A Multi-phase Transition Model for Dislocations with Interfacial Microstructure

We study, by means of Γ-convergence, the asymptotic behavior of a variational model for dislocations moving on a slip plane. The variational problem is a two-dimensional multi-phase transition-type energy given by a nonlocal term and a nonlinear potential which penalizes noninteger values for the components of the phase. In the limit we obtain an anisotropic sharp interfaces model. The relevant feature of this problem is that optimal sequences in general are not given by a one dimensional profile, but they can create microstructure.