
International Nuclear Information System (INIS)
Pfeifle, T.W.; Mellegard, K.D.; Senseny, P.E.
1983-04-01
Results are presented from laboratory strength and creep tests performed on salt specimens from the Richton dome in Mississippi, the Vacherie dome in Louisiana, the Permian basin in Texas, and the Paradox basin in Utah. The constitutive properties obtained are the elastic moduli and the failure envelope at 24 0 C and parameter values for the baseline creep law. Some additional data are presented to indicate how the elastic moduli and strength change with temperature. The constitutive properties given in this report and subsequent numerical simulations will serve as input to the screening of site locations for a nuclear-waste repository. The matrix of tests performed is the minimum effort required to obtain these constitutive properties. Comparison of results with those obtained for sites that have been characterized in greater detail suggests that the constitutive parameter values obtained are adequate for site-screening activity
Modeling of nonlinear responses for reciprocal transducers involving polarization switching
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Linxiang
2007-01-01
Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...
Orozco, Gustavo A; Tanska, Petri; Mononen, Mika E; Halonen, Kimmo S; Korhonen, Rami K
2018-02-02
Ligaments provide stability to the human knee joint and play an essential role in restraining motion during daily activities. Compression-tension nonlinearity is a well-known characteristic of ligaments. Moreover, simpler material representations without this feature might give reasonable results because ligaments are primarily in tension during loading. However, the biomechanical role of different constitutive representations and their fibril-reinforced poroelastic properties is unknown. A numerical knee model which considers geometric and material nonlinearities of meniscus and cartilages was applied. Five different constitutive models for the ligaments (spring, elastic, hyperelastic, porohyperelastic, and fibril-reinforced porohyperelastic (FRPHE)) were implemented. Knee joint forces for the models with elastic, hyperelastic and porohyperelastic properties showed similar behavior throughout the stance, while the model with FRPHE properties exhibited lower joint forces during the last 50% of the stance phase. The model with ligaments as springs produced the lowest joint forces at this same stance phase. The results also showed that the fibril network contributed substantially to the knee joint forces, while the nonfibrillar matrix and fluid had small effects. Our results indicate that simpler material models of ligaments with similar properties in compression and tension can be used when the loading is directed primarily along the ligament axis in tension.
Nonlinear analysis of RC cylindrical tank and subsoil accounting for a low concrete strength
Directory of Open Access Journals (Sweden)
Lewiński Paweł M.
2017-01-01
Full Text Available The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Two kinds of constitutive models for ground and structure were adopted for a nonlinear interaction analysis of the RC cylindrical tank with subsoil. The constitutive laws for concrete and subsoil were developed in compliance with the deformational and flow theories of plasticity. Moreover, a non-linear elastic-brittle-plastic analysis of RC axi-symmetric structures using finite element iterative techniques is presented. The results of the two types of FE analysis of soil-structure interaction are compared taking into account a low concrete strength of tank structure.
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
Engelbrecht, Jüri
2015-01-01
This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Vliet, Jurg; Wel, Steven; Dowd, Dara
2011-01-01
While it's always been possible to run Java applications on Amazon EC2, Amazon's Elastic Beanstalk makes the process easier-especially if you understand how it works beneath the surface. This concise, hands-on book not only walks you through Beanstalk for deploying and managing web applications in the cloud, you'll also learn how to use this AWS tool in other phases of development. Ideal if you're a developer familiar with Java applications or AWS, Elastic Beanstalk provides step-by-step instructions and numerous code samples for building cloud applications on Beanstalk that can handle lots
Directory of Open Access Journals (Sweden)
J. Javorova
2016-06-01
Full Text Available The purpose of this paper is to study the performance of a finite length journal bearing, taking into account effects of non-Newtonian Rabinowitsch flow rheology and elastic deformations of the bearing liner. According to the Rabinowitsch fluid model, the cubic-stress constitutive equation is used to account for the non-Newtonian effects of pseudoplastic and dilatant lubricants. Integrating the continuity equation across the film, the nonlinear non-Newtonian Reynolds-type equation is derived. The elasticity part of the problem is solved on the base of Vlassov model of an elastic foundation. The numerical solution of the modified Reynolds equation is carried out by using FDM with over-relaxation technique. The results for steady state bearing performance characteristics have been calculated for various values of nonlinear factor and elasticity parameters. It was concluded that in comparison with the Newtonian lubricants, higher values of film pressure and load carrying capacity have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants.
Nonlinear coherent structures in granular crystals
Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.
2017-10-01
The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.
The Constitutional Amendment Process
Chism, Kahlil
2005-01-01
This article discusses the constitutional amendment process. Although the process is not described in great detail, Article V of the United States Constitution allows for and provides instruction on amending the Constitution. While the amendment process currently consists of six steps, the Constitution is nevertheless quite difficult to change.…
Constitutional Rights in Indonesia
Judhariksawan
2018-01-01
The constitution is fundamental to the life of the modern state as a major foothold in state governance. Includes the guarantee of constitutional rights of citizens. The The constitution is the basis of state organizers to be implemented so that the state is obliged to guarantee the fulfillment of citizens' constitutional rights. Human rights have become an important part of the modern constitution. This study will describe how human rights guarantees become part of consti...
Constitutional changes and the dilemmas of constitutionalism
Directory of Open Access Journals (Sweden)
Arsen Bačić
2009-01-01
Full Text Available The need to develop constitutional mechanisms whose aim is to resolve fundamental relations in society demands the widest possible inclusion of all of society’s active participants in the discussion on the need to adopt or revise the Constitution. The opening of every new round of constitutional changes is of great importance because it always unlocks certain new and important questions. The answers to those questions should be offered by state authority (policy and civil society including science and its disciplines. In this paper, the author mentions several topics which are of interest in the current discussion on the significance of current constitutional changes for the future of the development of constitutionalism and democracy in the Republic of Croatia. These are above all topics of political and legal constitutionalism and suggestions linked to strengthening the independence of judicial powers. The author advocates consistent application of constitutional control and check mechanisms which exclude all insularity of judicial powers in relation to democratic control.
Directory of Open Access Journals (Sweden)
Helbig K.
2006-12-01
Full Text Available The propagation of elastic waves is generally treated under four assumptions: - that the medium is isotropic,- that the medium is homogeneous, - that there is a one-to-one relationship between stress and strain, - that stresses are linearly related to strains (equivalently, that strains are linearly related to stresses. Real media generally violate at least some-and often all-of these assumptions. A valid theoretical description of wave propagation in real media thus depends on the qualitative and quantitative description of the relevant inhomogeneity, anisotropy, and non-linearity: one either has to assume (or show that the deviation from the assumption can - for the problem at hand - be neglected, or develop a theoretical description that is valid even under the deviation. While the effect of a single deviation from the ideal state is rather well understood, difficulties arise in the combination of several such deviations. Non-linear elasticity of anisotropic (triclinic rock samples has been reported, e. g. by P. Rasolofosaon and H. Yin at the 6th IWSA in Trondheim (Rasolofosaon and Yin, 1996. Non-linear anisotropic elasticity matters only for non-infinitesimalamplitudes, i. e. , at least in the vicinity of the source. How large this vicinity is depends on the accuracy of observation and interpretation one tries to maintain, on the source intensity, and on the level of non-linearity. This paper is concerned with the last aspect, i. e. , with the meaning of the numbers beyond the fact that they are the results of measurements. As a measure of the non-linearity of the material, one can use the strain level at which the effective stiffness tensor deviates significantly from the zero-strain stiffness tensor. Particularly useful for this evaluation is the eigensystem (six eigenstiffnesses and six eigenstrains of the stiffness tensor : the eigenstrains provide suitable strain typesfor the calculation of the effective stiffness tensor, and the
Moussawi, Ali; Lubineau, Gilles; Florentin, É ric; Blaysat, Benoî t
2013-01-01
We revisit here the concept of the constitutive relation error for the identification of elastic material parameters based on image correlation. An additional concept, so called constitutive compatibility of stress, is introduced defining a subspace
International Nuclear Information System (INIS)
Leader, Elliot
1991-01-01
With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees
Directory of Open Access Journals (Sweden)
Leng Fei
2008-09-01
Full Text Available This paper discusses the seismic analysis of concrete dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with consideration of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the two models, a nonlinear analysis of the seismic response of the Koyna Gravity Dam and the Dagangshan Arch Dam was conducted. The results were compared with those of a linear elastic model and two rate-independent thermodynamics-based constitutive models, and the influences of constitutive models and strain rate on the seismic response of concrete dams were discussed. It can be concluded from the analysis that, during seismic response, the tensile stress is the control stress in the design and seismic safety evaluation of concrete dams. In different models, the plastic strain and plastic strain rate of concrete dams show a similar distribution. When the influence of the strain rate is considered, the maximum plastic strain and plastic strain rate decrease.
Constitutional reform as process
Schultze, Rainer-Olaf (Prof.)
2000-01-01
Constitutional reform as process. - In: The politics of constitutional reform in North America / Rainer-Olaf Schultze ... (eds.). - Opladen : Leske + Budrich, 2000. - S. 11-31. - (Politikwissenschaftliche paperbacks ; 30)
Transnational Constitutional Law
Zumbansen, P (Peer); K.I. Bhatt (Kinnari)
2018-01-01
textabstractThis chapter provides an overview of the emerging field of transnational constitutional law (TCL). Whilst questions of constitutional law are typically discussed in the context of a specific domestic legal setting, a salient strategy of TCL is to understand constitutional law and its
Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach
Energy Technology Data Exchange (ETDEWEB)
Wu, Long, E-mail: L.Wu-1@tudelft.nl [Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering (Netherlands); Tiso, Paolo, E-mail: ptiso@ethz.ch [ETH Zürich, Institute for Mechanical Systems (Switzerland)
2016-04-15
An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives stemming from the derivative of the eigenvalue problem. Furthermore, the Craig–Bampton method is applied to couple the different reduced components. Based on the linear projection, the configuration-dependent internal force can be expressed as cubic polynomials in the reduced coordinates. Coefficients of these polynomials can be precomputed for efficient runtime evaluation. The numerical results show that the modal derivatives are essential for the correct approximation of the nonlinear elastic deflection with respect to the body reference. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.
In Situ elastic property sensors
International Nuclear Information System (INIS)
Olness, D.; Hirschfeld, T.; Kishiyama, K.; Steinhaus, R.
1987-01-01
Elasticity is an important property of many materials. Loss of elasticity can have serious consequences, such as when a gasket deteriorates and permits leakage of an expensive or hazardous material, or when a damping system begins to go awry. Loss of elasticity can also provide information related to an ancillary activity such as degradation of electrical insulation, loss of plasticizer in a plastic, or changes in permeability of a thin film. In fact, the mechanical properties of most organic compounds are altered when the compound degrades. Thus, a sensor for the mechanical properties can be used to monitor associated characteristics as well. A piezoelectric material in contact with an elastomer forms an oscillating system that can provide real-time elasticity monitoring. This combination constitutes a forced harmonic oscillator with damping provided by the elastomer. A ceramic oscillator with a total volume of a few mm 3 was used as an elasticity sensor. It was placed in intimate contact with an elastomer and then monitored remotely with a simple oscillator circuit and standard frequency counting electronics. Resonant frequency shifts and changes in Q value were observed corresponding to changes in ambient temperature and/or changes in pressure applied to the sample. Elastomer samples pretreated with ozone (to simulate aging) showed changes in Q value and frequency response, even though there were no visible changes in the elastic samples
Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes
Goriely, A.; Tabor, M.
2013-01-01
Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells
Composite Beam Theory with Material Nonlinearities and Progressive Damage
Jiang, Fang
Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping
Nonlinearly coupled thermo-visco-elasticity
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš
2013-01-01
Roč. 20, č. 3 (2013), s. 1243-1275 ISSN 1021-9722 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : kelvin-voigt rheology * small strains * nonsimple materials Subject RIV: BA - General Mathematics Impact factor: 0.971, year: 2013 http://link.springer.com/article/10.1007%2Fs00030-012-0207-9
UNDERSTANDING INFORMAL CONSTITUTIONAL CHANGE
Directory of Open Access Journals (Sweden)
Stephen M. Griffin
2016-01-01
Full Text Available Amid much recent American work on the problem of informal constitutional change, this article stakes out a distinctive position. I argue that theories of constitutional change in the US must address the question of the relationship between the “small c” and “big C” Constitution and treat seriously the possibility of conflict between them. I stress the unavoidable role the text of the Constitution and structural doctrines of federalism and separation of powers play in this relationship and thus in constitutional change, both formal and informal. I therefore counsel against theories that rely solely on a practice-based approach or analogies between “small c” constitutional developments and British or Commonwealth traditions of the “unwritten” constitution and constitutional “conventions.” The alternative I advocate is to approach constitutional change from a historicist perspective that focuses attention on state building and the creation of new institutional capacities. This approach will allow us to make progress by highlighting that there can be multiple constitutional orders in a given historical era, thus accounting for the conflictual nature of contemporary constitutional development in the US.
Elastic-plastic transition: A universal law
Directory of Open Access Journals (Sweden)
Chen Zhong
2016-01-01
Full Text Available Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following: 1.There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2.Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3.Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.
A constitutive law for degrading bioresorbable polymers.
Samami, Hassan; Pan, Jingzhe
2016-06-01
This paper presents a constitutive law that predicts the changes in elastic moduli, Poisson's ratio and ultimate tensile strength of bioresorbable polymers due to biodegradation. During biodegradation, long polymer chains are cleaved by hydrolysis reaction. For semi-crystalline polymers, the chain scissions also lead to crystallisation. Treating each scission as a cavity and each new crystal as a solid inclusion, a degrading semi-crystalline polymer can be modelled as a continuum solid containing randomly distributed cavities and crystal inclusions. The effective elastic properties of a degrading polymer are calculated using existing theories for such solid and the tensile strength of the degrading polymer is predicted using scaling relations that were developed for porous materials. The theoretical model for elastic properties and the scaling law for strength form a complete constitutive relation for the degrading polymers. It is shown that the constitutive law can capture the trend of the experimental data in the literature for a range of biodegradable polymers fairly well. Copyright © 2016 Elsevier Ltd. All rights reserved.
Transnational Constitutional Law
Zumbansen, P (Peer); Bhatt, Kinnari
2018-01-01
textabstractThis chapter provides an overview of the emerging field of transnational constitutional law (TCL). Whilst questions of constitutional law are typically discussed in the context of a specific domestic legal setting, a salient strategy of TCL is to understand constitutional law and its values by placing them ‘in context’ with existing and evolving cultural norms and political, social and economic discourses and struggles. Drawing on socio-legal investigations into the relationships ...
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Staber, B; Guilleminot, J
2017-01-01
In this work, we address the constitutive modeling, in a probabilistic framework, of the hyperelastic response of soft biological tissues. The aim is on the one hand to mimic the mean behavior and variability that are typically encountered in the experimental characterization of such materials, and on the other hand to derive mathematical models that are almost surely consistent with the theory of nonlinear elasticity. Towards this goal, we invoke information theory and discuss a stochastic model relying on a low-dimensional parametrization. We subsequently propose a two-step methodology allowing for the calibration of the model using standard data, such as mean and standard deviation values along a given loading path. The framework is finally applied and benchmarked on three experimental databases proposed elsewhere in the literature. It is shown that the stochastic model allows experiments to be accurately reproduced, regardless of the tissue under consideration. Copyright © 2016 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Jansohn, W.
