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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Book ChapterDOI
Molecular Approaches for Multifield Continua: origins and current developments
TL;DR: In this paper, the authors focus on multiscale approaches which aim to deduce properties and relations at a given macroscale by bridging information at proper underlying microlevel via energy equivalence criteria.
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A constitutive model for shape memory polymers with application to torsion of prismatic bars
TL;DR: In this article, a 3D constitutive model for shape memory polymers is presented, which is based on an additive decomposition of the strain into four p-means.
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Lattice defect approach to plasticity and viscoplasticity
E. Kröner,C. Teodosiu +1 more
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Characterisation of a polymer using biaxial tension tests. Part I: Hyperelasticity
Michael Johlitz,Stefan Diebels +1 more
TL;DR: The focus of the work lies on the detailed description of a new experimental set-up and the adaptation of the material model and the performance of models fitted to experimental data of uniaxial tests is compared to the adjustment of the models to data from biaXial tests.
Journal ArticleDOI
A simple theory of plasticity
TL;DR: In this paper, an internal variable model of rate-independent plastic behavior based on loading-unloading irreversibility is proposed, which assumes no yield or loading function, stability postulate or specific nature of the internal variables.
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.