Pinning and depinning behavior of martensitic phase boundaries in a heterogeneous environment

We study the role of defect in the quasistatic evolution of martensitic phase boundaries. This transformation involves a change in shape of the underlying crystal. Therefore, the propagation of the phase boundary is accompanied by an evolving mechanical stress and strain field. We derive, in the sense of Gamma-convergence, an approximate model for a shallow slope phase boundary. We show that, in this quasilinear approximation, the evolution reduces to a one- dimensional problem that exhibits stick-slip behavior, and thus gives rise to hysteresis. We also present numerical simulations of the de- pinning transition showing a power-law behavior in the average velocity.