Non-laminate Microstructures in Monoclinic-I Martensite

Details Non-laminate Microstructures in Monoclinic-I Martensite Non-laminate Microstructures in Monoclinic-I Martensite

2012-01-31

arxiv.org/abs/1201.6679v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We show that this hull is strictly larger than the symmetrised lamination convex hull by constructing sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of 3-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. Along the way we show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, so 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.

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