Stability of microstructure for tetragonal to monoclinic martensitic transformations

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transfor mations. The energy density for tetragonal to monoclinic transformations ha s four rotationally invariant wells since the transformation has four varia nts. One of these tetragonal to monoclinic martensitic transformations corr esponds to the shearing of the rectangular side, one corresponds to the she aring of the square base, and one corresponds to the shearing of the plane orthogonal to a diagonal in the square base. We show that the simply lamina ted microstructure is stable except for a class of special material paramet ers. In each case that the microstructure is stable, we derive error estima tes for the finite element approximation. Mathematics Subject Classificatio n. 49J45, 65N15, 65N30, 73C50, 73G05, 73K20, 73V05.