Uniqueness and stability of the simply laminated microstructure for martensitic crystals that undergo a cubic to orthorhombic phase transformation
Kaushik Bhattacharya, Bo Li, Mitchell Luskin · 1998
. We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic to orthorhombic transformation of type P (432) ! P (222) 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 fixed simple laminate. We first 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 finite element approximation to obtain the corresponding error estimates for the finite element energy minimizers. 1. Introduction One of the most frequently observed microstructures of a martensitic crystal is a fine-scale twin or a simple laminate which is an arra...