DMS-9501433 Truskinovsky For solid materials undergoing martensitic phase transformations, the system of conservation laws is of the mixed type. It has recently become clear that additional constitutive information is required to close this system of equations and to describe phenomena like nucleation, kinetics of phase boundaries, reconnection of phase boundaries and formation of finite scale microstructures. We propose three alternative ways to regularize the classical elastodynamics for materials supporting seteral phases in order to derive rather than postulate the missing conditions. The regularization involves high derivatives, additional variables and/ or consideration of discrete system. Large strains observed in smart materials are produced by the coordinated migration of the glissile interfaces in processes such as martensitic phase transformations, deformation twinning or electromagnetic domain switching. A knowledge of the evolution of the mobile microstructure, and the way in which it can influence macroscopic properties, forms the basis of any attempt to control mechanical properties through materials selection and metallurgical processing. We address the foremost open problem which concerns the history and rate sensitivity in the constitutive structure for smart materials through the description of the internal structure of the dissipative phase boundaries.
