29 citations · 40 across the 5 of their papers we have counts for
5 papers
Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics
Diana Al Zareef, Ahmad El Hajj, Hassan Ibrahim +1
In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimat…
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…
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,…
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…
Derivation and study of dynamical models of dislocation densities
Ahmad El Hajj, H. Ibrahim, Régis Monneau
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. Essen…