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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DissertationDOI
A hybridizable discontinuous Galerkin method for nonlinear porous media viscoelasticity with applications in ophthalmology
TL;DR: The model is used to theoretically investigate the influence of tissue viscoelasticity on the blood perfusion of the lamina cribrosa in the ONH, and suggests that changes in viscoels may compromise tissue perfusion in response to sudden variations of intraocular pressure, possibly leading to optic disc hemorrhages.
Journal ArticleDOI
From the thermodynamics of constitutive laws to the thermomechanical experimental characterization of a semicrystalline polymer from IR imaging
TL;DR: In this paper, the authors present a model based on irreversible thermodynamics that allows straightforward formulation of the set of the required state laws, which leads to the heat equation allowing for the identification of the different contributions involved in the apparent Thermomechanical Heat Source (THS).
Journal ArticleDOI
Shock-wave structure according to a linear irreversible thermodynamic model.
TL;DR: A phenomenological model is presented to look for a better understanding of the shock-wave structure in dilute monatomic gases and a new coupling appears between the stress tensor and the heat flux.
Modellierung und Simulation der Aushärtung polymerer Werkstoffe
TL;DR: In this paper, a general material model for the simulation of curing processes in different polymers is developed, which is formulated within the framework of nonlinear continuum mechanics and thus is applicable for materials at large deformations.
Journal ArticleDOI
Deformation induced elasto-plastic anisotropy in metal foams – modelling and simulation
TL;DR: In this paper, the authors define, analyse and quantify the elastic and plastic anisotropy that develops after some deformation history involving finite (plastic) strains in a two-dimensional cellular material.
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.