1997-10-01
This report deals with the formulation and numerical integration of constitutive models in the framework of finite deformation thermomechanics. Based on the concept of dual variables, plasticity and viscoplasticity models exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules are presented. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. In view of the development of an efficient numerical integration procedure, simplified versions of these constitutive models are supposed. In these versions, the thermoelastic strains are assumed to be small and a simplified kinematic hardening rule is considered. Additionally, in view of an implementation into the ABAQUS finite element code, the elasticity law is approximated by a hypoelasticity law. For the simplified onstitutive models, an implicit time-integration algorithm is developed. First, in order to obtain a numerical objective integration scheme, use is made of the HUGHES-WINGET-Algorithm. In the resulting system of ordinary differential equations, it can be distinguished between three differential operators representing different physical effects. The structure of this system of differential equations allows to apply an operator split scheme, which leads to an efficient integration scheme for the constitutive equations. By linearizing the integration algorithm the consistent tangent modulus is derived. In this way, the quadratic convergence of Newton's method used to solve the basic finite element equations (i.e. the finite element discretization of the governing thermomechanical field equations) is preserved. The resulting integration scheme is implemented as a user subroutine UMAT in ABAQUS. The properties of the applied algorithm are first examined by test calculations on a single element under tension-compression-loading. For demonstrating the capabilities of the constitutive theory
Zhao, Xin
2013-01-01
Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects
Remarks on stability of magneto-elastic shocks
Directory of Open Access Journals (Sweden)
Włodzimierz Domański
2015-12-01
Full Text Available The problem of stability of plane shock waves for a model of perfect magnetoelasticityis investigated. Important mathematical properties, like loss of strict hyperbolicityand loss of genuine nonlinearity, and their consequences for the stability ofmagneto-elastic shocks are discussed. It is shown that some of these shocks do not satisfyclassical Lax stability conditions. Both compressible and incompressible models ofmagneto-elasticity are discussed.[b]Keywords[/b]: perfect magneto-elasticity, shock waves, stability conditions
Zhao, Xin
2013-05-01
Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.
International Nuclear Information System (INIS)
Topchyan, I.I.; Dokhner, R.D.
1977-01-01
The effect of reorientation of anisotropic point defects in uniform fields of elastic stresses on the relaxation of the elastic coefficients of a crystal was investigated in the nonlinear elasticity theory approximation. In calculating the interaction of point defects with elastic-stress fields was taken into consideration. The expression for the relaxations of the elasticity coefficients are obtained in an analytical form. The relaxation of the second-order elasticity coefficients is due to the dimentional interaction of a point defect with an applied-stress field, whereas the relaxation of the higher-order elasticity coefficients is determined both by dimentional and module effects
Nonlinear dynamical triggering of slow slip
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE
2010-12-10
Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred
Frequency response functions for nonlinear convergent systems
Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.
2007-01-01
Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency
Constitutive model for porous materials
International Nuclear Information System (INIS)
Weston, A.M.; Lee, E.L.
1982-01-01
A simple pressure versus porosity compaction model is developed to calculate the response of granular porous bed materials to shock impact. The model provides a scheme for calculating compaction behavior when relatively limited material data are available. While the model was developed to study porous explosives and propellants, it has been applied to a much wider range of materials. The early development of porous material models, such as that of Hermann, required empirical dynamic compaction data. Erkman and Edwards successfully applied the early theory to unreacted porous high explosives using a Gruneisen equation of state without yield behavior and without trapped gas in the pores. Butcher included viscoelastic rate dependance in pore collapse. The theoretical treatment of Carroll and Holt is centered on the collapse of a circular pore and includes radial inertia terms and a complex set of stress, strain and strain rate constitutive parameters. Unfortunately data required for these parameters are generally not available. The model described here is also centered on the collapse of a circular pore, but utilizes a simpler elastic-plastic static equilibrium pore collapse mechanism without strain rate dependence, or radial inertia terms. It does include trapped gas inside the pore, a solid material flow stress that creates both a yield point and a variation in solid material pressure with radius. The solid is described by a Mie-Gruneisen type EOS. Comparisons show that this model will accurately estimate major mechanical features which have been observed in compaction experiments
On the concept of elasticity used in some fast reactor accident analysis codes
International Nuclear Information System (INIS)
Malmberg, T.
1975-01-01
The analysis to be presented will restrict attention to the elastic part of the elastic-plastic constitutive equation used in several Fast Reactor Accident Analysis Codes and originally applied by M.L. Wilkins: Calculation of Elastic-Plastic Flow, UCRL-7322, Rev. 1, Jan. 1969. It is shown that the used elasticity concept is within the frame of hypo-elasticity. On the basis of a test found by Bernstein it is proven that the state of stress is generally depending on the path of deformation. Therefore this concept of elasticity is not compatible with finite elasticity. For several simple deformation processes this special hypo-elastic constitutive equation is integrated to give a stress-strain relation. The path-dependence of this relation is demonstrated. Further the phenomenon of hypo-elastic yield under shear deformation is pointed out. The relevance to modelling material behaviour in primary containment analysis is discussed
Karimi, Alireza; Navidbakhsh, Mahdi; Haghighatnama, Maedeh; Haghi, Afsaneh Motevalli
2015-01-01
The skin, being a multi-layered material, is responsible for protecting the human body from the mechanical, bacterial, and viral insults. The skin tissue may display different mechanical properties according to the anatomical locations of a body. However, these mechanical properties in different anatomical regions and at different loading directions (axial and circumferential) of the mice body to date have not been determined. In this study, the axial and circumferential loads were imposed on the mice skin samples. The elastic modulus and maximum stress of the skin tissues were measured before the failure occurred. The nonlinear mechanical behavior of the skin tissues was also computationally investigated through a suitable constitutive equation. Hyperelastic material model was calibrated using the experimental data. Regardless of the anatomic locations of the mice body, the results revealed significantly different mechanical properties in the axial and circumferential directions and, consequently, the mice skin tissue behaves like a pure anisotropic material. The highest elastic modulus was observed in the back skin under the circumferential direction (6.67 MPa), while the lowest one was seen in the abdomen skin under circumferential loading (0.80 MPa). The Ogden material model was narrowly captured the nonlinear mechanical response of the skin at different loading directions. The results help to understand the isotropic/anisotropic mechanical behavior of the skin tissue at different anatomical locations. They also have implications for a diversity of disciplines, i.e., dermatology, cosmetics industry, clinical decision making, and clinical intervention.
A three-dimensional constitutive model for shape memory alloy
International Nuclear Information System (INIS)
Zhou, Bo; Yoon, Sung-Ho; Leng, Jin-Song
2009-01-01
Shape memory alloy (SMA) has a wide variety of practical applications due to its unique super-elasticity and shape memory effect. It is of practical interest to establish a constitutive model which predicts its phase transformation and mechanical behaviors. In this paper, a new three-dimensional phase transformation equation, which predicts the phase transformation behaviors of SMA, is developed based on the results of a differential scanning calorimetry (DSC) test. It overcomes both limitations: that Zhou's phase transformation equations fail to describe the phase transformation from twinned martensite to detwinned martensite of SMA and Brinson's phase transformation equation fails to express the influences of phase transformation peak temperatures on the phase transformation behaviors of SMA. A new three-dimensional constitutive equation, which predicts the mechanical behaviors associated with the super-elasticity and shape memory effect of SMA, is developed on the basis of thermodynamics and solid mechanics. Results of numerical simulations show that the new constitutive model, which includes the new phase transformation equation and constitutive equation, can predict the phase transformation and mechanical behaviors associated with the super-elasticity and shape memory effect of SMA precisely and comprehensively. It is proved that Brinson's constitutive model of SMA can be considered as one special case of the new constitutive model
Communicative Constitution of Organizations
DEFF Research Database (Denmark)
Schoeneborn, Dennis; Vasquez, Consuelo
2017-01-01
The notion of the communicative constitution of organizations (CCO) is at the center of a growing theoretical development within organizational communication studies. CCO scholarship is based on the idea that organization emerges in and is sustained and transformed by communication. This entry...
Ginsburg, Ruth Bader
1975-01-01
In discussing the constitutional aspects of the sex-role debate in the U.S. the author traces the tradition, compares the present criterion of equal protection to the equal rights argument, and analyzes the equality principle with reference to affirmative action and to childbearing and childrearing, supporting the proposed equal rights amendment.…
constitutional adjudication in ethiopia
African Journals Online (AJOL)
eliasn
2000-01-25
Jan 25, 2000 ... Thus the seeds of what some authors call. “federal .... Pre-WWII Europe trusted its legislature and led to .... European and Civil Law Forum v. 11 ...... on the sovereignty of nationalities and the fact that language constitutes one.
DEFF Research Database (Denmark)
Hanghøj, Sara
2009-01-01
personal values materialize through a hand-made everyday artefact, and how can the artefact constitute action and self-perception? The empirical research and analysis concerns how a former textile crafts teacher's subjective values and professional identity materialize through a hand-woven sofa cushion...
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
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.
Faiz, Pan Mohamad
2016-01-01
A jurisdiction of the Indonesian Constitutional Court concerning constitutional adjudication is only limited to review the constitutionality of national law. There is no mechanism for challenging any decision or action made by public authorities that violate fundamental rights enshrined in the Indonesian Constitution. This article argues that constitutional complaint and constitutional question might be adopted as new jurisdictions of the Indonesian Constitutional Court in order to strengthen...
International Nuclear Information System (INIS)
Senseny, P.E.; Pfeifle, T.W.; Mellegard, K.D.
1985-01-01
Results are presented from laboratory tests performed on salt and nonsalt rocks from the Palo Duro Basin in Texas. The Unit 5 salt from the Lower San Andres is assumed to be the repository horizon and is more completely characterized than other strata. For the Unit 5 salt, values are given for the parameters in the exponential-time constitutive law that models the time-independent elastic deformation and the time-dependent inelastic deformation. Both linear and nonlinear failure envelopes for this salt at 20 0 C are also determined. Data reported for twenty other salt and nonsalt horizons include tangent moduli and principal strain ratios, as well as linear failure envelopes at 20 0 C. The matrix of tests performed is adequate for conceptual repository design and performance analysis. However, final repository design and performance analysis requires more extensive characterization of the constitutive behavior of the stratigraphy, especially the repository-horizon salt
FEAST: a two-dimensional non-linear finite element code for calculating stresses
International Nuclear Information System (INIS)
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Rajagopal, K. R.
2011-01-06
This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.
Nonlinear elastic properties of bulk metallic glasses Zr52.5Ti5Cu17.9Ni14.6Al10 and Pd40Cu30Ni10P20
International Nuclear Information System (INIS)
Kobelev, N.P.; Kolyvanov, E.L.; Khonik, V.A.
2005-01-01
The influence of uniaxial compression on the propagation of ultrasonic vibrations in Zr 52.5 Ti 5 Cu 17.9 Ni 14.6 Al 10 and Pd 40 Cu 30 Ni 10 P 20 bulk metallic glasses produced by melt quenching at a rate of 100 K/s is investigated. Elastic deformation was realized by compression of the samples along their long axis up to strains of about 1 GPa. Deriving of major ratios used during the calculation of the third-order elastic moduli of the glasses is described in brief, the results of the calculations being provided. A qualitative agreement between the calculated results and available data on the influence of the uniform pressure on the sound wave propagation rate was obtained [ru
What constitutes information integrity?
Directory of Open Access Journals (Sweden)
S. Flowerday
2008-01-01
Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'
What constitutes information integrity?
Directory of Open Access Journals (Sweden)
S. Flowerday
2007-12-01
Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'
Directory of Open Access Journals (Sweden)
Roberto Horácio Sá Pereira
2016-05-01
Full Text Available http://dx.doi.org/10.5007/1808-1711.2016v20n2p165 This brief paper is devoted to criticizing the widespread reading of Kant’s first Critique, according to which reference to subject-independent objects is “constituted” by higherorder cognitive abilities (concepts. Let us call this the “constitutional view”. In this paper, I argue that the constitutional reading confuses the un-Kantian problem of how we come to represent objects (which I call the intentionality thesis, with the quite different problem of how we cognize (erkennen (which I call the “cognition thesis” that we do represent objects, that is, things that exist independently of the subject.
Transnational Governance and Constitutionalism
DEFF Research Database (Denmark)
Joerges, Christian; Sand, Inger-Johanne; Teubner, Gunther
of democratic governance. The book refers to this term as a yardstick to which then contributors feel committed even where they plead for a reconceptualisation of constitutionalism or a discussion of its functional equivalents. 'Transnational governance' is neither public nor private, nor purely international......The term transnational governance designates untraditional types of international and regional collaboration among both public and private actors. These legally-structured or less formal arrangements link economic, scientific and technological spheres with political and legal processes...
Nonlinear kinematics for piezoelectricity in ALEGRA-EMMA.
Energy Technology Data Exchange (ETDEWEB)
Mitchell, John Anthony; Fuller, Timothy Jesse
2013-09-01
This report develops and documents nonlinear kinematic relations needed to implement piezoelectric constitutive models in ALEGRA-EMMA [5], where calculations involving large displacements and rotations are routine. Kinematic relationships are established using Gausss law and Faradays law; this presentation on kinematics goes beyond piezoelectric materials and is applicable to all dielectric materials. The report then turns to practical details of implementing piezoelectric models in an application code where material principal axes are rarely aligned with user defined problem coordinate axes. This portion of the report is somewhat pedagogical but is necessary in order to establish documentation for the piezoelectric implementation in ALEGRA-EMMA. This involves transforming elastic, piezoelectric, and permittivity moduli from material principal axes to problem coordinate axes. The report concludes with an overview of the piezoelectric implementation in ALEGRA-EMMA and small verification examples.
Implicit constitutive models with a thermodynamic basis: a study of stress concentration
Bridges, C.; Rajagopal, K. R.
2015-02-01
Motivated by the recent generalization of the class of elastic bodies by Rajagopal (Appl Math 48:279-319, 2003), there have been several recent studies that have been carried out within the context of this new class. Rajagopal and Srinivasa (Proc R Soc Ser A 463:357-367, 2007, Proc R Soc Ser A: Math Phys Eng Sci 465:493-500, 2009) provided a thermodynamic basis for such models and appealing to the idea that rate of entropy production ought to be maximized they developed nonlinear rate equations of the form where T is the Cauchy stress and D is the stretching tensor as well as , where S is the Piola-Kirchhoff stress tensor and E is the Green-St. Venant strain tensor. We follow a similar procedure by utilizing the Gibb's potential and the left stretch tensor V from the Polar Decomposition of the deformation gradient, and we show that when the displacement gradient is small one arrives at constitutive relations of the form . This is, of course, in stark contrast to traditional elasticity wherein one obtains a single model, Hooke's law, when the displacement gradient is small. By solving a classical boundary value problem, with a particular form for f( T), we show that when the stresses are small, the strains are also small which is in agreement with traditional elasticity. However, within the context of our model, when the stress blows up the strains remain small, unlike the implications of Hooke's law. We use this model to study boundary value problems in annular domains to illustrate its efficacy.
Advanced development of BEM for elastic and inelastic dynamic analysis of solids
Banerjee, P. K.; Ahmad, S.; Wang, H. C.
1989-01-01
Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.
Elastic scattering and quasi-elastic transfers
International Nuclear Information System (INIS)
Mermaz, M.C.
1978-01-01
Experiments are presented which it will be possible to carry out at GANIL on the elastic scattering of heavy ions: diffraction phenomena if the absorption is great, refraction phenomena if absorption is low. The determination of the optical parameters can be performed. The study of the quasi-elastic transfer reactions will make it possible to know the dynamics of the nuclear reactions, form exotic nuclei and study their energy excitation spectrum, and analyse the scattering and reaction cross sections [fr
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Nonlinear rock behavior and its implications on deeper-level platinum mining
CSIR Research Space (South Africa)
Watson, BP
2008-10-01
Full Text Available Uniaxial tests performed on core from instrumented sites at Amandelbult 1 shaft, Impala 10 shaft and Union Section Spud-shaft showed a nonlinear elastic relationship between applied load and induced deformation. This nonlinear behaviour does...
