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 variational multiscale method to incorporate strain gradients in a phenomenological plasticity model
S. L. Creighton,Richard A. Regueiro,Krishna Garikipati,P. A. Klein,E.B. Marin,Douglas J. Bammann +5 more
TL;DR: In this article, mathematical and computational issues related to the incorporation of strain gradient terms in a phenomenological plasticity model are treated. But they are posed in the setting of a variationally-based multiscale method.
Journal ArticleDOI
Finite thermo-elastic decoupled two-scale analysis
Journal ArticleDOI
Formulation of a macroscale corrosion damage internal state variable model
TL;DR: In this paper, a new consistent formulation coupling kinematics, thermodynamics and kinetics with damage using an extended multiplicative decomposition of the deformation gradient that accounts for corrosion effects is proposed.
DissertationDOI
Mehrskalenmodelle in der Festkörpermechanik und Kopplung von Mehrgittermethoden mit Homogenisierungsverfahren
TL;DR: In this paper, the authors formulate nonlinear homogenized models for micro-heterogeneous materials and the construction of problem dependent transfer operators for multigrid methods, respectively, in order to describe the efficient description of heterogeneous solid structures.
Journal ArticleDOI
A field theory of distortion incompatibility for coupled fracture and plasticity
TL;DR: In this paper, the authors apply the mechanics of dislocation fields to the case of cracks in elastic and elasto-plastic solids through finite element modeling, and show that cracks can be consistently described by the transport scheme.
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.