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
Modelling of a Cellular Rubber with Nonlinear Viscosity Functions
TL;DR: In this paper, a porous carbon black-filled rubber is investigated under uniaxial tension and the main focus of attention lies on the Mullins effect, the thixotropic and the viscoelastic behaviour.
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Non-stationary thermodynamics and wave propagation in heat conducting viscous fluids
TL;DR: In this paper, the behaviour of heat conducting viscous fluids is described through a suitable set of hidden variables whose (objective) evolution equations account also for cross-effect coupling terms.
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Formation of the internal structure of solids under severe load.
TL;DR: An alternative form of kinetic equations, involving the internal and free energies symmetrically, has been derived in the framework of the theory of vacancies, illustrated by simulation of processes during severe plastic deformation.
Journal ArticleDOI
Kinematics, electromechanics, and kinetics of dielectric and piezoelectric crystals with lattice defects
TL;DR: In this paper, a mathematical framework is formulated to address the electromechanical behavior of dielectric and piezoelectric solids containing lattice imperfections, and a free energy function dependent upon lattice distortion, polarization, temperature, and defect densities is suggested.
Journal ArticleDOI
A field boundary element formulation for material nonlinear problems at finite strains
A. Foerster,G. Kuhn +1 more
TL;DR: In this article, a boundary element formulation for geometrical nonlinear problems is presented, which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration.
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.