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
Theoretical and Numerical Aspects in the Thermo-Viscoelastic Material Behaviour of Rubber-Like Polymers
Stefanie Reese,Sanjay Govindjee +1 more
TL;DR: In this paper, a model for finite deformation viscoelasticity that utilizes a nonlinear evolution law to include thermal effects is presented. But the model is restricted to linear evolution laws for the viscous behaviour and to thermorheologically simple materials.
Journal ArticleDOI
Thermodynamic theory of dislocation-mediated plasticity
TL;DR: In this paper, the theory of polycrystalline plasticity in externally driven, nonequilibrium situations was reformulated by writing equations of motion for the flow of energy and entropy associated with dislocations.
Journal ArticleDOI
A maximum-dissipation principle in generalized plasticity
TL;DR: In this paper, it was shown that in large deformation generalized plasticity, a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold.
Journal ArticleDOI
On the thermodynamics of second sound in dielectric crystals
Journal ArticleDOI
A robust algorithm for configurational‐force‐driven brittle crack propagation with R‐adaptive mesh alignment
Christian Miehe,Ercan Gürses +1 more
TL;DR: In this article, the authors considered a variational formulation of brittle fracture in elastic solids and proposed a numerical implementation by a finite element method, where the authors exploited this variational structure in terms of crack-driving configurational forces.
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.