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
Some comments on formulations of anisotropic plasticity
TL;DR: In this article, the authors compare some recently proposed formulations of phenomenological plasticity in regard to the underlying assumptions about the elastic behaviour and the formulation of the associated flow rule. And they show that the use of the logarithmic stress rate in a Eulerian formulation is inconsistent with the Hill and Rice notion of normality.
Book ChapterDOI
Micromechanical Basis of Phenomenological Models
TL;DR: In this article, the authors show that the majority of the existing models have a common base which can be readily derived from the micromechanical considerations, and that these models are applicable only in special cases (isotropic, orthotropic, etc.) of microcrack distribution.
Journal ArticleDOI
Thermodynamic influences on acceleration waves in inhomogeneous isotropic elastic bodies with internal state variables
Ray M. Bowen,C. C. Wang +1 more
TL;DR: In this paper, the authors studied thermal properties effects on transverse acceleration wave propagation in inhomogeneous isotropic elastic bodies with internal state variables, and showed that the effects of thermal properties on the propagation of acceleration wave propagate with respect to the internal states of the elastic body.
Journal ArticleDOI
Three-Dimensional Viscoelastic Model with Nonconstant Coefficients
TL;DR: In this paper, a 3D viscoelastic model is presented to predict the creep and relaxation behavior of anisotropic materials based on a phenomenological approach using internal variables and is applicable to nonconstant coefficients.
Journal ArticleDOI
On the equivalence between the multiplicative hyper-elasto-plasticity and the additive hypo-elasto-plasticity based on the modified kinetic logarithmic stress rate
Yang Jiao,Jacob Fish +1 more
TL;DR: In this paper, it was shown that for isotropic materials, hyper-elasto-plasticity models based on the multiplicative decomposition of the deformation gradient coincide with an additive hypo-elasticity model (see Section 3.2) that employs the spin tensor based on modified kinetic logarithmic rate.
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.