The simply laminated microstructure in martensitic crystals that undergo acubic-to-orthorhombic phase transformation

We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic-to-orthorhombic transformation of type. P-(432) --> P -(222)' The free energy density modeling such a crystal is minimized on six energy wells that art: pairwise rank-one connected, We consider the energy minimization problem with Dirichlet boundary data compatible with an arbit rary but fixed simple laminate. We first show that for all but a few isolat ed values of transformation strains, this problem has a unique Young measur e solution solely characterized:by the boundary data that represents the si mply laminated microstructure. We then present-a theory of stability for su ch a microstructure, and apply it to the conforming finite element approxim ation to obtain the corresponding error estimates for the finite:element en ergy minimizers.