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.
Indentation of elastically soft and plastically compressible solids
DEFF Research Database (Denmark)
Needleman, A.; Tvergaard, Viggo; Van der Giessen, E.
2015-01-01
rapidly for small deviations from plastic incompressibility and then decreases rather slowly for values of the plastic Poisson's ratio less than 0.25. For both soft elasticity and plastic compressibility, the main reason for the lower values of indentation hardness is related to the reduction......The effect of soft elasticity, i.e., a relatively small value of the ratio of Young's modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking...... rigid sharp indenter into a cylinder modeling indentation of a half space. The material is characterized by a finite strain elastic-viscoplastic constitutive relation that allows for plastic as well as elastic compressibility. Both soft elasticity and plastic compressibility significantly reduce...
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.
1989-01-01
This document contains provisions of Cambodia's Constitution of May 5, 1989. Article 7 gives men and women equal rights in marriage and the family, calls for monogamous marriages, and affords social protection to mothers and children. Article 8 guides parent-child relationships. The 14th article defines state property, and the 15th gives citizens full rights to own, use, and inherit land. The use of agricultural and forested land can only be changed with permission. Article 22 assigns educational responsibilities to the state, including free elementary education and a gradual expansion of higher education. Adult literacy classes are also promoted. Article 26 guarantees free medical consultations, and article 27 gives women a 90-day paid maternity leave. Breast-feeding women are also given special privileges. Article 33 guarantees the right to pay equity and to social security benefits. Article 36 grants the freedom to travel, the inviolability of homes, and privacy in correspondence of all types.
Crushed-salt constitutive model update
International Nuclear Information System (INIS)
Callahan, G.D.; Loken, M.C.; Mellegard, K.D.; Hansen, F.D.
1998-01-01
Modifications to the constitutive model used to describe the deformation of crushed salt are presented in this report. Two mechanisms--dislocation creep and grain boundary diffusional pressure solutioning--defined previously but used separately are combined to form the basis for the constitutive model governing the deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. New creep consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant and southeastern New Mexico salt to determine material parameters for the constitutive model. Nonlinear least-squares model fitting to data from the shear consolidation tests and a combination of the shear and hydrostatic consolidation tests produced two sets of material parameter values for the model. The change in material parameter values from test group to test group indicates the empirical nature of the model but demonstrates improvement over earlier work with the previous models. Key improvements are the ability to capture lateral strain reversal and better resolve parameter values. To demonstrate the predictive capability of the model, each parameter value set was used to predict each of the tests in the database. Based on the fitting statistics and the ability of the model to predict the test data, the model appears to capture the creep consolidation behavior of crushed salt quite well
Crushed-salt constitutive model update
Energy Technology Data Exchange (ETDEWEB)
Callahan, G.D.; Loken, M.C.; Mellegard, K.D. [RE/SPEC Inc., Rapid City, SD (United States); Hansen, F.D. [Sandia National Labs., Albuquerque, NM (United States)
1998-01-01
Modifications to the constitutive model used to describe the deformation of crushed salt are presented in this report. Two mechanisms--dislocation creep and grain boundary diffusional pressure solutioning--defined previously but used separately are combined to form the basis for the constitutive model governing the deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. New creep consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant and southeastern New Mexico salt to determine material parameters for the constitutive model. Nonlinear least-squares model fitting to data from the shear consolidation tests and a combination of the shear and hydrostatic consolidation tests produced two sets of material parameter values for the model. The change in material parameter values from test group to test group indicates the empirical nature of the model but demonstrates improvement over earlier work with the previous models. Key improvements are the ability to capture lateral strain reversal and better resolve parameter values. To demonstrate the predictive capability of the model, each parameter value set was used to predict each of the tests in the database. Based on the fitting statistics and the ability of the model to predict the test data, the model appears to capture the creep consolidation behavior of crushed salt quite well.
Constitutive behavior of reconsolidating crushed salt
International Nuclear Information System (INIS)
Callahan, G.D.; Mellegard, K.D.; Hansen, F.D.
1998-02-01
The constitutive model used to describe deformation of crushed salt is presented in this paper. Two mechanisms--dislocation creep and grain boundary diffusional pressure solutioning--are combined to form the basis for the constitutive model governing deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. Recently completed creep consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant (WIPP) and southeastern New Mexico salt to determine material parameters for the constitutive model. Nonlinear least-squares model fitting to data from shear consolidation tests and a combination of shear and hydrostatic tests produces two sets of material parameter values for the model. Changes in material parameter values from test group to test group indicate the empirical nature of the model but show significant improvement over earlier work. To demonstrate the predictive capability of the model, each parameter value set was used to predict each of the tests in the database. Based on fitting statistics and ability of the model to predict test data, the model appears to capture the creep consolidation behavior of crushed salt quite well
1989-01-01
This document contains major provisions of the constitution adopted by Brazil on 5 October 1988. This constitution seeks to promote the welfare of all citizens without discrimination. The equality of all citizens is guaranteed, and the equal rights of women are specifically mentioned. Property rights are also guaranteed and defined. Female inmates are granted the right to remain with their children while breast feeding. Workers are guaranteed a minimum wage, a family allowance for dependents, maternity/paternity leave, specific incentives to protect the labor market for women, retirement benefits, free day care for preschool-age children, pay equity, and equal rights between tenured and sporadically employed workers. Agrarian reform provisions are given, including the authority to expropriate land. Social and economic policies to promote health are called for, and public health services are to be decentralized, to be integrated, and to foster community participation. Pension plan and social assistance provisions are outlined as are duties of the state in regard to education. The amount of money to be dedicated to education is set out, and a national educational plan is called for to achieve such goals as the eradication of illiteracy, the universalization of school attendance, the improvement of instruction, and the provision of vocational training. Specific measures are set out to protect and preserve the environment. Family policy deals with issues of marriage, the definition of a family, divorce, the right to family planning services, and the deterrence of domestic violence. Social protection provisions cover mothers and children, handicapped persons, and protection of minors. Finally, the customs and rights of Indians are protected, with special provisions given to protect land tenure and to protect the rights of Indians in water resource development and prospecting and mining activities.
Modeling elastic anisotropy in strained heteroepitaxy.
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
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.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Constitutive Modelling of Resins in the Stiffness Domain
Klasztorny, M.
2004-09-01
An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.
Target Soil Impact Verification: Experimental Testing and Kayenta Constitutive Modeling.
Energy Technology Data Exchange (ETDEWEB)
Broome, Scott Thomas [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Flint, Gregory Mark [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Dewers, Thomas [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Newell, Pania [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-11-01
This report details experimental testing and constitutive modeling of sandy soil deformation under quasi - static conditions. This is driven by the need to understand constitutive response of soil to target/component behavior upon impact . An experimental and constitutive modeling program was followed to determine elastic - plastic properties and a compressional failure envelope of dry soil . One hydrostatic, one unconfined compressive stress (UCS), nine axisymmetric compression (ACS) , and one uniaxial strain (US) test were conducted at room temperature . Elastic moduli, assuming isotropy, are determined from unload/reload loops and final unloading for all tests pre - failure and increase monotonically with mean stress. Very little modulus degradation was discernable from elastic results even when exposed to mean stresses above 200 MPa . The failure envelope and initial yield surface were determined from peak stresses and observed onset of plastic yielding from all test results. Soil elasto - plastic behavior is described using the Brannon et al. (2009) Kayenta constitutive model. As a validation exercise, the ACS - parameterized Kayenta model is used to predict response of the soil material under uniaxial strain loading. The resulting parameterized and validated Kayenta model is of high quality and suitable for modeling sandy soil deformation under a range of conditions, including that for impact prediction.
Paro, Alberto
2013-01-01
Written in an engaging, easy-to-follow style, the recipes will help you to extend the capabilities of ElasticSearch to manage your data effectively.If you are a developer who implements ElasticSearch in your web applications, manage data, or have decided to start using ElasticSearch, this book is ideal for you. This book assumes that you've got working knowledge of JSON and Java
Rock salt constitutive modeling
International Nuclear Information System (INIS)
Nickell, R.E.
1980-01-01
The Serata model is the best operational model available today because it incorporates: (1) a yield function to demarcate between viscoelastic and viscoplastic behavior of rock salt; (2) a pressure and temperature dependence for yield stresses; and (3) a standard linear solid, which can be readily extended into the non-linear regime, to represent creep behavior. Its only deficiencies appear to be the lack of secondary creep behavior (a free dashpot) and some unsettling arbitrariness about the Poisson's ratio (ν → 0.5) argument for viscoplasticity. The Sandia/WIPP model will have good primary and secondary creep capability, but lacks the viscoplastic behavior. In some cases, estimated inelastic strains may be underpredicted. If a creep acceleration mechanism associated with brine inclusions is observed, this model may require extensive revision. Most of the other models available (SAI, RE-SPEC, etc.) are only useful for short-term calculations, because they employ temporal power law (t/sup n/) primary creep representations. These models are unsatisfactory because they cannot represent dual mechanisms with differing characteristic times. An approach based upon combined creep and plasticity is recommended in order to remove the remaining deficiency in the Serata model. DOE/Sandia/WIPP should be encouraged to move aggressively in this regard
ECHR and national constitutional courts
Directory of Open Access Journals (Sweden)
Nastić Maja
2015-01-01
Full Text Available Comprising fundamental rights and freedoms and establishing the effective control system, the European Convention on Human Rights (ECHR encroaches upon the area that is traditional reserved for constitutional law. Although built on the doctrine reserved for international treaty law, the Convention goes beyond the traditional boundaries that exist between international and constitutional law. It has gradually infiltrated into the national legal systems. Constitutional courts have had the crucial role in this process. This paper will focus on the applicability of the ECHR in proceedings before national constitutional courts. Having in mind the jurisdiction of the national constitutional court, the ECHR may be applied in two ways: first, in the process of constitutional review by national constitutional courts and, second, in the process of deciding on constitutional complaints.
VALUATION IN THE CONSTITUTIONAL ERA
African Journals Online (AJOL)
Brimer
16 ..... stem from the pre-constitutional era, and the constitutional framework and its legitimate reform efforts. A decision on what is just ...... Carroll L Alice's Adventures in Wonderland (Digital Scanning Scituate MA. 2007). Dagan 1999 Va L Rev.
Constitutive modeling of two phase materials using the Mean Field method for homogenization
Perdahcioglu, Emin Semih; Geijselaers, Hubertus J.M.
2010-01-01
A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent
Legal theology in imposed constitutionalism
DEFF Research Database (Denmark)
Abat Ninet, Antoni
2018-01-01
The focus of this paper is the question of legitimacy, and how can we consider legitimate an imposed constitution and the subsequent constitutional principles, practices and values that go hand-in-hand with the legal and political acculturation. Constitutional texts around the world are good...
The diffusion of constitutional rights
Goderis, B.V.G.; Versteeg, M.
Constitutions are commonly regarded as uniquely national products, shaped by domestic ideals and politics. This paper develops and empirically investigates a novel hypothesis, which is that constitutions are also shaped by transnational influence, or “diffusion.” Constitutional rights can diffuse
Ontoteleological Constitution of Entrepreneurship
Directory of Open Access Journals (Sweden)
Diego Luiz Teixeira Boava
2017-06-01
Full Text Available Entrepreneurship is a pluri-disciplinary phenomenon, object of research in several areas of knowledge. However, studies on this theme present approaches that start to consider entrepreneurship as a field of private knowledge in the phase of epistemological construction. In this context, the aim of this investigation is to contribute to the discussions on the theme, through studies on the ontoteleological constitution of entrepreneurship, in propaedeutic character, deflagrating new approaches. Thus, there is a presentation concerning the study of entrepreneurship, which may emphasize its ontical and ontological aspects. In addition, the reason why it is complex to define entrepreneurship is investigated. Subjects regarding the philosophy of entrepreneurship are introduced, seeking to present the bases for an ontoteleological approach to the phenomenon. Such an approach assumes that the finality of the entrepreneurial act relates to the main principles and transformations required into the organization. Finally, it is concluded that man is an entrepreneurial being, the meta-entrepreneur, and his entrepreneurial actions are not determined by external factors, but rather by the condition of his potentiality.
On the concept of elasticity used in some fast reactor accident analysis codes
International Nuclear Information System (INIS)
Malmberg, T.
1975-01-01
The analysis presented restricts attention to the elastic part of the elastic-plastic equation used in several Fast Reactor Accident Analysis Codes and originally applied by M.L. Wilkins: Calculation of Elastic-Plastic Flow, UCRL-7322, Rev. 1, Jan 1969. It is shown that the used elasticity concept is within the frame of hypo-elasticity. On the basis of a test found by Bernstein it is proven that the state of stress is generally depending on the path of deformation. Therefore this concept of elasticity is not compatible with finite elasticity. For several deformation processes this special hypo-elastic constitutive equation is integrated to give a stress-strain relation. The path-dependence of this relation is demonstrated. Further the phenomenon of hypo-elastic yield under shear deformation is pointed out. The relevance to modelling material behaviour in primary containment analysis is discussed. (Auth.)
Dynamical soil-structure interactions: influence of soil behaviour nonlinearities
International Nuclear Information System (INIS)
Gandomzadeh, Ali
2011-01-01
The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in
Modeling dynamic acousto-elastic testing experiments: validation and perspectives.
Gliozzi, A S; Scalerandi, M
2014-10-01
Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Constitution, 1989. [Selected provisions].
1989-01-01
Chapter XII of the Hungarian Constitution, 1989, details the Fundamental Rights and Duties of Citizens. Everyone lawfully within the territory of Hungary has the right to liberty of movement and the freedom to choose his or her residence, except when restricted by law, including the right to leave his or her residence or county. The Republic of Hungary grants asylum to foreign citizens who were persecuted for racial, religious ethnic, linguistic, or political reasons. Men and women shall equally enjoy all civil, political, economic, social and political rights. Mothers are entitled to special care and protection before and after childbirth; women and juveniles are protected at work by special regulations. Every child has the right to special care an assistance from his or her family, the State, and society, for appropriate physical, spiritual, and moral development. Parents shall decide the kind of education their children receive. Hungary grants equal rights to all person within its territories, without regard to race, color, sex, language, religion, political, or other opinion, national, and social origin, property, birth and other status. Prejudicial discrimination shall be severely punished. Everyone has the right to work, to the free choice of employment and profession and to equal pay for equal work. Citizens have the right to social security, including social services necessary in old age, sickness, disability, widowhood, orphanhood an unemployment through no fault of their own. Hungary guarantees the right to culture for its citizens and realized this right by free and compulsory elementary education, by secondary and higher education which is accessible to all on the basis of capacity, and by the financial support of those receiving an education.
