Rigidity of shape memory alloys

For a geometrically linear variational model for a shape memory alloy undergoing cubic-to-tetragonal transformations involving a small non-dimensional parameter we prove a rigidity theorem for generic sequences whose energy is on the order of well-known branching constructions of habit planes. Without assuming any further regularity of their limits, we recover rank-one connectedness of the average strains at macroscopic interfaces between mixtures of martensite variants. The proof proceeds via a non-convex differential inclusion for the limit and exploits a balance of the inclusion and “discontinuity” of the strain: If the strain is less regular, the differential inclusion provides more information.