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
Elastodynamics of thin plates with internal dissipative processes Part I. Theoretical foundations
TL;DR: In this article, an integral representation of the dynamic behavior of thin plates is developed where two distinct types of internal defects, namely viscoplastic flow and ductile microfracture are considered.
Journal ArticleDOI
On the mechanical behaviour under cyclic loading of ceramic matrix composites
TL;DR: In this paper, a constitutive law is presented to model the mechanical behavior of ceramic matrix composites, allowing matrix-cracking, interfacial debonding, sliding and wear to be accounted for in the framework of continuum mechanics.
Journal ArticleDOI
Friction coefficient evaluation using physically based viscoplasticity model at the contact region during high velocity sliding
TL;DR: In this article, the formulation of Molinari et al.'s work (J Tribology Trans ASME 35-41, 1999) is revisited in order to investigate the coefficient of dry friction for steel on steel in the high velocity range using physically based viscoplastic constitutive relations.
Book ChapterDOI
Thermodynamics of Solids
TL;DR: In this paper, an implicit representation of a functional relation is obtained from the formulation of a system of ordinary differential equations for a set of additional internal variables, specifying the rate of change of internal variables depending on their present values and the strain (or stress) input.
Journal ArticleDOI
An anisotropic thermomechanical damage model for concrete at transient elevated temperatures.
Graham Baker,René de Borst +1 more
TL;DR: A fully coupled anisotropic thermomechanical damage model for concrete under high stress and transient temperature is developed, with emphasis on the adherence of the model to the laws of thermodynamics.
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.