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Internal Variables and Generalized Continuum Theories

Berezovski, Arkadi / Engelbrecht, Jüri / Maugin, Gérard A.

Abstract The canonical thermomechanics on the material manifold is enriched by the introduction of dual weakly non-local internal variables and extra entropy fluxes. In addition to the dissipative reaction-diffusion equation for a single internal variable of state, a hyperbolic evolution equation for the internal degree of freedom can be also recovered in the non-dissipative case. It is demonstrated that the Mindlin mi-cromorphic theory can be represented in terms of dual internal variables in a natural way in the framework of the canonical thermomechanics.

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Internal Variables and Generalized Continuum Theories

Berezovski, Arkadi / Engelbrecht, Jüri / Maugin, Gérard A.

Abstract The canonical thermomechanics on the material manifold is enriched by the introduction of dual weakly non-local internal variables and extra entropy fluxes. In addition to the dissipative reaction-diffusion equation for a single internal variable of state, a hyperbolic evolution equation for the internal degree of freedom can be also recovered in the non-dissipative case. It is demonstrated that the Mindlin mi-cromorphic theory can be represented in terms of dual internal variables in a natural way in the framework of the canonical thermomechanics.

Internal Variables and Generalized Continuum Theories

Berezovski, Arkadi / Engelbrecht, Jüri / Maugin, Gérard A.

Abstract The canonical thermomechanics on the material manifold is enriched by the introduction of dual weakly non-local internal variables and extra entropy fluxes. In addition to the dissipative reaction-diffusion equation for a single internal variable of state, a hyperbolic evolution equation for the internal degree of freedom can be also recovered in the non-dissipative case. It is demonstrated that the Mindlin mi-cromorphic theory can be represented in terms of dual internal variables in a natural way in the framework of the canonical thermomechanics.

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Title:

Internal Variables and Generalized Continuum Theories

Contributors:

Berezovski, Arkadi (author) / Engelbrecht, Jüri (author) / Maugin, Gérard A. (author)

Published in:

IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics ; 149-158

IUTAM Bookseries ; 17

Publication date:

2009-01-01

Size:

10 pages

ISBN:

978-90-481-3447-2 , 978-90-481-3446-5

ISSN:

DOI:

https://doi.org/10.1007/978-90-481-3447-2_14

Type of media:

Article/Chapter (Book)

Type of material:

Electronic Resource

Language:

English

Keywords:

Internal Variable , Internal Degree , Dissipation Inequality , Mindlin Theory , Material Manifold Physics , Numerical and Computational Physics , Mechanics , Thermodynamics , Computational Intelligence , Theoretical and Applied Mechanics , Continuum Mechanics and Mechanics of Materials

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