Constitutive relation of concrete containing meso-structural characteristics
Directory of Open Access Journals (Sweden)
Li Guo
Full Text Available A constitutive model of concrete is proposed based on the mixture theory of porous media within thermodynamic framework. By treating concrete as a multi-phase multi-component mixture, we constructed the constitutive functions for elastic, interfacial, and plastic strain energy respectively. A constitutive law of concrete accommodating internal micro-cracks and interfacial boundaries was established. The peak stress predicted with the developed model depends primarily on the volume ratio of aggregate, and the results explain very well reported experimental phenomena. The strain-stress curve under uniaxial loading was found in a good agreement with experimental data for concrete with three different mixing proportions. Keywords: Constitutive model of concrete, Mixture theory of porous media, Meso-structure, Interfacial energy
Borckmans, P; Khokhlov, A. R; Métens, S; Chemomechanical Instabilities in Responsive Materials
2009-01-01
This volume contains a selection of the papers presented by renowned specialists of each field. It is the first book in which the communities of nonlinear chemists and gel specialist communicate and show how interactions between the two fields can actually produce working devices based on the transduction of chemical to mechanical energy and vice-versa. Beside subtle ways of using the slaving of responsive materials devices to oscillatory reactions, emphasis is brought on emerging properties that are possessed by neither of the separated constituents. Several contributions on these aspects are included, in relation to their potential relevance to biological, medical and technological applications. The whole constitutes a specific multidisciplinary "new" field. Both advanced and basic aspects of the two fields can be found the this collection of lectures. The book will not only benefit to doctoral students or young post-docs to learn the ropes of both subjects, but also to active researchers from one field, to...
Paro, Alberto
2015-01-01
If you are a developer who implements ElasticSearch in your web applications and want to sharpen your understanding of the core elements and applications, this is the book for you. It is assumed that you've got working knowledge of JSON and, if you want to extend ElasticSearch, of Java and related technologies.
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.; Goriely, A.
2012-01-01
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects
Riemann-Cartan geometry of nonlinear disclination mechanics
Yavari, A.; Goriely, A.
2012-01-01
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Energy Technology Data Exchange (ETDEWEB)
Cochrane, Alexander P. [Aerospace Engineering Department, University of Glasgow, University Avenue, Glasgow, Lanarkshire (United Kingdom); Merrett, Craig G. [Mechanical and Aerospace Engineering Department, Carleton Univ., 1125 Col. By Dr., Ottawa, ON (Canada); Hilton, Harry H. [Aerospace Engineering Department in the College of Engineering and Private Sector Program Division at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801 (United States)
2014-12-10
which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V{sub ∞}∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one.
International Nuclear Information System (INIS)
Cochrane, Alexander P.; Merrett, Craig G.; Hilton, Harry H.
2014-01-01
(V REV E ). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V REV< ≧ V REV E , but furthermore does so in time at 0 < t REV ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V ∞ ∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one
Elasticity theory and applications
Saada, Adel S; Hartnett, James P; Hughes, William F
2013-01-01
Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...
Computer implementation of an elastic-plastic concrete relationship
International Nuclear Information System (INIS)
Murray, D.W.; Chitnuyanondh, L.; Wong, C.
1979-01-01
The purpose of this paper is to describe the difficulties that arose, and the strategies that were developed to overcome these difficulties, during the incorporation of a relatively complex elastic-plastic concrete constitutive relationship into an existing computer code for the analysis of axisymmetric loading acting on thin shells of revolution. The program had the capability of elastic-plastic analysis using a von-Mises yield curve prior to any modification by the writers. (orig.)
Constitutional judges (guarantee of the Constitution and responsibility
Directory of Open Access Journals (Sweden)
Francisco Javier Ansuátegui Roig
2012-06-01
Full Text Available My aim in this paper is to propose a reflection on the position and the importance that the constitutional judge has in the legal systems of contemporary constitutionalism. The figure of the judge responsible of protecting the Constitution is a key institution, without which we cannot understand the laws of constitutional democracies, their current lines of development, and the guarantee of rights and freedoms that constitute the normative core of these systems. Moreover, the reflection on the exercise of the powers of the judge, its scope and its justification is an important part of contemporary legal discussion, still relevant, albeit not exclusively - in the field of legal philosophy. The object of attention of my reflection is the judge who has the power of judicial review, in a scheme of defense of the Constitution, regardless the specific ways of this defense.
Modeling Pseudo-elastic Behavior of Springback
International Nuclear Information System (INIS)
Xia, Z. Cedric
2005-01-01
constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied
Nonlinear viscoelastic behavior of shells of revolution under arbitrary loading
International Nuclear Information System (INIS)
Leonard, J.W.; Arbaki-Kanjoori, F.
1975-01-01
The requirement of some structural components such as propulsion systems and gas turbines to operate at high temperatures and pressures make the accurate evaluation of the creep phenomenon exigent (in fast breeder reactor for example). For the expected increases in operating temperatures and pressures, it becomes necessary to perform a thorough analysis of integral structural components of nuclear power plants throughout their life span. Since a large class of structures operating at elevated temperatures are composed of rotationally symmetric shells, a solution technique can be developed which involves the numerical integration of the governing shell equations. This method has been successfully applied to the static and dynamic analysis of thin elastic shells of revolution and for some cases of inelastic material behavior. It has been shown to render solutions efficiently and accurately, usually with only a fraction of computer time and storage requirements and data manipulation that is required for other numerical schemes such as the finite element method. Furthermore, the numerical integration method allows more flexibility for varying the integration step lengths than does the finite difference method and can provide uniform accuracy throughout the analysis. For nonlinear viscoelastic behavior the numerical integration technique is expected to provide similar efficiency to that obtained for the elastic problems. The computer program developed can accept time variation of material properties. Since a single form for the material constitutive law cannot encompass all materials, provisions are made so that the analysis of a very large class of material behavior can be accomplished
Essential Medicines in National Constitutions
Toebes, Brigit; Hogerzeil, Hans
2016-01-01
Abstract A constitutional guarantee of access to essential medicines has been identified as an important indicator of government commitment to the progressive realization of the right to the highest attainable standard of health. The objective of this study was to evaluate provisions on access to essential medicines in national constitutions, to identify comprehensive examples of constitutional text on medicines that can be used as a model for other countries, and to evaluate the evolution of constitutional medicines-related rights since 2008. Relevant articles were selected from an inventory of constitutional texts from WHO member states. References to states’ legal obligations under international human rights law were evaluated. Twenty-two constitutions worldwide now oblige governments to protect and/or to fulfill accessibility of, availability of, and/or quality of medicines. Since 2008, state responsibilities to fulfill access to essential medicines have expanded in five constitutions, been maintained in four constitutions, and have regressed in one constitution. Government commitments to essential medicines are an important foundation of health system equity and are included increasingly in state constitutions. PMID:27781006
An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials
Mohd Nor, M. K.; Ma'at, N.; Ho, C. S.
2018-03-01
This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill's yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic-plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic-plastic constitutive model is the introduction of anisotropic effect in the Mie-Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM's version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie-Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \\varvec{ψ} tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic-plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and {895 ms}^{-1} impact velocities is performed. A good agreement is obtained in each test.
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Constitutional aneuploidy and cancer predisposition.
Ganmore, Ithamar; Smooha, Gil; Izraeli, Shai
2009-04-15
Constitutional aneuploidies are rare syndromes associated with multiple developmental abnormalities and the alterations in the risk for specific cancers. Acquired somatic chromosomal aneuploidies are the most common genetic aberrations in sporadic cancers. Thus studies of these rare constitutional aneuploidy syndromes are important not only for patient counseling and clinical management, but also for deciphering the mechanisms by which chromosomal aneuploidy affect cancer initiation and progression. Here we review the major constitutional aneuploidy syndromes and suggest some general mechanisms for the associated cancer predisposition.
Economic Reforms and Constitutional Transition
Jeffrey D. Sachs; Wing Thye Woo; Xiaokai Yang
2000-01-01
This paper investigates the relationship between economic reforms and constitutional transition, which has been neglected by many transition economists. It is argued that assessment of reform performance might be very misleading if it is not recognized that economic reforms are just a small part of large scale of constitutional transition. Rivalry and competition between states and between political forces within each country are the driving forces for constitutional transition. We use Russia...
ECHR and national constitutional courts
Nastić, Maja
2015-01-01
Comprising fundamental rights and freedoms and establishing the effective control system, the European Convention on Human Rights (ECHR) encroaches upon the area that is traditional reserved for constitutional law. Although built on the doctrine reserved for international treaty law, the Convention goes beyond the traditional boundaries that exist between international and constitutional law. It has gradually infiltrated into the national legal systems. Constitutional courts have had the cruc...
Nonlinear and Nonequilibrium Dynamics in Geomaterials
TenCate, James A.; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A.
2004-01-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a s...
Constitutional Issues--Watergate and the Constitution. Teaching with Documents.
National Archives and Records Administration, Washington, DC.
When U.S. President Richard Nixon resigned in 1974 in the wake of the Watergate scandal, it was only the second time that impeachment of a president had been considered. Although the U.S. Constitution has provisions for a person removed from office to be indicted, there are no guidelines in the Constitution about a President who has resigned. The…
National constitutional courts in the European Constitutional Democracy
DEFF Research Database (Denmark)
Komárek, Jan
2014-01-01
This article critically assesses the transformation of national constitutional courts’ place in the law and politics of the EU and its member states. This process eliminates the difference between constitutional and ordinary national courts, which is crucial for the institutional implementation...... of the discourse theory of law and democracy. It also disrupts the symbiotic relationship between national constitutional democracies established after World War II and European integration. The article argues that maintaining the special place of national constitutional courts is in the vital interest of both...... the EU and its member states, understood together as the European Constitutional Democracy—the central notion developed in this article in order to support an argument that should speak to both EU lawyers and national constitutionalists....
Constitutive modelling of composite biopolymer networks.
Fallqvist, B; Kroon, M
2016-04-21
The mechanical behaviour of biopolymer networks is to a large extent determined at a microstructural level where the characteristics of individual filaments and the interactions between them determine the response at a macroscopic level. Phenomena such as viscoelasticity and strain-hardening followed by strain-softening are observed experimentally in these networks, often due to microstructural changes (such as filament sliding, rupture and cross-link debonding). Further, composite structures can also be formed with vastly different mechanical properties as compared to the individual networks. In this present paper, we present a constitutive model presented in a continuum framework aimed at capturing these effects. Special care is taken to formulate thermodynamically consistent evolution laws for dissipative effects. This model, incorporating possible anisotropic network properties, is based on a strain energy function, split into an isochoric and a volumetric part. Generalisation to three dimensions is performed by numerical integration over the unit sphere. Model predictions indicate that the constitutive model is well able to predict the elastic and viscoelastic response of biological networks, and to an extent also composite structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Superelastic stress-strain behavior in ferrogels with different types of magneto-elastic coupling
Cremer, Peet; Löwen, Hartmut; Menzel, Andreas M.
Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various applications like dampers, vibration absorbers, or actuators. Under appropriate conditions, the stress-strain behavior of a ferrogel can display a fascinating feature: superelasticity, the capability to reversibly deform by a huge amount while barely altering the applied load. In a previous work, using numerical simulations, we investigated this behavior assuming that the magnetic moments carried by the embedded particles can freely reorient to minimize their magnetic interaction energy. Here, we extend the analysis to ferrogels where restoring torques by the surrounding matrix hinder rotations towards a magnetically favored configuration. For example, the particles can be chemically cross-linked into the polymer matrix and the magnetic moments can be fixed to the particle axes. We demonstrate that these systems still feature a superelastic regime. As before, the nonlinear stress-strain behavior can be reversibly tailored during operation by external magnetic fields. Yet, the different coupling of the magnetic moments causes different types of response to external stimuli. For instance, an external magnetic field applied parallel to the stretching axis hardly affects the superelastic regime but stiffens the system beyond it. Other smart materials featuring superelasticity, e.g. metallic shape-memory alloys, have already found widespread applications. Our soft polymer systems offer many additional advantages like a typically higher deformability and enhanced biocompatibility combined with high tunability.
Statistical mechanics of elasticity
Weiner, JH
2012-01-01
Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.
Elasticity of energy consumption
International Nuclear Information System (INIS)
Stam, M.
2004-01-01
Insight is given into the price elasticities of several energy carriers. Next, attention is paid to the impact of the discussion on changes of the Regulating Energy Levy (REB, abbreviated in Dutch) in the Netherlands [nl
Kuc, Rafal
2013-01-01
A practical tutorial that covers the difficult design, implementation, and management of search solutions.Mastering ElasticSearch is aimed at to intermediate users who want to extend their knowledge about ElasticSearch. The topics that are described in the book are detailed, but we assume that you already know the basics, like the query DSL or data indexing. Advanced users will also find this book useful, as the examples are getting deep into the internals where it is needed.
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.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Constitutive Effects of Performance Indicators
DEFF Research Database (Denmark)
Dahler-Larsen, Peter
2014-01-01
that are demonstrably problematic. Based on a distinction between trivial and advanced measure fixation, an argument is made for constitutive effects that are based on less problematic assumptions. Through this conceptual move, the political dimension of performance indicators is appreciated. The conceptual dimensions...... of constitutive effects are carved out, empirical illustrations of their applicability are offered and implications discussed....
Petrov-Galerkin mixed formulations for bidimensional elasticity
International Nuclear Information System (INIS)
Toledo, E.M.; Loula, A.F.D.; Guerreiro, J.N.C.
1989-10-01
A new formulation for two-dimensional elasticity in stress and displacements is presented. Consistently adding to the Galerkin classical formulation residuals forms of constitutive and equilibrium equations, the original saddle point is transformed into a minimization problem without any restrictions. We also propose a stress post processing technique using both equilibrium and constitutive equations. Numerical analysis error estimates and numerical results are presented confirming the predicted rates of convergence. (A.C.A.S.) [pt
Political dimension of European constitutionalism
Directory of Open Access Journals (Sweden)
Kaplánová Patricia
2015-04-01
Full Text Available Author in the article tries to analyse different elements of document called European Constitution. Analysis is supported with theoretical framework of federalism, presented by Brezovšek. Authors is playing with idea of (confederal and international organization elements of European Constitution and their mix. They are also trying to set some connections between so called common European identity as necessary condition to give legitimacy to the European Constitution. This became important question after „votes of non-confidence“ to the European Constitution in France, despite it should be addressed already before. However, European Constitution is important document on the path of European integration and lack of support to it will slow down this process of widening and deepening European ties.
Nonlinear dynamics of a nonsmooth shape memory alloy oscillator
International Nuclear Information System (INIS)
Cardozo dos Santos, Bruno; Amorim Savi, Marcelo
2009-01-01
In the last years, there is an increasing interest in nonsmooth system dynamics motivated by different applications including rotor dynamics, oil drilling and machining. Besides, shape memory alloys (SMAs) have been used in various applications exploring their high dissipation capacity related to their hysteretic behavior. This contribution investigates the nonlinear dynamics of shape memory alloy nonsmooth systems considering a linear oscillator with a discontinuous support built with an SMA element. A constitutive model developed by Paiva et al. [Paiva A, Savi MA, Braga AMB, Pacheco PMCL. A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 2005;42(11-12):3439-57] is employed to describe the thermomechanical behavior of the SMA element. Numerical investigations show results where the SMA discontinuous support can dramatically change the system dynamics when compared to those associated with a linear elastic support system. A parametric study is of concern showing the system behavior for different system characteristics, forcing excitation and also gaps. These results show that smart materials can be employed in different kinds of mechanical systems exploring some of the remarkable properties of these alloys.
WE-E-9A-01: Ultrasound Elasticity
Energy Technology Data Exchange (ETDEWEB)
Emelianov, S [University of Texas at Austin, Austin, TX (United States); Hall, T [University of WI-Madison, Madison, WI (United States); Bouchard, R [UT MD Anderson Cancer Center and UTHSC at Houston Graduate School of Biomed, Houston, TX (United States)
2014-06-15
Principles and techniques of ultrasound-based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained. Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging. Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force-based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement
WE-E-9A-01: Ultrasound Elasticity
International Nuclear Information System (INIS)
Emelianov, S; Hall, T; Bouchard, R
2014-01-01
Principles and techniques of ultrasound-based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained. Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging. Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force-based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Morphoelasticity: A theory of elastic growth
Goriely, Alain; Moulton, Derek
2011-01-01
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
Morphoelasticity: A theory of elastic growth
Goriely, Alain
2011-10-11
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
Asymptotic behaviour of a rescattering series for nonlinear reggeons
International Nuclear Information System (INIS)
Akkelin, S.V.; Martynov, E.S.
