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
Phenomenological model for the macroscopical material behavior of ferroelectric ceramics
TL;DR: In this paper, a thermodynamically consistent phenomenological model for the simulation of the macroscopic behavior of ferroelectric polycrystalline ceramics is presented, based on the choice of microscopically motivated internal state variables, which describe the texture and the polarization state of the polycrystal.
Journal ArticleDOI
Permanent set and stress-softening constitutive equation applied to rubber-like materials and soft tissues
Marie Rebouah,Grégory Chagnon +1 more
TL;DR: In this paper, a new constitutive equation is proposed to describe the Mullins effect in an intially isotropic material based on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers.
Journal ArticleDOI
Formulation of a nonlinear porosity law for fully saturated porous media at finite strains
TL;DR: In this article, a mathematical formulation of a nonlinear porosity law suitable for finite strain and high pore pressure conditions in porous media has been developed, which is built around the physical restriction that, by definition, the actual porosity is bounded in the interval [0, 1] for any admissible process.
Journal ArticleDOI
Magneto-diffusion-viscohyperelasticity for magneto-active hydrogels: Rate dependences across time scales
TL;DR: In this paper, the authors proposed a general continuum framework to couple magnetics, solvent diffusion and nonlinear mechanics, which is specialised to and implemented within the finite element method for 3D problems.
Journal ArticleDOI
A constitutive model for ice as a damaging visco-elastic material
TL;DR: In this article, a general three dimensional theory is proposed for describing constitutive properties for ice as a viscoelastic brittle material, where the elastic and viscous properties of ice are assumed to be initially orthotropic.
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.