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
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Book
Viscoplastic Model Development to Account for Strength Differential: Application to Aged Inconel 718 at Elevated Temperature
Saiganesh K. Iyer,Brad Lerch +1 more
TL;DR: In this paper, a unified viscoplastic model was developed that is able to account for the strength differential (SD) effect in aged Inconel 718 using both theory and experiments.
Journal ArticleDOI
A constitutive formulation and numerical procedure to model rate effects on porous materials at finite strains
TL;DR: In this paper, a constitutive formulation for viscoplastic porous materials subjected to finite deformations is developed, which is implemented inside the Finite Element Method context and numerically assessed by the analysis of some classical examples, such as the isostatic compression, simple shear, and die pressing testing.
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Higher Order Thermo-mechanical Gradient Plasticity Model: Non-proportional Loading with Energetic and Dissipative Components
George Z. Voyiadjis,Yooseob Song +1 more
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An enhanced concept of rheological models to represent nonlinear thermoviscoplasticity and its energy storage behavior, part 2: spatial generalization for small strains
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TL;DR: In this paper, the spatial formulation of the enhanced concept of rheological models is provided for small deformations and the graphical representation of the Rheological network for three-dimensional material behavior.
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Dependence of instability strain upon damage in thermoviscoplastic materials
TL;DR: In this paper, the authors derived the instability strain in a thermoviscoplastic body deformed in simple shear and simultaneously subjected to a uniform hydrostatic tensile stress.
References
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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.
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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.