1990-01-01
A series of elastic re-scattering (both quasi-eikonal and U-matrix ones) for reggeons with nonlinear trajectories are estimated asymptotically. The calculations are performed for models of supercritical and dipole pomerons. A weak dependence of the series of re-scattering on reggeon trajectory nonlinearity is revealed. 13 refs.; 3 figs
Twist and Stretch of Helices Explained via the Kirchhoff-Love Rod Model of Elastic Filaments
Đuričković, Bojan; Goriely, Alain; Maddocks, John H.
2013-01-01
that within the context of the classic Kirchhoff-Love rod model of elastic filaments, both behaviors are possible, depending on the precise constitutive relations of the polymer. More generally, our analysis provides an effective linear response theory
Bulk solitary waves in elastic solids
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
Radioactive waste disposal and constitution
International Nuclear Information System (INIS)
Stober, R.
1983-01-01
The radioactive waste disposal has many dimensions with regard to the constitutional law. The central problem is the corret delimitation between adequate governmental precautions against risks and or the permitted risk which the state can impose on the citizen, and the illegal danger which nobody has to accept. The solution requires to consider all aspects which are relevant to the constitutional law. Therefore, the following analysis deals not only with the constitutional risks and the risks of the nuclear energy, but also with the liberal, overall-economic, social, legal, and democratic aspects of radioactive waste disposal. (HSCH) [de
Constitutional aneuploidy and cancer predisposition†
Ganmore, Ithamar; Smooha, Gil; Izraeli, Shai
2009-01-01
Constitutional aneuploidies are rare syndromes associated with multiple developmental abnormalities and the alterations in the risk for specific cancers. Acquired somatic chromosomal aneuploidies are the most common genetic aberrations in sporadic cancers. Thus studies of these rare constitutional aneuploidy syndromes are important not only for patient counseling and clinical management, but also for deciphering the mechanisms by which chromosomal aneuploidy affect cancer initiation and progression. Here we review the major constitutional aneuploidy syndromes and suggest some general mechanisms for the associated cancer predisposition. PMID:19297405
A framework for the automated data-driven constitutive characterization of composites
J.G. Michopoulos; John Hermanson; T. Furukawa; A. Iliopoulos
2010-01-01
We present advances on the development of a mechatronically and algorithmically automated framework for the data-driven identification of constitutive material models based on energy density considerations. These models can capture both the linear and nonlinear constitutive response of multiaxially loaded composite materials in a manner that accounts for progressive...
LDRD report nonlinear model reduction
Energy Technology Data Exchange (ETDEWEB)
Segalman, D.; Heinstein, M.
1997-09-01
The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.
Flutter analysis of an airfoil with multiple nonlinearities and uncertainties
Directory of Open Access Journals (Sweden)
Haitao Liao
2013-09-01
Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.
Nonlinear dynamics and control of a vibrating rectangular plate
Shebalin, J. V.
1983-01-01
The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.
Constitutive Modelling in Geomechanics Introduction
Puzrin, Alexander M
2012-01-01
The purpose of this book is to bridge the gap between the traditional Geomechanics and Numerical Geotechnical Modelling with applications in science and practice. Geomechanics is rarely taught within the rigorous context of Continuum Mechanics and Thermodynamics, while when it comes to Numerical Modelling, commercially available finite elements or finite differences software utilize constitutive relationships within the rigorous framework. As a result, young scientists and engineers have to learn the challenging subject of constitutive modelling from a program manual and often end up with using unrealistic models which violate the Laws of Thermodynamics. The book is introductory, by no means does it claim any completeness and state of the art in such a dynamically developing field as numerical and constitutive modelling of soils. The author gives basic understanding of conventional continuum mechanics approaches to constitutive modelling, which can serve as a foundation for exploring more advanced theories....
The Constitution's Prescription for Freedom.
Peach, Lucinda
1986-01-01
Examines how the framers of the Constitution came to choose our system of government, how that system was designed to function, and how the separation of powers has served to maintain our democracy despite attempts to violate it. (JDH)
Jonathan's Constitutional Conference in Nigeria
African Journals Online (AJOL)
ian
2013-10-01
Oct 1, 2013 ... Adeniyi S. Basiru is an independent researcher and a PhD candidate ... constitution-making are fundamentally the exclusive reserve of the elites, ..... agenda must be situated against the background of events that heralded his.
A survey on constitutional justice
Directory of Open Access Journals (Sweden)
Kheirollah Parvin
2015-05-01
Full Text Available The idea of supervising the conformity of statutory law with constitutional law, is due to necessities rooted in two essential principles: the supremacy of constitution and the hierarchy of the law. Constitution as the supreme law in the sense of status and legal value , is placed at the top of the legal pyramid of every political system and therefore requires a special organization and discipline that will act as the sanction of the principles and the main content incorporated in this legal instrument. this special organization and discipline known as Constitutional justice in legal Literature now and have studing in two main patterns. Firs pattern based on Supervision of courts on rules and other pattern is Apply by Emphasis on role of Political Institutions in Supervision on rules. This two patterns have common purpose but have different backgrounds and methods.
THE EMERGING INTERNATIONAL CONSTITUTIONAL ORDER ...
African Journals Online (AJOL)
Dr Tanya du Plessis
CFI) affirmed ... primarily include the value system of the international legal order, meaning norms of ... the existence of such a traditional constitutional demos. Europe's ..... between the African Development Bank (BAD) and one of its employees,.
Constitutional Verbosity and Social Trust
DEFF Research Database (Denmark)
Bjørnskov, Christian; Voigt, Stefan
2014-01-01
A common argument in the trust literature is that high-trust cultures allow efficient commercial contracts to be shorter, covering fewer contingencies. We take this idea to the topic of social contracts. Specifically, we ask whether social trust affects the length and detail of constitutions. Cross......-country estimates suggest that national trust levels are indeed robustly and negatively associated with the length of countries’ constitutions....
Constitutional orders in multinational firms
DEFF Research Database (Denmark)
Hull Kristensen, Peer; Morgan, Glenn
Multinationals are faced with the problem of how to coordinate different actors and stop `fiefdoms' emerging that inhibits the achievement of transnational cooperation? We identify this as a problem of `constitutional ordering' in the firm. Drawing on Varieties of Capitalism approaches, we explore...... how multinationals from different contexts seek to create constitutional orders. We argue that the models which exist appear to be destructive of coordination. We explore the implications for MNCs....
Elastic anisotropy of crystals
Directory of Open Access Journals (Sweden)
Christopher M. Kube
2016-09-01
Full Text Available An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.
International Nuclear Information System (INIS)
Das, Y.C.; Kedia, K.K.
1977-01-01
No realistic analytical work in the area of Shells on Elastic Foundations has been reported in the literature. Various foundation models have been proposed by several authors. These models involve one or more than one parameters to characterise the foundation medium. Some of these models cannot be used to derive the basic equations governing the behaviour of shells on elastic foundations. In the present work, starting from an elastic continuum hypothesis, a mathematical model for foundation has been derived in curvilinear orthogonal coordinates by the help of principle of virtual displacements, treating one of the virtual displacements as known to satisfy certain given conditions at its edge surfaces. In this model, several foundation parameters can be considered and it can also be used for layered medium of both finite and infinite thickness. (Auth.)
Right Product, Wrong Packaging: Not 'Constitution', but 'Constitutional Charter'
Directory of Open Access Journals (Sweden)
John Law
2007-05-01
Full Text Available The article seeks to locate the principal cause of Europe’s prevailing ratification crisis in the inappropriate title arrived at in the European Convention, Treaty Establishing a Constitution for Europe. This over-ambitious styling led the media to characterise the text as simply an ‘EU Constitution’. Yet, the text was not a Constitution as we traditionally understand the term, i.e. the founding document of a State: scholars are agreed that the EU is not, and will not become upon ratification, a State.In terms of substance, whilst the text certainly strengthened some emerging constitutional aspects, it was not a major departure from the status quo like the Single European Act and Treaty on European Union had been; and it remained technically a treaty like all its predecessors. Arguably, therefore, it did not require referenda to ratify. However, confusion over the scale and importance of what was proposed, stemming from ambiguity in the title, pushed politicians down this unfortunate path.The article identifies a high level of consensus among commentators as to the true nature of the text: most are happy designating it a treaty (noun with constitutional (adjective aspects. The early proposed title Constitutional Treaty for Europe was arguably, therefore, the correct one; but it is now too late to choose this option, as the terms Constitution and Constitutional Treaty have already been muddled in debate. A more distinctive change is required. One idea could be to follow the principle employed elsewhere in the text of codifying the generally accepted but presently unwritten legal concepts of the European Court of Justice, as was done for example for ‘primacy’ and ‘direct effect’. The Court has characterised the EU treaties as a ‘constitutional charter’ for over twenty years now, and on this basis a modified title could read Treaty Establishing a Constitutional Charter for Europe. Importantly, the term ‘charter’ is recognised
Negative stiffness honeycombs as tunable elastic metamaterials
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.
Hwu, Chyanbin
2010-01-01
As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only in plane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element a
Lai, Yun
2011-06-26
Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays super anisotropy-in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications. © 2011 Macmillan Publishers Limited. All rights reserved.
Lai, Yun; Wu, Ying; Sheng, Ping; Zhang, Zhaoqing
2011-01-01
Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays super anisotropy-in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications. © 2011 Macmillan Publishers Limited. All rights reserved.
Directory of Open Access Journals (Sweden)
Sergio Cesare Masin
2010-01-01
Full Text Available Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight-a cognitive law analogous to Hooke¿s law of elasticity. Participants also estimated the total imagined elongation of springs joined either in series or in parallel. This total elongation was longer for serial than for parallel springs, and increased proportionally to the number of serial springs and inversely proportionally to the number of parallel springs. The results suggest that participants integrated load weight with imagined elasticity rather than with spring length.
Rogozinski, Marek
2014-01-01
This book is a detailed, practical, hands-on guide packed with real-life scenarios and examples which will show you how to implement an ElasticSearch search engine on your own websites.If you are a web developer or a user who wants to learn more about ElasticSearch, then this is the book for you. You do not need to know anything about ElastiSeach, Java, or Apache Lucene in order to use this book, though basic knowledge about databases and queries is required.
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)
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
A novel nonlinear damage resonance intermodulation effect for structural health monitoring
Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele
2017-04-01
This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.
Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.
2014-01-01
Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
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
Converging shocks in elastic-plastic solids.
Ortega, A López; Lombardini, M; Hill, D J
2011-11-01
We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the
1985-03-20
performed a perturbation calculation suggested by Heitler [15] using a canonical transfo lition. The N + 2 level structure of fig. la) is assumed...fluctuating hyperfine fields, or rates r, and F can often be simply related to the re- ion-ion interactions. At low temperatures. phonon taxation time T, as we...competition of other possible elastic collision mechanisms will be ,.. discussed later. 2.3 Two Pulse Delayed Nutation Consider that two brief laser
Internal resonance of an elastic body levitated above high-Tc superconducting bulks
International Nuclear Information System (INIS)
Kokuzawa, T; Toshihiko, S; Yoshizawa, M
2010-01-01
In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.
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.
Pretko, Michael; Radzihovsky, Leo
2018-05-01
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.
Cocco, Alberto; Masin, Sergio Cesare
2010-01-01
Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight--a cognitive law analogous to Hooke's law of elasticity. Participants also estimated the total imagined elongation of springs joined…
Constitutional compatibility of energy systems
International Nuclear Information System (INIS)
Rossnagel, A.
1983-01-01
The paper starts from the results of the Enquiry Commission on 'Future Nuclear Energy Policy' of the 8th Federal German Parliament outlining technically feasible energy futures in four 'pathways'. For the purpose of the project, which was to establish the comparative advantages and disadvantages of different energy systems, these four scenarios were reduced to two alternatives: cases K (= nuclear energy) and S (= solar energy). The question to Ge put is: Which changes within our legal system will be ushered in by certain technological developments and how do these changes relate to the legal condition intended so far. Proceeding in this manner will not lead to the result of a nuclear energy system or a solar energy system being in conformity or in contradiction with the constitutional law, but will provide a catalogue of implications orientated to the aims of legal standards: a person deciding in favour of a nuclear energy system or a solar energy system supports this or that development of constitutional policy, and a person purishing this or that aim of legal policy should be consistent and decide in favour of this or that energy system. The investigation of constitutional compatibility leads to the question what effects different energy systems will have on the forms of political intercourse laid down in the constitutional law, which are orientated to models of a liberal constitutional tradition of citizens. (orig./HSCH) [de
Corrugated Membrane Nonlinear Deformation Process Calculation
Directory of Open Access Journals (Sweden)
A. S. Nikolaeva
2015-01-01
Full Text Available Elastic elements are widely used in instrumentation. They are used to create a particular interference between the parts, for accumulating mechanical energy, as the motion transmission elements, elastic supports, and sensing elements of measuring devices. Device reliability and quality depend on the calculation accuracy of the elastic elements. A corrugated membrane is rather common embodiment of the elastic element.The corrugated membrane properties depend largely on its profile i.e. a generatrix of the meridian surface.Unlike other types of pressure elastic members (bellows, tube spring, the elastic characteristics of which are close to linear, an elastic characteristic of the corrugated membrane (typical movement versus external load is nonlinear. Therefore, the corrugated membranes can be used to measure quantities, nonlinearly related to the pressure (e.g., aircraft air speed, its altitude, pipeline fluid or gas flow rate. Another feature of the corrugated membrane is that significant movements are possible within the elastic material state. However, a significant non-linearity of membrane characteristics leads to severe complicated calculation.This article is aimed at calculating the corrugated membrane to obtain the elastic characteristics and the deformed shape of the membrane meridian, as well as at investigating the processes of buckling. As the calculation model, a thin-walled axisymmetric shell rotation is assumed. The material properties are linearly elastic. We consider a corrugated membrane of sinusoidal profile. The membrane load is a uniform pressure.The algorithm for calculating the mathematical model of an axisymmetric corrugated membrane of constant thickness, based on the Reissner’s theory of elastic thin shells, was realized as the author's program in C language. To solve the nonlinear problem were used a method of changing the subspace of control parameters, developed by S.S., Gavriushin, and a parameter marching method
Autonomic Vertical Elasticity of Docker Containers with ElasticDocker
Al-Dhuraibi , Yahya; Paraiso , Fawaz; Djarallah , Nabil; Merle , Philippe
2017-01-01
International audience; Elasticity is the key feature of cloud computing to scale computing resources according to application workloads timely. In the literature as well as in industrial products, much attention was given to the elasticity of virtual machines, but much less to the elasticity of containers. However, containers are the new trend for packaging and deploying microservices-based applications. Moreover, most of approaches focus on horizontal elasticity, fewer works address vertica...
Failure strength and elastic limit for concrete
International Nuclear Information System (INIS)
Robutti, G.; Ronzoni, E.; Ottosen, N.S.
