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
A localized mapped damage model for orthotropic materials
TL;DR: In this article, an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models is proposed to simulate the failure loci of common orthotropic materials, such as masonry, fiber-reinforced composites and wood.
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A constitutive model for amorphous shape memory polymers based on thermodynamics with internal state variables
TL;DR: A thermoviscoelastic finite deformation constitutive model with structural and stress relaxation to capture the material behavior in the vicinity of the glass transition is developed for thermally activated amorphous SMPs in this article.
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A continuum constitutive model for FDM 3D printed thermoplastics
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Journal ArticleDOI
A continuum framework for finite viscoplasticity
Mike Scheidler,Thomas W Wright +1 more
TL;DR: In this article, a continuum framework for finite viscoplasticity based on Lee's multiplicative decomposition with internal variables is developed, which includes a thermodynamically consistent treatment of the storage of cold work and plastic volume change and a careful examination of the restrictions imposed by the entropy inequality.
Journal ArticleDOI
A comparative study of kinematic hardening rules at finite deformations
Ch. Tsakmakis,A. Willuweit +1 more
TL;DR: In this article, three possible extensions, from small to finite deformations, of the Armstrong-Frederick rule, which are derived as sufficient conditions for the validity of the second law are discussed.
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.