Energetics in martensites

Martensitic transformations are shape-deforming phase transitions which can be induced in certain alloys as a result of changes in the imposed strains, stresses or temperatures. The interest in these alloys, which undergo a shape-deforming phase transition form a high temperature phase to a low temperature phase, stems in part from their applicability as elements in active structures. In this paper we focus on the energy transfers that accompany the martensitic phase change. We discuss, in three concrete examples, the ways in which temperature, together with the elastic and dissipated energies, determine the equilibria as well as the quasi-static dynamics in martensites. Thus, in §1 we consider the pseudoelastic hysteresis in shape- memory wires; our treatment draws from (7, 3). In §2, on the other hand, we follow and discuss equilibrium configurations in polycrystalline martensitic polycrystals. In §3, finally, we present some new theoretical computations for certain typical microstructural lengthscales, the twin widths, observed in single- crystalline martensite twinning.