1979-01-01
Due to increased demand for realistic analysis of structures such as prestressed concrete reactor vessels and reactor containments, the formulation of general constitutive equations for concrete is of considerable importance. In the field of constitutive equations the correct definition of the limit state represented by the concrete failure surface is a fundamental need. In this paper carried out by a Danish-Italian cooperation, several failure criteria obtained by different authors are compared with failure experimental data obtained with triaxial tests on concrete specimens. Such comparison allow to carry out conclusive considerations on the characteristics of the concrete failure surface and on the advantages and disadvantages of the different criteria. Considerations are also reported on the definition of a limit elastic surface, whose knowledge is of fundamental importance for designers of complex structures in concrete. (orig.)
Directory of Open Access Journals (Sweden)
M. Shaban
Full Text Available This paper studies free vibration and bending behavior of singlewalled carbon nanotubes (SWCNTs embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radiusto-length ratio.
International Nuclear Information System (INIS)
Biffle, J.H.
1991-01-01
1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory
Nonlocal elasticity tensors in dislocation and disclination cores
International Nuclear Information System (INIS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-01-01
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams
Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin
2017-09-01
Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.
Constitutionalism and Development in Nigeria: The 1999 Constitution
African Journals Online (AJOL)
Fr. Ikenga
the 3 arms of government the Executive, Legislative, Judiciary, Public Service and Marketing .... Rotation principle of a presidency position in Nigeria which will cultivate a sense of ... the issues survived inclusion in the 1999 Constitution of the Federal Republic of Nigeria. 13. S. 2 of Decree No. ..... Oxford, 5th Edition p.245.
The Spanish Constitution, the Constitutional Court and the Catalan Referendum
DEFF Research Database (Denmark)
Abat Ninet, Antoni
2015-01-01
and politeia that Aristotle defined now clashes between two powerful symbolic and romantic phenomena. In the Spanish-Catalan binomial scenario, there are some elements that need to be analysed to obtain a complete picture of the constitutional possibilities to of accommodating a Catalan self...
Time and constitution of sense
Directory of Open Access Journals (Sweden)
Pedro Gerardo Acosta
2014-06-01
Full Text Available This article proposes a reflection over our time-consciousness under the Phenomenology of Edmund Husserl. The idea is make a release the key role of the sense constitution like the fundament and development of the ongoing intentionality, a shape that make the possibility to catch sight of the sense of every life situation like conscience experience that displays itself over the time, and open the world of the Phenomenon World, constituted in the flux and flow of our live experience. The immanent time in which the things served in a lived-present inevitably displays to its own immediate-past of retentions, then of commemorations, constituting and enabling, not just the sense of ever present, but the sense of our own past like memory and our future like expectative. This reflection is based and supporter over the text “Phenomenology Lesson of the Internal Time-Consiusness” (Husserl, 2002.
A Communicatively Constituted Online Crisis
DEFF Research Database (Denmark)
Valentini, Chiara; Romenti, Stefania; Kruckeberg, Dean
2017-01-01
into specific public crisis perceptions. Drawing from a communicative constitution perspective, the authors argue that if crises are perceptions or experiences of difficult situations that exceed a person’s current resources and coping mechanisms, and if perceptions and experiences in social media are typically...... by offering suggestions on how to study online critical conversations through the lens of a communicative constitution perspective that could inform how critical issues eventually transform and become crises and how crisis perceptions evolve and are discursively shaped by communicative practices occurring...
Constitutional and acquired autosomal aneuploidy.
Jackson-Cook, Colleen
2011-12-01
Chromosomal imbalances can result from numerical or structural anomalies. Numerical chromosomal abnormalities are often referred to as aneuploid conditions. This article focuses on the occurrence of constitutional and acquired autosomal aneuploidy in humans. Topics covered include frequency, mosaicism, phenotypic findings, and etiology. The article concludes with a consideration of anticipated advances that might allow for the development of screening tests and/or lead to improvements in our understanding and management of the role that aneuploidy plays in the aging process and acquisition of age-related and constitutional conditions.
Identification of elastic properties of composite plate
International Nuclear Information System (INIS)
Kovalovs, A; Rucevskis, S
2011-01-01
Composite laminates are used extensively in the aerospace industry, especially for the fabrication of high-performance structures. The determination of stiffness parameters for complex materials, such as fibre-reinforced composites, is much more complicated than for isotropic materials. A conventional way is testing the coupon specimens, which are manufactured by technology similar to that used for the real, large structures. When such a method is used, the question arises of whether the material properties obtained from the coupon tests are the same as those in the large structure. Therefore, the determination of actual material properties for composite laminates using non-destructive evaluation techniques has been widely investigated. A number of various non-destructive evaluation techniques have been proposed for determining the material properties of composite laminates. In the present study, attention is focused on the identification of the elastic properties of laminated plate using vibration test data. The problem associated with vibration testing is converting the measured modal frequencies to elastic constants. A standard method for solving this problem is the use of a numerical-experimental model and optimization techniques. The identification functional represents the gap between the numerical model response and the experimental one. This gap should be minimized, taking into account the side constraints on the design variables (elastic constants). The minimization problem is solved by using non-linear mathematical programming techniques and sensitivity analysis. The results obtained were verified by comparing the experimentally measured eigenfrequencies with the numerical ones obtained by FEM at the point of optima
Designing interactively with elastic splines
DEFF Research Database (Denmark)
Brander, David; Bærentzen, Jakob Andreas; Fisker, Ann-Sofie
2018-01-01
We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes neglig...... negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline....
Elastic properties of Ti-24Nb-4Zr-8Sn single crystals with bcc crystal structure
International Nuclear Information System (INIS)
Zhang, Y.W.; Li, S.J.; Obbard, E.G.; Wang, H.; Wang, S.C.; Hao, Y.L.; Yang, R.
2011-01-01
Research highlights: → The single crystals of Ti2448 alloy with the bcc crystal structure were prepared. → The elastic moduli and constants were measured by several resonant methods. → The crystal shows significant elastic asymmetry in tension and compression. → The crystal exhibits weak nonlinear elasticity with large elastic strain ∼2.5%. → The crystal has weak atomic interactions against crystal distortion to low symmetry. - Abstract: Single crystals of Ti2448 alloy (Ti-24Nb-4Zr-8Sn in wt.%) were grown successfully using an optical floating-zone furnace. Several kinds of resonant methods gave consistent Young's moduli of 27.1, 56.3 and 88.1 GPa and shear moduli of 34.8, 11.0 and 14.6 GPa for the , and oriented single crystals, and C 11 , C 12 and C 44 of 57.2, 36.1 and 35.9 GPa respectively. Uniaxial testing revealed asymmetrical elastic behaviors of the crystals: tension caused elastic softening with a large reversible strain of ∼4% and a stress plateau of ∼250 MPa, whereas compression resulted in gradual elastic stiffening with much smaller reversible strain. The crystals exhibited weak nonlinear elasticity with a large elastic strain of ∼2.5% and a high strength, approaching ∼20% and ∼30% of its ideal shear and ideal tensile strength respectively. The crystals showed linear elasticity with a small elastic strain of ∼1%. These elastic deformation characteristics have been interpreted in terms of weakened atomic interactions against crystal distortion to low crystal symmetry under external applied stresses. These results are consistent with the properties of polycrystalline Ti2448, including high strength, low elastic modulus, large recoverable strain and weak strengthening effect due to grain refinement.
Heterogenous Intertemporal Elasticity of Substitution and Relative Risk Aversion
DEFF Research Database (Denmark)
Khorunzhina, Natalia; Gayle, Wayne-Roy
This paper investigates the existence and degree of variation across house holds and over time in the intertemporal elasticity of substitution (IES) and the coefficient of relative risk aversion (RRA) that is generated by habit forming preferences. To do so, we develop a new nonlinear GMM estimator...... in food consumption. Using these estimates, we develop bounds for the expectation of the implied heterogenous intertemporal elasticity of substitution and relative risk aversion that account for measurement errors and compute asymptotically valid confidence intervals on these bounds. We find...
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.
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Optimization for nonlinear inverse problem
International Nuclear Information System (INIS)
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
International Nuclear Information System (INIS)
Kasahara, Naoto; Takasho, Hideki
1998-12-01
Elevated temperature structural design codes pay attention to strain concentration at structural discontinuities due to creep and plasticity, since it causes to enlarge creep-fatigue damage of material. One of the difficulties to predict strain concentration is its dependency on loading, constitutive equations, and relaxation time. This study investigated fundamental mechanism of strain concentration and its main factors. It was clarified that strain concentration was caused from strain redistribution between elastic and inelastic regions, which can be quantified by the elastic follow-up parameter. As a function of inelastic strain, the elastic follow-up parameter can describe variation of strain concentration during incremental loading and relaxation process, caused by transition of strain distribution from peak strain concentration to secondary stress redistribution. Structures have their own elastic follow-up characteristics as a function of inelastic strain, which is insensitive to constitutive equations. It means that application of inelastic analysis is not difficult to obtain elastic follow-up characteristics. (author)
[Constitutional mismatch repair deficiency syndrome
Jongmans, M.C.J.; Gidding, C.E.M.; Loeffen, J.; Wesseling, P.; Mensenkamp, A.; Hoogerbrugge, N.
2015-01-01
BACKGROUND: Constitutional mismatch repair deficiency (CMMR-D) syndrome is characterised by a significantly increased risk for developing cancer in childhood. It arises when both parents have a mutation in the same mismatch repair gene and pass it on to their child. CASE DESCRIPTION: An 8-year-old
The Constitution and Academic Freedom.
Gilbertson, Eric R.
During the past 150 years U.S. courts have demonstrated a special protectiveness toward academics and academic institutions. Academic freedom was not a concern when the U.S. Constitution and the First Amendment were drafted and is not mentioned in the "Federalist Papers." However, decisions by a series of Supreme Court justices led to…
Optimality criteria for the components of anisotropic constitutive matrix
DEFF Research Database (Denmark)
Pedersen, Pauli; Pedersen, Niels Leergaard
2014-01-01
densities is equal value for the weighted elastic energy densities, as a natural extension of the optimality criterion for a single load case. The second optimality criterion for the components of a constitutive matrix (of unit norm) is proportionality to corresponding weighted strain components...... with the same proportionality factor $widehat lambda $ for all the components, as shortly specified by $C_{i j k l} = widehat lambda sum _{n} eta _{n} (epsilon _{i j})_{n} (epsilon _{k l})_{n}$, in traditional notation (n indicate load case). These simple analytical results should be communicated, in spite...
Elasticity in Elastics-An in-vitro study.
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
Enhancing Thermoelectric Performance Using Nonlinear Transport Effects
Jiang, Jian-Hua; Imry, Yoseph
2017-06-01
We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators. The former device refers to phonon-assisted hopping in double quantum dots, while the latter device is represented by elastic tunneling through a single quantum dot. We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices. A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport-induced improvements of the maximum efficiency and power are overall much more significant for inelastic devices than for elastic devices, even for temperature biases as small as Th=1.2 Tc (Th and Tc are the temperatures of the hot and cold reservoirs, respectively). The underlying mechanism is revealed as due to the fact that, unlike the Fermi distribution, the Bose distribution is not bounded when the temperature bias increases. A large flux density of absorbed phonons leads to a great enhancement of the electrical current, output power, and energy efficiency, dominating over the concurrent increase of the parasitic heat current. Our study reveals that nonlinear transport effects can be a useful tool for improving thermoelectric performance.
Finsler Geometry of Nonlinear Elastic Solids with Internal Structure
2017-01-01
the locally relaxed intermediate state of the crystal, following earlier classical differential–geometric treatments by the Japanese school [24]. Kondo...Remark 8. Components of F and f are defined in an identical fashion by Bejancu [12]. Tensor definitions (2.39) and (2.40) potentially differ in two ways...transformations (i.e., push-forwards and pull-backs) of vectors and tensors to be calculated in a completely analogous fashion to transformations between
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer...velocity, which clearly follow the prin- cipal solitary wave (highlighted in red color ). It should be noted that the velocities involved in the
Introduction to linear elasticity
Gould, Phillip L
2013-01-01
Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also: Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...
Relativistic electrodynamics of dissipative elastic media
International Nuclear Information System (INIS)
Kranys, M.
1980-01-01
A phenomenological general relativistic electrodynamics is proposed for a dissipative elastic solid which is polarizable and magnetizable and whose governing equations form a hyperbolic system. Non-stationary transport equations are proposed for dissipative fluxes (and constitutive equations of electrodynamics) containing new cross-effect terms, as required for compatibility with an entropy principle expressed by a new balance equation (including a new Gibbs equation). The dynamic equations are deduced from the unified Minkowski-Abraham-Eckart energy-momentum tensor. The theory, formed by a set of 29 (reducible to 23) partial differential equations (in special relativity) governing the material behaviour of the system characterized by generalizing the constitutive equations of quasineutral media, together with Maxwell's equations, may be referred to as the electrodynamics of dissipative elastic media (or fluid). The proposed transport laws for polarization and magnetization generalize the well-known Debye law for relaxation and show the influence of shear and bulk viscosity on polarization and magentization. Besides the form of the entropy function, the free energy function in the non-stationary regime is also formulated. (auth)
A programmable nonlinear acoustic metamaterial
Directory of Open Access Journals (Sweden)
Tianzhi Yang
2017-09-01
Full Text Available Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic “editing” capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.
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
Energy Technology Data Exchange (ETDEWEB)
Aprile, E; Cantale, G; Degli-Agosti, S; Hausammann, R; Heer, E; Hess, R; Lechanoine-LeLuc, C; Leo, W; Morenzoni, S; Onel, Y [Geneva Univ. (Switzerland). Dept. de Physique Nucleaire et Corpusculaire
1983-01-01
The aim of the elastic pp experimental program at SIN was to measure enough spin dependent parameters in order to do a direct experimental reconstruction of the elastic scattering amplitudes at a few energies between 400 and 600 MeV and at several angles between 38/sup 0/ cm and 90/sup 0/ cm. This reconstruction was not possible until recently due to lack of experimental data. Information instead has come mainly from phase shift analysis (PSA). The only way to extract the elastic scattering amplitudes without any hypotheses except those of basic symmetries, is to measure a sufficient set of spin dependent parameters at a given angle and energy. With this in view, the authors have measured at 448, 494, 515, 536 and 579 MeV, the polarization, the spin correlation parameters Asub(00nn), Asub(00ss), Asub(00kk), Asub(00ks), the 2-spin parameters Dsub(n0n0), Ksub(n00n), Dsub(s'0s0), Dsub(s'0k0) and the 3-spin parameters Msub(s'0sn), Msub(s'0kn) between 34/sup 0/ cm and 118/sup 0/ cm. A few of these parameters have also been measured at 560 and 470 MeV and at a few energies below 448 MeV. The indices refer to the polarization orientation of the scattered, recoil, beam and target particle respectively.
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.
Morphoelastic rods. Part I: A single growing elastic rod
Moulton, D.E.
2013-02-01
A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling. © 2012 Elsevier Ltd. All rights reserved.
Morphoelastic rods. Part I: A single growing elastic rod
Moulton, D.E.; Lessinnes, T.; Goriely, A.
2013-01-01
A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling. © 2012 Elsevier Ltd. All rights reserved.
de Raadt, J.B.
2009-01-01
What were the effects of constitution-making procedures on the acceptance of the new "rules of the political game" in postcommunist Central Europe? This article sets out to scrutinise the increasingly popular claim among politicians and scholars of democratisation that inclusiveness and popular
Valuation In The Constitutional Era
Directory of Open Access Journals (Sweden)
Elmien du Plessis
2015-12-01
Full Text Available The Constitution brought about a new compensation regime for expropriations. Compensation for expropriation must now be "just and equitable". Whereas before the Constitution came into force market value played a central role in compensation for expropriation, market value is now only one factor or aspect of compensation that the court needs to take into account. Yet we find that courts tend to focus on market value and to still employ the valuation methods used to calculate market value. This article argues that the methods used to calculate the market value, once thought to be objective, are not as objective as was believed. While it is impossible to give judges specific tools for the assessment of market value, this article provides guidelines on how the calculation of compensation should be approached.
