Uniqueness and Stability of the Simply Laminated Microstructure for Martensitic Crystals That Undergo a Cubic to Orthorhombic Phase Transformation

We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic to orthorhombic transformation of type P ! P 0 . The free energy density modeling such a crystal is minimized on six energy wells that are pairwise rank-one connected. We consider the energy minimization problem with Dirichlet boundary data compatible with an arbitrary but xed simple laminate. We rst show that for all but a few isolated values of transformation strains, this problem has a unique Young measure solution that represents the simply laminated microstructure solely characterized by the boundary data. We then present a theory of stability for such a microstructure, and apply it to the conforming nite element approximation to obtain the corresponding error estimates for the nite element energy minimizers.