29 citations · 40 across the 5 of their papers we have counts for
Showing math.APShow all
3 papers · 1 filter
math.AP2009★ 4 cited
Homogenization of dislocation dynamics
A. El Hajj, H. Ibrahim, R. Monneau
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 t…
math.AP2009★ 29 cited
Dislocation dynamics: from microscopic models to macroscopic crystal plasticity
A. El Hajj, H. Ibrahim, R. Monneau
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,…
math.AP2009★ 7 cited
Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system
H. Ibrahim, M. Jazar, R. Monneau
We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the sol…