Stress-free strains in martensitic microstructures

The peculiar properties of shape-memory alloys are the result of a solid/solid phase transformation between different crystallographic structures (austenite and martensite). This paper is concerned with the theoretical prediction of the set of strains that minimize the effective (or macroscopic) energy. Those strains, classically refered to as recoverable strains, play a central role in the shape memory effect displayed by alloys such as NiTi or CuAlNi. They correspond to macroscopic strains that can be achieved in stress-free states. Adopting the framework of nonlinear elasticity, the theoretical prediction of stress-free strains amounts to find the austenite/martensite microstructures which minimize the global energy. Closed-form solutions to that problem have been obtained only in few special cases. This paper aims at complementing existing results on that problem, essentially by deriving bounds on the set of stress-free strains.