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
Continuum physics of phase and defect microstructures: bridging the gap between physical metallurgy and plasticity of aluminum alloys
Michael V. Glazoff,Michael V. Glazoff,Frédéric Barlat,Frédéric Barlat,Hasso Weiland,Hasso Weiland +5 more
TL;DR: A survey of recent developments in this direction is presented in this article, where similar conceptual problems arising both in plasticity theory and in classical thermodynamics are analyzed, which can be traced to the absence of characteristic length scales in the corresponding phenomenological formalisms.
Journal ArticleDOI
Concurrent multi-scale crush simulations with a crystal plasticity model
TL;DR: In this article, the texture generated by deforming a single element model with an embedded polycrystalline aggregate of face center cubic (FCC) crystals under basic loading paths, including uniaxial tension and simple shear, is used at each integration point in the explicit crush simulations of a square tube model made of an FCC aluminum alloy.
Journal ArticleDOI
Energy based mechano-electrophysiological model of CNS damage at the tissue scale
TL;DR: A novel mechano-electrophysiological framework able to model the mechanics of spinal cord and brain tissue and its translation into electrophysiology dysfunction through energetic terms at the tissue level is provided.
Journal ArticleDOI
Surface effects, boundary conditions and evolution laws within second strain gradient plasticity
TL;DR: In this article, the virtual power (PVP) is used in conjunction with the concepts of energy residual and insulation condition to address second strain gradient plasticity, where the energy residual with its typical divergence format is an extra stress power playing the role of basic state variable to describe the gradient effects, whereas the insulation condition constitutes a global energy characterization of the body.
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.