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
Thermo-mechanically coupled model of diffusionless phase transformation in austenitic steel
TL;DR: In this paper, a constitutive model of thermo-mechanically coupled finite strain plasticity considering martensitic phase transformation is presented, where the model is formulated within a thermodynamic framework, giving a physically sound format where the thermodynamic mechanical and chemical forces that drive the phase transformation are conveniently identifiable.
Journal ArticleDOI
Viscoplasticity model at finite deformations with combined isotropic and kinematic hardening
TL;DR: In this paper, a phenomenological constitutive model of viscoplasticity at finite strains is presented, which generalizes the classical Perzyna or Duvaut-Lions models to finite strains.
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Il secondo suono nei cristalli : termodinamica ed equazioni costitutive
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Journal ArticleDOI
Thermoviscoplasticity by finite element: Tensile and compression test
H. Ghoneim,S. Matsuoka +1 more
TL;DR: In this paper, coupled thermoviscoplasticity equations are developed based on the rational theory of thermodynamics for solving the adiabatic uniaxial tensile and compression tests of Inconel 100 at an elevated temperature (1000K).
Journal ArticleDOI
Precipitate growth in multi-component systems with stress relaxation by diffusion and creep
TL;DR: In this paper, the authors studied the growth of spherical precipitates having a volumetric misfit and derived the evolution equations for the state variables (e.g., precipitate radius, chemical composition of the precipitate).
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.