  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.
