Approximation of Martensitic Microstructure with General Homogeneous Boundary Data

We consider the approximation of martensitic microstructure for a class of martensitic transformations. We model such microstructures by multi-well energy minimization problems with general homogeneous boundary data. Under our assumptions on such boundary data, the underlying microstructure can be nonunique. We first show that any energy-minimizing sequence converges strongly to a unique macroscopic deformation that is precisely the homogeneous deformation in the boundary condition. We then prove a series of estimates for the approximation of admissible deformations to the unique macroscopic deformation of the microstructure and for the closeness of the gradients of admissible deformations to the energy wells.