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
Thermochemistry of Reacting Materials
TL;DR: In this paper, the Clausius-Duhem inequality is used to derive a set of necessary and sufficient conditions that the constitutive functions must obey, among these conditions are ones that determine the role of De Donder's chemical affinity in determining whether or not chemical reactions are present.
Journal ArticleDOI
Local and non-local Gurson-based ductile damage and failure modelling at large deformation
TL;DR: In this paper, a non-local extension of existing Gurson-based modeling for isotropic ductile damage and attendant crack growth is presented, where void coalescence results not only in accelerated damage development, but also in damage delocalisation via interaction between neighbouring Gurson RVE's.
Journal ArticleDOI
A thermomechanical model for a 1-D shape memory alloy wire with propagating instabilities
TL;DR: In this article, a thermomechanical boundary value problem and constitutive model for a shape memory alloy (SMA) wire under uniaxial loading are presented for finite element analyses.
Journal ArticleDOI
Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials
TL;DR: In this paper, the authors modify the spectral decomposition technique to models that include kinematic hardening and perform some numerical simulations to demonstrate quadratic convergence for these models.
Journal ArticleDOI
Rate-dependent extensional deformation resulting from crack growth in rock
TL;DR: In this paper, the authors derived a specific internal state variable constitutive law relating uniaxial stress to crack density and crack propagation rate, which is based on the instantaneous crack extension force.
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.