Energy minimizing strains in martensitic microstructures

This communication is concerned with the theoretical prediction of the energy-minimizing (or stress-free) strains that can be realized by martensitic microstructures. Polyconvexification and related notions are used to derive some upper bounds (in the sense of inclusion) on the set of energy-minimizing strains. Lower bounds are obtained from lamination techniques. Three-, four-, and twelve-well problems are considered. In particular, the structure of the set of energy-minimizing strains in cubic to monoclinic transformations is investigated in detail.