Journal ArticleDOI
Thermodynamics with Internal State Variables
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In this paper, the authors study the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations, and employ a method developed by Coleman and Noll to find the general restrictions which the Clausius-Duhem inequality places on response functions.Abstract:
This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.read more
Citations
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Journal ArticleDOI
Nonlinear thermomechanics for analysis of weak shock profile data in ductile polycrystals
TL;DR: In this paper, a semi-analytical method is proposed for extracting inelastic constitutive response information from particle velocity histories of polycrystalline samples under planar shock loading.
Journal ArticleDOI
Thermodynamical setting for gradient continuum theories with vectorial internal variables: Application to granular materials
TL;DR: In this paper, the generalized Liu procedure was applied to the equations of a continuum with vectorial internal variable and first-order non-local state space, and a thermodynamic model for continua with scalar microstructure was developed.
Journal ArticleDOI
Exact and approximate Maxwell-Cattaneo-type descriptions of heat conduction: A comparative analysis
TL;DR: In this paper, the authors compare consequences of the Maxwell-Cattaneo view on the heat flux and the choice of considering its approximation as an exact relation defining per se a class of conductors.
Journal ArticleDOI
A physically motivated modification of the strain equivalence approach
Mattias Olsson,Matti Ristinmaa +1 more
TL;DR: In this paper, a modification of the postulate of strain equivalence is proposed based on physical arguments, which predicts the elastic strain to vanish when failure takes place, and the results reveal that the modification gives promising results.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Supersonic flow and shock waves
Richard Courant,Kurt Friedrichs +1 more
TL;DR: In this article, the authors proposed a method to compressible ecoulement for compressible compressible and supersonique and onde de choc Reference Record created on 2005-11-18, modified on 2016-08-08
Book ChapterDOI
The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity
TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.