  In this work we introduce a moving mask approximation 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 must be of the form $\mathsf{1}
+\mathbf{a}\otimes \mathbf{n}$ a.e. in the martensite phase. This 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, and provides a selection mechanism for physically-relevant
energy-minimising microstructures. 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.
