Numerical and analytical aspects of the pinning of martensitic phase boundaries

Abstract

AbstractWe study the pinning and depinning behavior of interfaces immersed in a heterogeneous medium. For a continuum elasticicity model of the martensitic phase transformation, we numerically estimate the critical depinning stress of a phase boundary intersecting a non‐transforming inclusion in the material. In the limit of a nearly flat phase boundary, the elastic energy of the phase boundary can be approximated by an elliptic operator of order 1. For such an approximation we study the depinning transition near the critical point. Finally, we prove existence of a pinned solution for a parabolic model for the evolution of phase boundaries in a random environment (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)