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
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Book ChapterDOI
Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries
TL;DR: In this article, the authors reviewed the recent studies on the nucleation and kinetics of propagating phase boundaries in an elastic bar and related them to various admissibility criteria.
Journal ArticleDOI
Quasi-linear versus potential-based formulations of force–flux relations and the GENERIC for irreversible processes: comparisons and examples
Markus Hütter,Bob Svendsen +1 more
TL;DR: In this paper, it was shown that the class of models formulated by quasi-linear relations is larger than what can be described in a potential-based formulation, while the relation between the two methods is shown in general terms, and demonstrated also with the help of three examples.
Journal ArticleDOI
Fractional-order relaxation laws in non-linear viscoelasticity
TL;DR: In this paper, the stress is a nonlinear function of the current strain and of a set of internal variables satisfying relaxation equations of fractional order, and the dependence of the relaxation equations on the strain can also be nonlinear.
Journal ArticleDOI
A constitutive model for the periodontal ligament as a compressible transversely isotropic visco-hyperelastic tissue
TL;DR: A new constitutive model for the human periodontal ligament based on the non-linear large deformation theory, involving the Lagrangian description is proposed and the macroscopic continuum approach is used.
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.