Energy bounds for polycrystalline shape memory alloys

Abstract
In polycrystalline shape memory alloys at equilibrium under a prescribed loading, one typically observes the formation of austenite/martensite microstructures in each grain. The prediction of the resulting effective energy is a difficult question that still remains largely open. A related problem is the prediction of the set of recoverable (or zero-energy) strains of polycrystals. This article presents some recents results that have been achieved in that field, contrasting the geometrically linear theory (’infinitesimal strains’) with the geometrically nonlinear theory (’finite strains’).