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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Equilibrium configurations and stability of a damaged body under uniaxial tractions
TL;DR: In this paper, the equilibrium problem in nonlinear dissipative inelasticity of damaged bodies subject to uniaxial loading is dealt with, and explicit expressions governing the global development of the equilibrium paths are written.
Book ChapterDOI
Mechanics of Material Mutations
TL;DR: In this paper, the notion of relative power has been used to derive standard, microstructural, and configurational actions from a unique source, and the description of crack nucleation in simple and complex materials in terms of a variational selection in a family of bodies differing from one another by the defect pattern.
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An intrinsic dissipation model for high-cycle fatigue life prediction
TL;DR: In this paper, a new intrinsic dissipation model for high-cycle fatigue life prediction of metallic materials is proposed, taking into account two critical stress amplitudes related to the corresponding microstructure motion.
Journal ArticleDOI
A comparison of Gurtin type and micropolar theories of generalized single crystal plasticity
TL;DR: In this article, the authors compare and contrast the governing equations and numerical predictions of two higher-order theories of extended single crystal plasticity, specifically, Gurtin type and micropolar models.
Journal ArticleDOI
Bayesian uncertainty analysis of finite deformation viscoelasticity
TL;DR: In this article, the authors quantified both the hyperelastic and viscoelastic constitutive behavior of the dielectric elastomer VHB 4910 and used Bayesian uncertainty analysis to assess several key modeling attributes.
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.