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
Predictions of the solubility of gases in glassy polymers based on the NELF model
TL;DR: In this paper, a reliable, predictive model for the solubility of gases and vapours in glassy polymers has been presented: it is based on the free energy expression for the polymer penetrant mixture as obtained from the lattice fluid theory and on the idea that the partial polymer density is an internal state variable for the system.
Journal ArticleDOI
Modeling of anisotropic softening phenomena: Application to soft biological tissues
TL;DR: In this paper, a thermodynamically consistent dissipative model is proposed to describe softening phenomena in anisotropic materials, based on a generalized polyconvex aisotropic strain energy function represented by a series.
Journal ArticleDOI
Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics
Simone Rossi,Simone Rossi,Toni Lassila,Ricardo Ruiz-Baier,Adélia Sequeira,Alfio Quarteroni,Alfio Quarteroni +6 more
TL;DR: In this article, the authors derived an evolution equation for the active fiber contraction based on configurational forces, which is thermodynamically consistent. And they linked microscopic and macroscopic deformations giving rise to an orthotropic contraction mechanism that is able to represent physiologically correct thickening of the ventricular wall.
Journal ArticleDOI
On finite linear viscoelasticity of incompressible isotropic materials
TL;DR: In this paper, the authors present two natural possibilities to generalise the familiar Maxwell-model to finite strains; both tensor-valued differential equations are integrated to yield the present Cauchy stress as a functional of the relative Piola or Green strain history.
Journal ArticleDOI
Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects
TL;DR: A framework for continuum elastoplastic-damage modelling, which employs irreversible thermodynamics and internal state variables, is investigated and the development of an algorithm consistent with the present formulation is given where, for the plastic part, it leaves the standard return mapping algorithms unchanged.
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.