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Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-…

Soft Condensed Matter · Physics 2013-01-30 Michel Destrade , Michael D. Gilchrist , G. Saccomandi

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic…

Mathematical Physics · Physics 2013-04-23 Mohammad H. Abedinnasab , Mahmoud I. Hussein

We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…

Fluid Dynamics · Physics 2025-05-20 Philippe H. Trinh , Stephen K. Wilson , Howard A. Stone

The effect of finite temperature $T$ and finite strain rate $\dot\gamma$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the…

Statistical Mechanics · Physics 2015-05-19 Smarajit Karmakar , Edan Lerner , Itamar Procaccia , Jacques Zylberg

This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials. Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the…

Numerical Analysis · Mathematics 2022-01-12 Thaís C. da Costa Haveroth , Geovane A. Haveroth , Marco L. Bittencourt , José L. Boldrini

Distributed order fractional model of viscoelastic body is used in order to describe wave propagation in infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem, corresponding to fractional wave…

Mathematical Physics · Physics 2019-03-12 Sanja Konjik , Ljubica Oparnica , Dusan Zorica

We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…

Numerical Analysis · Mathematics 2015-11-25 Kristoffer Virta , Christopher Juhlin , Gunilla Kreiss

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…

Numerical Analysis · Mathematics 2015-05-13 A. V. Shutov , R. Kreissig

A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…

Numerical Analysis · Mathematics 2025-11-25 Hongpeng Li , Cristian Carcamo , Hongxing Rui , Volker John

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…

Analysis of PDEs · Mathematics 2018-02-06 Yi-Hsuan Lin , Shixu Meng

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent…

Materials Science · Physics 2017-07-19 K. C. Le , T. M. Tran , J. S. Langer

Built on the tenets of rational thermodynamics, this article proposes a theory of strain gradient thermo-visco-plasticity for isotropic polycrystalline materials under high strain rates. The effect of micro-inertia, which arises due to…

Materials Science · Physics 2016-01-28 Md M Rahaman , A Pathak , D Roy , J N Reddy

A comprehensive 3-D finite element formulation for the coupled thermoelastic system is proposed based on the Total Lagrangian framework to study the thermoelastic damping (TED) in small scale structures. The proposed formulation takes into…

Computational Engineering, Finance, and Science · Computer Science 2024-09-25 Saurabh Dixit

We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a…

Astrophysics of Galaxies · Physics 2015-05-19 Richard Wunsch , James E. Dale , Jan Palous , Anthony P. Whitworth

Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…

Analysis of PDEs · Mathematics 2026-05-01 Miroslav Bulíček , Tomáš Los , Jakub Woźnicki

The balance equations of energy-momentum and spin together with Einstein's field equations are investigated by the Liu procedure to find constraints for the constitutive equations in such a way that the Second Law is satisfied. Special…

General Relativity and Quantum Cosmology · Physics 2015-01-13 Wolfgang Muschik , Horst-Heino v. Borzeszkowski

The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…

Classical Physics · Physics 2012-07-31 E Hanukah , Bella Goldshtein

In a continuum description of materials, the stress tensor field $\bar{% \bar{\sigma}}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that…

Soft Condensed Matter · Physics 2007-05-23 Marius Asipauskas , Miguel Aubouy , James A. Glazier , François Graner , Yi Jiang

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…

Classical Physics · Physics 2019-09-12 Roger A. Sauer , Reza Ghaffari , Anurag Gupta

The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was…

Statistical Mechanics · Physics 2020-09-02 Peter Ván