The Constitutive Power of Twitter
DEFF Research Database (Denmark)
Albu, Oana Brindusa; Etter, Michael Andreas
Twitter is an increasingly used new information and communication technology (ICT) in organizational settings. Predominant research, however, tends to adopt functionalist standpoints and investigates new ICTs as platforms of information transmission through which organizations interact with their......Twitter is an increasingly used new information and communication technology (ICT) in organizational settings. Predominant research, however, tends to adopt functionalist standpoints and investigates new ICTs as platforms of information transmission through which organizations interact...... with their constituents. Such focus leaves little knowledge concerning the tensions new ICTs bring to organizational life. For a more nuanced understanding of the constitutive role of new ICTs in organizing, this paper unfolds a communication centered perspective and examines the strategic Twitter use in two...... organizations. The analysis illustrates how specific Twitter interactions, i.e., hashtags, become hypertexts—a type of authoritative texts—which simultaneously constitute an organizational actor or act as a pastiche of it. The study contributes to extant research by illustrating how hypertextuality...
[Women, gender, and the Constitution].
1993-12-01
Although all the constitutions of Latin America directly or indirectly acknowledge the juridical equality of the sexes, these patriarchal societies continue to maintain institutional power in male hands and to neutralize legal actions favoring women. International instruments such as the Convention on Elimination of All Forms of Discrimination Against Women, approved by the UN in 1979, have given a firmer basis to policies and actions to improve the status of women. Obstacles to full equality of Latin American women are rooted in economic and sociopolitical factors, but lack of true political will also plays a significant role. A number of new laws in the past several years as well as the new Constitution have improved the legal position of Colombian women. The new Constitution recognizes fundamental rights that may be claimed directly before a judge, and social, economic, and collective rights requiring legislative development. Article 43 of the new Constitution states that women will not be subjected to any form of discrimination. Another norm states that women will enjoy special assistance and protection before and after childbirth, in recognition of the social functions of maternity. Article 43 also states that women who are heads of households will receive special assistance, but the corresponding regulations have not yet been promulgated. The mechanism of tutelage has become an important recourse that has been used in several cases in which fundamental rights of women have been violated or threatened because of their sex. The order of tutelage has been used in cases of adolescents expelled from school for pregnancy and of abused wives, as well as to force recognition of the social and economic contributions of housework.
European constitution and EURATOM treaty
International Nuclear Information System (INIS)
Heller, W.
2003-01-01
The European Council held in Laeken in December 2001 had decided to call a convention preparing the next conference of the heads of state and government which, among other topics, was to deliberate the question of a fully formulated European constitution. Under the presidency of Giscard d'Estaing, all delegates to the European Convention on July 10, 2003 signed the draft treaty for a European constitution. This final document is the basis of the conference of the heads of state and government to begin in October 2003. On this occasion, the draft of a separate chapter on energy could well come up again for examination. This chapter had been introduced only at the end of the deliberations of the convention and adds to the competences of the EU institutions. Also the Euratom Treaty was a topic of the convention preparing the constitution. As the presidency felt that no specific issues had been raised in the Laeken declaration, it is proposed to adapt the Euratom Treaty to the new provisions of the constitution by adding a protocol. This would mean that the European Atomic Energy Community, for the time being, would retain its independent legal status. The contents would have to be examined at some later date. Consequently, the real discussion of the Euratom Treaty is yet to come. Also, the speedy completion of the single market for electricity would make it desirable for the Community to adopt a uniform, positive stance in the use of nuclear power at the best possible safety standards so as to ensure a level playing field. Current events entailing power failures in the United States and the United Kingdom have alerted the public to the problem of the continuity of power supply. This could well be the beginning of a new, unbiased, balanced energy discussion in a bigger Europe. (orig.)
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Stochastic isotropic hyperelastic materials: constitutive calibration and model selection
Mihai, L. Angela; Woolley, Thomas E.; Goriely, Alain
2018-03-01
Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress-strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam's razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.
Constitutional collisions of criminal law
Directory of Open Access Journals (Sweden)
Sergey M. Inshakov
2016-12-01
Full Text Available Objective to identify and resolve conflicts between the norms of constitutional and criminal law which regulate the issue of legal liability of senior officials of the state. Methods formallogical systematic comparativelegal. Results the article analyzes the embodiment of the principle of citizensrsquo equality under the law regarding the criminal responsibility of the President of the Russian Federation as one of the segments of the elite right other criminal and legal conflicts are considered associated with the creation of conditions for derogation from the principle of equality. Basing on this analysis the means of overcoming collisions between the norms of constitutional and criminal law are formulated. Scientific novelty in the article for the first time it has been shown that in the Russian criminal law there are exceptions to the principle of citizensrsquo equality under the law relating to the President of the Russian Federation the conflicts are identified between the norms of constitutional and criminal law regulating the issue of legal liability of senior officials of the state ways of overcoming conflicts are suggested. Practical significance the main provisions and conclusions of the article can be used in research and teaching in the consideration of issues of senior state officialsrsquo criminal liability.
Form finding in elastic gridshells
Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.
2018-01-01
Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.
2011-05-11
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.; Goriely, A.; Tabor, M.
2011-01-01
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Constitutive relations in plasticity, damage and fracture mechanics based on a work property
International Nuclear Information System (INIS)
Marigo, J.J.
1989-01-01
This paper is devoted to restrictions imposed by a work property of Drucker-Iliushin's type on the general class of mechanical systems with an elastic range which contains plastic, damaged and cracked media. The analysis is purely mechanical and quasi-static. Starting from very weak assumptions relative to this constitutive class, we obtain a fundamental inequality which generalizes Hill's maximal work principle. So we can justify, for instance: the convexity of the elastic domain and the normality rule of the plastic strain rate in stress space for the infinitesimal and some finite plasticity theories, Griffith's criterion in brittle fracture mechanics, and we obtain some original results for elastic and elastic plastic damaged materials. It must be noted that the procedure is purely deductive, the assumptions are explicit and the results are implications
Constitutive Theory Developed for Monolithic Ceramic Materials
Janosik, Lesley A.
1998-01-01
With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated
Nonlinear buckling of woven fabrics, part I: elastic and non-elastic cases
CSIR Research Space (South Africa)
Anandjiwala, RD
2005-01-01
Full Text Available stream_source_info Anandjiwala_2006_d.pdf.txt stream_content_type text/plain stream_size 10 Content-Encoding ISO-8859-1 stream_name Anandjiwala_2006_d.pdf.txt Content-Type text/plain; charset=ISO-8859-1 ...
Evaluation of potential crushed-salt constitutive models
International Nuclear Information System (INIS)
Callahan, G.D.; Loken, M.C.; Sambeek, L.L. Van; Chen, R.; Pfeifle, T.W.; Nieland, J.D.; Hansen, F.D.
1995-12-01
Constitutive models describing the deformation of crushed salt are presented in this report. Ten constitutive models with potential to describe the phenomenological and micromechanical processes for crushed salt were selected from a literature search. Three of these ten constitutive models, termed Sjaardema-Krieg, Zeuch, and Spiers models, were adopted as candidate constitutive models. The candidate constitutive models were generalized in a consistent manner to three-dimensional states of stress and modified to include the effects of temperature, grain size, and moisture content. A database including hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant and southeastern New Mexico salt was used to determine material parameters for the candidate constitutive models. Nonlinear least-squares model fitting to data from the hydrostatic consolidation tests, the shear consolidation tests, and a combination of the shear and hydrostatic tests produces three sets of material parameter values for the candidate models. The change in material parameter values from test group to test group indicates the empirical nature of the models. To evaluate the predictive capability of the candidate models, each parameter value set was used to predict each of the tests in the database. Based on the fitting statistics and the ability of the models to predict the test data, the Spiers model appeared to perform slightly better than the other two candidate models. The work reported here is a first-of-its kind evaluation of constitutive models for reconsolidation of crushed salt. Questions remain to be answered. Deficiencies in models and databases are identified and recommendations for future work are made. 85 refs
Mathematical foundations of elasticity
Marsden, Jerrold E
1994-01-01
This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con
Elastic and viscoplastic properties
International Nuclear Information System (INIS)
Lebensohn, R.A.
2015-01-01
In this chapter, we review crystal elasticity and plasticity-based self-consistent theories and apply them to the determination of the effective response of polycrystalline aggregates. These mean-field formulations, which enable the prediction of the mechanical behaviour of polycrystalline aggregates based on the heterogeneous and/or directional properties of their constituent single crystal grains and phases, are ideal tools to establish relationships between microstructure and properties of these materials, ubiquitous among fuels and structural materials for nuclear systems. (author)
Constitutive Modelling of Resins in the Compliance Domain
Klasztorny, M.
2004-07-01
A rheological HWKK/H model for resins is developed taking into consideration the up-to-date analyses of experimental results. Constitutive compliance equations of linear are formulated for this model in the shear/bulk form, which describes, among other things, the first-rank reversible isothermal creep. The shear (distorsional) deformations are simulated with three independent stress history functions of fractional and normal exponential types. The volume deformations are simulated as perfectly elastic. The model is described by two elastic and six viscoelastic constants, namely three long-term creep coefficients and three retardation times. The constitutive compliance equations of viscoealsticity for resins are also formulated in the coupled form. Formulae for converting the constants of shear/bulk (uncoupled) viscoelasticity into the constants of coupled viscoelasticity are given too. An algorithm for identifying the material constants, based on the creep of uniaxially tensioned bar samples, is formulated in a way that gives unique results. The material constants are fiund for Epidian 53 epoxy and Polimal 109 polyester resins. The creep processes, simulated based on the experimental data, are presented graphically for both the resins examined.
Viscoplastic Constitutive Theory Demonstrated for Monolithic Ceramic Materials
Janosik, Lesley A.
1999-01-01
Development of accurate three-dimensional (multiaxial) inelastic stress-strain models is critical in utilizing advanced ceramics for challenging 21st century high-temperature structural applications. The current state of the art uses elastic stress fields as a basis for both subcritical crack growth and creep life prediction efforts aimed at predicting the time dependent reliability response of ceramic components subjected to elevated service temperatures. However, to successfully design components that will meet tomorrow's challenging requirements, design engineers must recognize that elastic predictions are inaccurate for these materials when subjected to high-temperature service conditions such as those encountered in advanced heat engine components. Analytical life prediction methodologies developed for advanced ceramics and other brittle materials must employ accurate constitutive models that capture the inelastic response exhibited by these materials at elevated service temperatures. A constitutive model recently developed at the NASA Lewis Research Center helps address this issue by accounting for the time-dependent (inelastic) material deformation phenomena (e.g., creep, rate sensitivity, and stress relaxation) exhibited by monolithic ceramics exposed to high-temperature service conditions. In addition, the proposed formulation is based on a threshold function that is sensitive to hydrostatic stress and allows different behavior in tension and compression, reflecting experimental observations obtained for these material systems.
Natural Frequencies and Mode Shapes of a Nonlinear, Uniform Cantilevered Beam
National Research Council Canada - National Science Library
Marquez-Chisolm, Daniel J
2006-01-01
A series of experiments in 1975, referred to as the Princeton Beam Experiments, were performed to measure natural frequencies and create a nonlinear elastic deformation model to improve helicopter main beam designs...
Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters
Abdelkefi, Abdessattar; Ghommem, Mehdi; Nuhait, Abdullah O.; Hajj, M. R.
2014-01-01
We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk
2015-01-01
Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.
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.)
Mathematical methods in elasticity imaging
Ammari, Habib; Garnier, Josselin; Kang, Hyeonbae; Lee, Hyundae; Wahab, Abdul
2015-01-01
This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic...
The Normative Constitution of Agency
Korsgaard, Christine M.
2014-01-01
On a naturalistic conception of agency, someone is an agent when certain of his own mental states are the cause of his movements. On a normative conception, a person constitutes his agency by following certain principles or laws. In Kant’s conception, for example, a movement counts as the agent’s own when it is chosen autonomously, that is, in accordance with the categorical imperative. To say that someone acts is to imply that his movements are a manifestation of his own activity and that it...
Spherocylindrical microplane constitutive model for shale and other anisotropic rocks
Li, Cunbao; Caner, Ferhun C.; Chau, Viet T.; Bažant, Zdeněk P.
2017-06-01
Constitutive equations for inelastic behavior of anisotropic materials have been a challenge for decades. Presented is a new spherocylindrical microplane constitutive model that meets this challenge for the inelastic fracturing behavior of orthotropic materials, and particularly the shale, which is transversely isotropic and is important for hydraulic fracturing (aka fracking) as well as many geotechnical structures. The basic idea is to couple a cylindrical microplane system to the classical spherical microplane system. Each system is subjected to the same strain tensor while their stress tensors are superposed. The spherical phase is similar to the previous microplane models for concrete and isotropic rock. The integration of stresses over spherical microplanes of all spatial orientations relies on the previously developed optimal Gaussian integration over a spherical surface. The cylindrical phase, which is what creates the transverse isotropy, involves only microplanes that are normal to plane of isotropy, or the bedding layers, and enhance the stiffness and strength in that plane. Unlike all the microplane models except the spectral one, the present one can reproduce all the five independent elastic constants of transversely isotropic shales. Vice versa, from these constants, one can easily calculate all the microplane elastic moduli, which are all positive if the elastic in-to-out-of plane moduli ratio is not too big (usually less than 3.75, which applies to all shales). Oriented micro-crack openings, frictional micro-slips and bedding plane behavior can be modeled more intuitively than with the spectral approach. Data fitting shows that the microplane resistance depends on the angle with the bedding layers non-monotonically, and compressive resistance reaches a minimum at 60°. A robust algorithm for explicit step-by-step structural analysis is formulated. Like all microplane models, there are many material parameters, but they can be identified sequentially
Energy Technology Data Exchange (ETDEWEB)
Loewenthal, M.; Loseke, K.; Dow, T.A.; Scattergood, R.O.
1988-12-01
Elastic emission polishing, also called elastic emission machining (EEM), is a process where a stream of abrasive slurry is used to remove material from a substrate and produce damage free surfaces with controlled surface form. It is a noncontacting method utilizing a thick elasto-hydrodynamic film formed between a soft rotating ball and the workpiece to control the flow of the abrasive. An apparatus was built in the Center, which consists of a stationary spindle, a two-axis table for the workpiece, and a pump to circulate the working fluid. The process is controlled by a programmable computer numerical controller (CNC), which presently can operate the spindle speed and movement of the workpiece in one axis only. This apparatus has been used to determine material removal rates on different material samples as a function of time, utilizing zirconium oxide (ZrO{sub 2}) particles suspended in distilled water as the working fluid. By continuing a study of removal rates the process should become predictable, and thus create a new, effective, yet simple tool for ultra-precision mechanical machining of surfaces.
International Nuclear Information System (INIS)
Mermaz, M.C.
