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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Journal ArticleDOI
Finite‐Strain Theory of Crystalline Elastic‐Inelastic Materials
TL;DR: In this article, the authors extended the thermodynamics of elastic-viscoplastic materials developed in two previous papers to account for finite strains and described the geometry of a body subjected to finite deformation based on the kinematic of a continuum with dislocations.
Journal ArticleDOI
Thermomechanical constitution of spalling elastic bodies
Lee Davison,A. L. Stevens +1 more
TL;DR: In this article, a theory of spallation of a brittle thermoelastic body and the interaction between propagating waves and accumulated damage was developed to predict the spall damage on the elastic stiffness and thermal conductivity of the material.
Journal ArticleDOI
A nonlinear quantum transport theory
TL;DR: In this article, a nonlinear quantum transport theory for many-body systems arbitrarily far away from equilibrium, based on the nonequilibrium statistical operator method, is discussed, and an iterative process is described that allows for the calculation of the collision operator in a series of instantaneous in time partial contributions of ever increasing power in the interaction strengths.
Journal ArticleDOI
A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric
TL;DR: In this article, a constitutive framework of large-strain elastoplasticity in both the Lagrangian and the Eulerian geometric setting is presented, which takes into account anisotropic material response.
Journal ArticleDOI
An extension of the local equilibrium hypothesis
TL;DR: In this article, an extension of the Gibbs equation is presented to extend the range of application of classical irreversible thermodynamics far from equilibrium, and the results are shown to be in agreement with the Boltzmann kinetic theory.
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.