A non-convex lower bound on the effective energy of polycrystalline shape memory alloys

This paper addresses the estimation of the effective free energy of polycrystalline shape memory alloys, in the framework of nonlinear elasticity and infinitesimal strains. The translation method is combined with a Hashin–Shtrikman type variational formulation to provide rigorous lower bounds on the effective free energy. Those bounds incorporate both intra-grain compatibility conditions (resulting in a non-convex bound) and inter-grain constraints (by taking one- and two-point statistics into account). Some examples are given to compare the results obtained with other bounds from the literature.