Homogenization of dislocation dynamics

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

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight dislocations and ii) the general case of curved dislocations. In each case, we perform rigorously the homogenization of the dynamics and predict the corresponding effective macroscopic elasto-visco-plastic flow rule.

Domaines: Equations aux dérivées partielles [math.AP]

Ahmad El Hajj, Hassan Ibrahim, Régis Monneau. Homogenization of dislocation dynamics. 2009. ⟨hal-00349567⟩