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 thermomechanical model for the analysis of light alloy solidification in a composite mould
TL;DR: In this article, a coupled thermomechanical model to simulate light alloy solidification problems in permanent composite moulds is presented, which is based on a general isotropic thermo-elasto-plasticity theory and considers the different thermomic behaviours of each component of the mould as well as those of the solidifying material during its evolution from liquid to solid.
Journal ArticleDOI
Large elasto-plastic deformations of materials with relaxed configurations. I: Constitutive assumptions
TL;DR: In this article, an axiomatic characterization of the thermoelastoviscoplastic behavior of materials, experimentally motivated and based on the concept of local current relaxed configuration (l.c.).
Journal ArticleDOI
Fatigue damage model of concrete materials
TL;DR: Based on the continuum damage mechanics theory of concrete materials under fatigue loading, a phenomenological fatigue damage model due to nuclei-propagation of microdefects, microvoids and fractal of rendered concrete in conjunction with more compliant are developed by utilizing internal variable theory of thermodynamics as discussed by the authors.
Journal ArticleDOI
Formulation and Verification of a Concrete Model with Strong Coupling between Isotropic Damage and Elastoplasticity and Comparison to a Weak Coupling Model
TL;DR: In this paper, a new concrete model that strongly couples continuum-damage-mechanics to elastoplasticity is presented, which incorporates a plasticity yield criterion written in terms of the nominal/damaged, rather than effective, stress space.
Journal ArticleDOI
Phase-field modeling of electromechanical fracture in piezoelectric solids: Analytical results and numerical simulations
Jian-Ying Wu,Wan-Xin Chen +1 more
TL;DR: In this paper, a length scale insensitive phase-field cohesive zone model (PF-CZM) was proposed for brittle fracture in linear piezoelectric solids, overcoming all the issues of mesh dependence, crack tracking complexity, length scale sensitivity and crack nucleation inconsistency.
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.