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
An internal variable theory of elastoplasticity based on the maximum plastic work inequality
TL;DR: In this paper, convex analysis is used to explore in greater depth the nature of the evolution equation in internal variable formulations of elastoplasticity, where the thermodynamic force belongs to a set defined by a multi-valued map G.
Journal ArticleDOI
Continuum modelling of damage in ceramic matrix composites
TL;DR: In this article, a continuum model for determining the mechanical response of unidirectionally fiber-reinforced ceramic matrix composites with damage is presented, where cracks, debonds and slipped surfaces are represented by second-order tensors which are regarded as internal variables.
Journal ArticleDOI
An elasto-plastic theory of dislocation and disclination fields
TL;DR: In this paper, a linear theory of the elasto-plasticity of crystalline solids based on a continuous representation of crystal defects is presented, which accounts for the translational and rotational aspects of lattice incompatibility associated with the presence of dislocations and disclinations.
Journal ArticleDOI
Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media
TL;DR: In this article, a general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws into a standard phase field model and two mixture rules for strain and stress are introduced, which are based on the Voigt/Taylor and Reuss/Sachs well-known homogenization schemes.
Journal ArticleDOI
Data-Driven multiscale modeling in mechanics
TL;DR: A proposed Data-Driven framework for multiscale mechanical analysis of materials is demonstrated, able to predict the material response under complex nonmonotonic loading paths, and compares well against plane strain and triaxial compression shear banding experiments.
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.