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
Viscosity and Relaxation Approximation for Hyperbolic Systems of Conservation Laws
TL;DR: These lecture notes deal with the approximation of conservation laws via viscosity or relaxation, and the following topics are covered.
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Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration
Antonio Orlando,Djordje Perić +1 more
TL;DR: In this paper, the authors illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate-independent plasticity problems solved by employing the incremental displacement conforming finite element method.
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Robust integration schemes for generalized viscoplasticity with internal-state variables
Atef F. Saleeb,T. E. Wilt,W. Li +2 more
TL;DR: In this article, the implicit time-stepping integrators for the flow and evolution equations in complex viscoplastic models were developed for both initially isotropic and anisotropic materials, in threedimensions as well as subspace applications.
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Application of the concept of evolving structure tensors to the modeling of initial and induced anisotropy at large deformation
TL;DR: In this article, a thermodynamic approach to the modeling and simulation of induced elastic and inelastic material behaviour in the phenomenological realm as based on the concept of evolving structure tensors is discussed.
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Thermomechanical response of non-local porous material
TL;DR: In this paper, a thermomechanical model of a porous material is presented, based on the Gurson model, formulated within a thermodynamic framework and adapted to large deformations.
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.