Non-laminate Microstructures in Monoclinic-I Martensite

We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T (3)s, which are (non-trivial) symmetrised rank-one convex hulls of three-tuples of pairwise incompatible strains. In addition, we construct a fivedimensional continuum of T (3)s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional.We also show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, as far as we know, has not been experimentally observed. Our strategy is to combine understanding of the algebraic structure of symmetrised rank-one convex cones with knowledge of the faceting structure of the convex polytope formed by the strains.