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
On the theory of dislocation and generalized disclination fields and its application to straight and stepped symmetrical tilt boundaries
Claude Fressengeas,Xiao-Yu Sun +1 more
TL;DR: The theory of dislocation and generalized dislocation fields as discussed by the authors was developed within a second-order mechanical framework, where the description of the internal state of the body and the balance equations involve the stress and hyper-stress tensors, work-conjugates to the strain and secondorder distortion tensors.
Journal ArticleDOI
On the restriction of processes by the Clausius-Duhem inequality
TL;DR: In this article, Clausius-Duhem-Ungleichung is interpreted as a Plastizitatstheorie, in which the Einschrankung der Prozesse sich als ebenso wesentlich herausstellt wie diejenige der Stoffgleichings.
Journal ArticleDOI
A thermodynamically consistent model for magnetic hysteresis
TL;DR: In this article, a phenomenological constitutive model is presented to describe the magnetization curve within the context of thermodynamics, and the basic structure of the proposed model comes from rate-dependent plasticity in continuum mechanics, namely viscoplasticity, which enables the frequency dependence of the hysteresis curve to be modeled.
Proceedings ArticleDOI
Nonlinear dynamics and chaos in a shape memory alloy pseudoelastic oscillator
TL;DR: In this paper, the authors discuss the dynamical response of one-degree of freedom (1-DOF) oscillator where the restitution force is provided by an SMA pseudoelastic element described by a smooth constitutive model built upon the Boyd-Lagoudas model.
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.