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
Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
TL;DR: In this paper, a formulation and algorithmic treatment of static and dynamic plasticity at finite strains based on the multiplicative decomposition is presented which inherits all the features of the classical models of infinitesimal plasticity.
Journal ArticleDOI
Associated coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation
Juan C. Simo,C. Miehe +1 more
TL;DR: In this paper, a complete formulation of a model of coupled associative thermoplasticity at finite strains is presented, addressing in detail the numerical analysis aspects involved in its finite element implementation, and assessing the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations.
Journal ArticleDOI
A theory of finite viscoelasticity and numerical aspects
Stefanie Reese,Sanjay Govindjee +1 more
TL;DR: In this article, a nonlinear evolution law for finite deformation viscoelasticity was proposed, which is not restricted to states close to the thermodynamic equilibrium, and upon appropriate linearization, it can recover several established models of finite linear viscoels and linear velocities.
Journal ArticleDOI
A constitutive theory for the inelastic behavior of concrete
TL;DR: In this paper, a general theory for the inelasticity of concrete is proposed, the main constituents being a new, rate independent model of distributed damage for mortar and the application of mixture theories to account for the composite nature of concrete.
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.