The dynamics of dislocation densities in a material subjected to a time-periodic stress were considered. The dislocation densities satisfied a set of two coupled first-order equations of Burgers’ type. The main aim was to provide a description of the long-term behaviour of the densities. By using an homogenization procedure within the framework of viscosity solutions, it was deduced that, at the limit, the dislocation densities satisfied a single diffusion equation.

Time-Homogenization of a First Order System Arising in the Modelling of the Dynamics of Dislocation Densities. A.Briani, R.Monneau: Comptes Rendus Mathematique, 2009, 347[5-6], 231-6