Derivation and study of dynamical models of dislocation densities

Ahmad El Hajj (1) , H. Ibrahim (2) , Régis Monneau (3)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

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.

Mots clés: dynamics of dislocation densities; Cauchy's problem; non-linear transport equations; non-local transport equations; hyperbolic equations; BMO estimate; dynamics of dislocation densities.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Ahmad El Hajj, H. Ibrahim, Régis Monneau. Derivation and study of dynamical models of dislocation densities. 2009. ⟨hal-00353621⟩