1984-01-01
Diffraction and refraction play an important role in particle elastic scattering. The optical model treats correctly and simultaneously both phenomena but without disentangling them. Semi-classical discussions in terms of trajectories emphasize the refractive aspect due to the real part of the optical potential. The separation due to to R.C. Fuller of the quantal cross section into two components coming from opposite side of the target nucleus allows to understand better the refractive phenomenon and the origin of the observed oscillations in the elastic scattering angular distributions. We shall see that the real part of the potential is responsible of a Coulomb and a nuclear rainbow which allows to determine better the nuclear potential in the interior region near the nuclear surface since the volume absorption eliminates any effect of the real part of the potential for the internal partial scattering waves. Resonance phenomena seen in heavy ion scattering will be discussed in terms of optical model potential and Regge pole analysis. Compound nucleus resonances or quasi-molecular states can be indeed the more correct and fundamental alternative
Design guidance for elastic followup
International Nuclear Information System (INIS)
Naugle, F.V.
1983-01-01
The basic mechanism of elastic followup is discussed in relation to piping design. It is shown how mechanistic insight gained from solutions for a two-bar problem can be used to identify dominant design parameters and to determine appropriate modifications where elastic followup is a potential problem. It is generally recognized that quantitative criteria are needed for elastic followup in the creep range where badly unbalanced lines can pose potential problems. Approaches for criteria development are discussed
Income Elasticity of Environmental Amenities
Daniel Miles; Andrés Pereyra; Máximo Rossi
2000-01-01
In this paper we are concerned with the estimation of income elasticities of environmental amenities. The novelty is the application of econometric methods that take into account the problem of measurement errors when estimating these elasticities, which are common in microeconomic data and are not usually considered in the applied literature related with this issue. Our aim is to discuss whether the measurement error has signi…cant e¤ects on the elasticities. Data from the Expenditure Budget...
International Nuclear Information System (INIS)
Magomedov, A.M.
1986-01-01
Rates of propagation of longitudinal and transverse acoustic waves in samples as well as density of Tl, Pb, Sn, Bi, Cd, Zn and their binary alloys with indium are determined. The results obtained are used for calculation of elasticity constants of these materials. It is stated that concentration dependences of elasticity constants for indium alloys have non-linear character; negative deflection from the additive line is observed
International Nuclear Information System (INIS)
Khidirov, I.; Khajdarov, T.
1995-01-01
Elasticity characteristics of cubic and tetragonal phases of titanium nitride in the homogeneity range were studied for the first time by ultrasonic resonance method. It is established that the Young modulus, the shift and volume module of cubic titanium nitride elasticity in the homogeneity range change nonlinearly with decrease in nitrogen concentration and correlate with concentration dependences of other physical properties.15 refs., 2 figs
Essence and constitution in Zubiri
Directory of Open Access Journals (Sweden)
Alfonso Gómez Fernández
2015-03-01
Full Text Available The aim of this article is to expound Zubiri’s concept of essence and to begin a critical discussion and evaluation of his proposal. Before explaining what essence is, it is necessary to observe that, for our author, not all things have an essence: only «reality-things» but not «meaning-things» form part of the «essentiable domain». This distinction between «reality-things» and «meaning-things» supposes a new conception of nature. (Nature is not the opposite of the artificial, as the Greek term physis is.«Reality-things» form a constitutional and «closed» system of non-causal and non-«external» characteristics or traits. These «foundational characteristics» of constitution, then, are precisely the essence. The article discusses critically the assumptions of this doctrine (reality, ontological pluralism, foundation and its possible limits in the light of contemporary science. It can be a useful theory for the philosophy of language.
System Reduction in Nonlinear Multibody Dynamics of Wind Turbines
DEFF Research Database (Denmark)
Holm-Jørgensen, Kristian; Nielsen, Søren R.K.; Rubak, Rune
2007-01-01
In this paper the system reduction in nonlinear multibody dynamics of wind turbines is investigated for various updating schemes of the moving frame of reference. In one case, the moving frame of reference is updated to a stiff body, relative to which the elastic deformations are fixed at one end....... In the other case, the stiff body motion is defined as the chord line connecting the end points of the beam, and the elastic deformations are simply supported at the end points. The system reduction is performed by discretizing the spatial motion into a set of rigid body modes and linear elastic eigenmodes...
Mechanical tests for validation of seismic isolation elastomer constitutive models
International Nuclear Information System (INIS)
Kulak, R.F.; Hughes, T.H.
1992-01-01
High damping laminated elastomeric bearings are becoming the preferred device for seismic isolation of large buildings and structures, such as nuclear power plants. The key component of these bearings is a filled natural rubber elastomer. This material exhibits nonlinear behavior within the normal design range. The material damping cannot be classified as either viscous or hysteritic, but it seems to fall somewhere in between. This paper describes a series of tests that can be used to characterize the mechanical response of these elastomers. The tests are designed to determine the behavior of the elastomer in the time scale of the earthquake, which is typically from 30 to 60 seconds. The test results provide data for use in determining the material parameters associated with nonlinear constitutive models. 4 refs
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
A Membrane Model from Implicit Elasticity Theory
Freed, A. D.; Liao, J.; Einstein, D. R.
2014-01-01
A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079
Application of viscoplastic constitutive equations in finite element programs
International Nuclear Information System (INIS)
Hornberger, K.; Stamm, H.
1987-04-01
The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de
Unborn children as constitutional persons.
Roden, Gregory J
2010-01-01
In Roe v. Wade, the state of Texas argued that "the fetus is a 'person' within the language and meaning of the Fourteenth Amendment." To which Justice Harry Blackmun responded, "If this suggestion of personhood is established, the appellant's case, of course, collapses, for the fetus' right to life would then be guaranteed specifically by the Amendment." However, Justice Blackmun then came to the conclusion "that the word 'person,' as used in the Fourteenth Amendment, does not include the unborn." In this article, it is argued that unborn children are indeed "persons" within the language and meaning of the Fourteenth and Fifth Amendments. As there is no constitutional text explicitly holding unborn children to be, or not to be, "persons," this argument will be based on the "historical understanding and practice, the structure of the Constitution, and thejurisprudence of [the Supreme] Court." Specifically, it is argued that the Constitution does not confer upon the federal government a specifically enumerated power to grant or deny "personhood" under the Fourteenth Amendment. Rather, the power to recognize or deny unborn children as the holders of rights and duties has been historically exercised by the states. The Roe opinion and other Supreme Court cases implicitly recognize this function of state sovereignty. The states did exercise this power and held unborn children to be persons under the property, tort, and criminal law of the several states at the time Roe was decided. As an effect of the unanimity of the states in holding unborn children to be persons under criminal, tort, and property law, the text of the Equal Protection Clause of the Fourteenth Amendment compels federal protection of unborn persons. Furthermore, to the extent Justice Blackmun examined the substantive law in these disciplines, his findings are clearly erroneous and as a whole amount to judicial error. Moreover, as a matter of procedure, according to the due process standards recognized in
Comparison of elastic and inelastic analyses
International Nuclear Information System (INIS)
Ammerman, D.J.; Heinstein, M.W.; Wellman, G.W.
1992-01-01
The use of inelastic analysis methods instead of the traditional elastic analysis methods in the design of radioactive material (RAM) transport packagings leads to a better understanding of the response of the package to mechanical loadings. Thus, better assessment of the containment, thermal protection, and shielding integrity of the package after a structure accident event can be made. A more accurate prediction of the package response can lead to enhanced safety and also allow for a more efficient use of materials, possibly leading to a package with higher capacity or lower weight. This paper discusses the advantages and disadvantages of using inelastic analysis in the design of RAM shipping packages. The use of inelastic analysis presents several problems to the package designer. When using inelastic analysis the entire nonlinear response of the material must be known, including the effects of temperature changes and strain rate. Another problem is that there currently is not an acceptance criteria for this type of analysis that is approved by regulatory agencies. Inelastic analysis acceptance criteria based on failure stress, failure strain , or plastic energy density could be developed. For both elastic and inelastic analyses it is also important to include other sources of stress in the analyses, such as fabrication stresses, thermal stresses, stresses from bolt preloading, and contact stresses at material interfaces. Offsetting these added difficulties is the improved knowledge of the package behavior. This allows for incorporation of a more uniform margin of safety, which can result in weight savings and a higher level of confidence in the post-accident configuration of the package. In this paper, comparisons between elastic and inelastic analyses are made for a simple ring structure and for a package to transport a large quantity of RAM by rail (rail cask) with lead gamma shielding to illustrate the differences in the two analysis techniques
The Constitutive Values of Science
Directory of Open Access Journals (Sweden)
Hugh Lacey
1997-06-01
Full Text Available Cognitive values are the characteristics that are constitutive of good theories, the criteria to which we appeal when choosing among competing theories. I argue that, in order to count as a cognitive value, a characteristic must be needed to explain actually made theory choices, and its cognitive significance must be well defended especially in view of considerations derived from the objective of science. A number of proposed objectives of science are entertained, and it is argued that adopting a par-ticular objective is dialectically intertwined with commitment to certain social values.Then, the ways in which science is, and is not value free is explored briefly, leading to the identification of a level of analysis where values may influence theory choice without causing paradox or threatening the impartiality of soundly-made scientific judgments.
[Constitutional mismatch repair deficiency syndrome].
Jongmans, Marjolijn C; Gidding, Corrie E; Loeffen, Jan; Wesseling, Pieter; Mensenkamp, Arjen; Hoogerbrugge, Nicoline
2015-01-01
Constitutional mismatch repair deficiency (CMMR-D) syndrome is characterised by a significantly increased risk for developing cancer in childhood. It arises when both parents have a mutation in the same mismatch repair gene and pass it on to their child. An 8-year-old girl was diagnosed with CMMR-D syndrome after she developed a brain tumour at the age of 4 and a T-cell non-Hodgkin lymphoma at the age of 6. She had multiple hyperpigmented skin lesions and died of myelodysplastic syndrome at the age of 11. In children with cancer CMMR-D syndrome can be recognized particularly if there are multiple primary malignancies and skin hyperpigmentations and hypopigmentations. The parents of these children are at high risk for colorectal and endometrial cancer (Lynch syndrome), amongst others.
Kinanthropometry - Components of body constitution
Directory of Open Access Journals (Sweden)
Maria Tereza Silveira Böhme
2000-12-01
Full Text Available The objective of this study is to present the conceptual and historical background to Kinanthropometry and to characterize this area of research. The components of body constitution relating to dimensions, proportions, shape and body composition that should be considered in Physical Education and Sports programs are also described. ARESUMO Este trabalho tem por objetivo apresentar os aspectos conceituais referentes à Cineantropometria, assim como os aspectos históricos e caracterização desta área de estudos. São também descritos os componentes de constituição corporal referentes à dimensões, proporções, forma e composição corporal que devem ser considerados em programas de Educação Física e Esporte.
Elasticity theory of ultrathin nanofilms
International Nuclear Information System (INIS)
Li, Jiangang; Yun, Guohong; Narsu, B; Yao, Haiyan
2015-01-01
A self-consistent theoretical scheme for describing the elastic behavior of ultrathin nanofilms (UTNFs) was proposed. Taking into account the lower symmetry of an UTNF compared to its bulk counterpart, additional elastic and magnetoelastic parameters were introduced to model the elasticity rigorously. The applications of current theory to several elastic and magnetoelastic systems gave excellent agreement with experiments. More importantly, the surface elastic and magnetoelastic parameters used to fit the experimental results are physically reasonable and in close agreement with those obtained from experiment and simulation. This fact suggests that the additional elastic (magnetoelastic) constants due to symmetry breaking are of great importance in theoretical description of the mechanical properties of UTNFs. And we proved that the elasticity of UTNFs should be described by a three-dimensional model just including the intrinsic surface and bulk parameters, but not the effective surface parameters. It is believed that the theory reported here is a universal strategy for elasticity and magnetoelasticity of ultrathin films. (paper)
The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline
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.
Energy Technology Data Exchange (ETDEWEB)
Sagdeev, R Z
1984-01-01
The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.
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...
Gradient effects in a new class of electro-elastic bodies
Arvanitakis, Antonios
2018-06-01
Continuum theories for electro-elastic solids suggest the development of electric field or polarization-based models. Advanced versions of these models are the so-called gradient models, i.e., polarization gradient and electric field gradient models, which prove to be more than capable of explaining the behavior of a continuum in a wider range of length scales. In this work, implicit constitutive relations for electro-elastic bodies are considered with the introduction of polarization and electric field gradient effects. In this sense, the new class of electro-elastic bodies extends even further to account for nonlocality in constitutive equations, besides strain-limiting behavior and polarization saturation for large values of stresses and electric field, respectively. Nonlocality in constitutive equations is essential in modeling various phenomena.
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
International Nuclear Information System (INIS)
Oyer, A.T.
1976-12-01
A measurement of the elastic cross section dsigma/dΩ was made for the reaction π + + 12 C → π + + 12 C with 142 MeV pions at ten angles ranging from 35 to 85 0 in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometer's focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic, and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55 0 . Finally, the carbon elastic cross sections were compared to similar π - + 12 C cross sections of Binon et al using the optical model
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
Energy Technology Data Exchange (ETDEWEB)
Oyer, A.T.
1976-12-01
A measurement of the elastic cross section dsigma/d..cap omega.. was made for the reaction ..pi../sup +/ + /sup 12/C ..-->.. ..pi../sup +/ + /sup 12/C with 142 MeV pions at ten angles ranging from 35 to 85/sup 0/ in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometer's focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic, and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55/sup 0/. Finally, the carbon elastic cross sections were compared to similar ..pi../sup -/ + /sup 12/C cross sections of Binon et al using the optical model.
Measurement of the elastic cross section for positive pions on carbon at 142 MeV
International Nuclear Information System (INIS)
Oyer, A.T.
1976-01-01
A measurement of the elastic cross section dsigma/dOMEGA was made for the reaction π + + 12 C yields π + + 12 C with 142 MeV pions at ten angles ranging from 35 to 85 0 in the laboratory. This experiment was done at the Los Alamos Meson Physics Facility. A double focusing magnetic spectrometer observed a cylindrical styrofoam target. The resulting momentum spectra were recorded by an array of nineteen totally depleted surface barrier detectors located at the spectrometers focal plane. The spectra from the styrofoam were composed of peaks representing proton elastic, carbon elastic, carbon inelastic and carbon quasi-elastic channels. A function made of Gaussians representing the two body channels and a distribution representing the quasi-elastic channel was fit to the data using a nonlinear least squares algorithm. The ratio of the carbon elastic to proton elastic cross sections was calculated from the areas of the corresponding Gaussians and then multiplied by the proton elastic cross section of Bugg et al., eliminating several sources of systematic errors such as beam normalization. The differential cross sections were found to have the usual diffraction structure with a forward peak and a minimum near 55 0 . Finally, the carbon elastic cross sections were compared to similar π - + 12 C cross sections of Binon et al., using the optical model
Cell Elasticity Determines Macrophage Function
Patel, Naimish R.; Bole, Medhavi; Chen, Cheng; Hardin, Charles C.; Kho, Alvin T.; Mih, Justin; Deng, Linhong; Butler, James; Tschumperlin, Daniel; Fredberg, Jeffrey J.; Krishnan, Ramaswamy; Koziel, Henry
2012-01-01
Macrophages serve to maintain organ homeostasis in response to challenges from injury, inflammation, malignancy, particulate exposure, or infection. Until now, receptor ligation has been understood as being the central mechanism that regulates macrophage function. Using macrophages of different origins and species, we report that macrophage elasticity is a major determinant of innate macrophage function. Macrophage elasticity is modulated not only by classical biologic activators such as LPS and IFN-γ, but to an equal extent by substrate rigidity and substrate stretch. Macrophage elasticity is dependent upon actin polymerization and small rhoGTPase activation, but functional effects of elasticity are not predicted by examination of gene expression profiles alone. Taken together, these data demonstrate an unanticipated role for cell elasticity as a common pathway by which mechanical and biologic factors determine macrophage function. PMID:23028423