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ESAIM: Proc., 2009, Vol. 27, pp. 311-321
DOI: 10.1051/proc/2009029
Derivation and study of dynamical models of dislocation densities
A. El Hajj1, H. Ibrahim2 and R. Monneau21 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
Published online: 25 June 2009
Abstract
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.
© EDP Sciences, ESAIM 2009
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