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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Elasto-plastic and damage modeling of reinforced concrete
TL;DR: In this paper, the authors present a detailed review of the STEEL MATERIAL MODEL and its application in the context of steel-concrete interfaces and concrete damage mechanics.
Journal ArticleDOI
Deformation behavior of ductile solids containing anisotropic damage
M. Stumvoll,G. Swoboda +1 more
TL;DR: In this paper, the authors considered the propagation of sets of cracks in mode II, where the loading axis does not coincide with the plane of the initial cracks, and derived a constitutive equation and a damage propagation law by means of the thermodynamic principles of irreversible processes.
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A coupled viscoplastic rate-dependent damage model for the simulation of fatigue failure of cement–bone interfaces
TL;DR: In this article, a computational model for bone-cement interfaces was developed to capture the behavior of the interface under static and cyclic mixed-mode loading, incorporating stiffness degradation (damage) and permanent deformation (plasticity).
Journal ArticleDOI
Thermodynamical frameworks for higher grade material theories with internal variables or additional degrees of freedom
C. Papenfuss,Samuel Forest +1 more
TL;DR: In this article, the authors compare several thermomechanical frameworks, taking into account the influence of strain gradient, internal variable, gradient of internal variables, and temperature gradient on the constitutive behavior of materials.
Journal ArticleDOI
A gradient thermodynamic theory of self-organization
TL;DR: In this paper, a gradient theory of internal variables in a thermodynamic context of the Gibbs free energy density o is presented, and a solution to the problem of a flat plate in nominal axial tension and derive various types of deformation patterns that result from small but unavoidable experimental deviations from this loading.
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.