1201.6679 (Isaac Vikram Chenchiah et al.)

Non-laminate Microstructures in Monoclinic-I Martensite    [PDF]

Isaac Vikram Chenchiah, Anja Schlömerkemper

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.

View original: http://arxiv.org/abs/1201.6679