Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

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 study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale.

Domaines: Equations aux dérivées partielles [math.AP]

Ahmad El Hajj, Hassan Ibrahim, Régis Monneau. Dislocation dynamics: from microscopic models to macroscopic crystal plasticity. 2009. ⟨hal-00349568⟩