Analysis of a Moving Mask Hypothesis for Martensitic Transformations

Abstract

In this work we introduce a moving mask hypothesis to describe the dynamics of austenite-to-martensite phase transitions at a continuum level. In this framework, we prove a new type of Hadamard jump condition, from which we deduce that the deformation gradient $\nabla \mathbf {y}$ must satisfy the differential constraint ${{\,\mathrm{\mathsf {cof}}\,}}(\nabla \mathbf {y} -\mathsf {1}) = \mathsf {0}$ a.e. in the martensite phase. This provides a selection mechanism for physically relevant energy-minimizing microstructures and is useful to better understand the complex microstructures and the formation of curved interfaces between phases in new ultra-low hysteresis alloys such as Zn₄₅Au₃₀Cu₂₅. In particular, we use the new type of Hadamard jump condition to deduce a rigidity theorem for the two-well problem. The latter provides more insight on the cofactor conditions, particular conditions of supercompatibility between phases believed to influence reversibility of martensitic transformations.