Journal ArticleDOI
Thermodynamics with Internal State Variables
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
Models for one-variant shape memory materials based on dissipation functions
TL;DR: In this article, simple models for the macroscopic behavior of shape memory materials whose microstructure can be described as a mixture of two phases are derived on the basis of a free energy and a dissipation function.
Journal ArticleDOI
A phenomenological theory of transformation superplasticity
K. Tanaka,R. Iwasaki +1 more
TL;DR: In this paper, a phenomenological theory of transformation superplasticity is presented from the point of view of thermomechanics, where the stretching tensor and entropy density are decomposed into the elastic part and the part due to the super-plastic process.
Journal ArticleDOI
A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation
TL;DR: In this paper, a finite element (FE) procedure is developed and implemented in an FE code, based on the proposed constitutive equations, which is used to predict the response of elastomer bushings.
Book ChapterDOI
Internal Variables in Non-Equilibrium Thermodynamics
TL;DR: The concept of internal variables is axiomatically introduced into nonequilibrium thermodynamics for avoiding small state spaces showing after effects as mentioned in this paper, and the connection between internal variables, projectors onto equilibrium subspace, and accompanying processes is demonstrated for discrete systems.
References
More filters
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.