Geodesic
Derivation and study of dynamical models of dislocation densities
A. El Hajj1 ; H. Ibrahim2 ; R. Monneau2
1 Université d'Orléans, Laboratoire MAPMO, Route de Chartres, B.P. 6759-45067 Orléans, cedex 2, France
2 Ecole Nationale des Ponts et Chaussées, CERMICS, 6 et 8 avenue Blaise Pascal Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France
ESAIM. Proceedings, Tome 27 (2009), pp. 311-321.

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In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the equations of elasticity. Rigorous results of existence of solutions are presented for some of these models and the main ideas of the proofs are given.

DOI : 10.1051/proc/2009029

A. El Hajj 1 ; H. Ibrahim 2 ; R. Monneau 2

1 Université d'Orléans, Laboratoire MAPMO, Route de Chartres, B.P. 6759-45067 Orléans, cedex 2, France
2 Ecole Nationale des Ponts et Chaussées, CERMICS, 6 et 8 avenue Blaise Pascal Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France 
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A. El Hajj; H. Ibrahim; R. Monneau. Derivation and study of dynamical models of dislocation densities. ESAIM. Proceedings, Tome 27 (2009), pp. 311-321. doi : 10.1051/proc/2009029. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009029/

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