Non-laminate Microstructures in Monoclinic-I Martensite

TL;DR

This paper investigates the complex convex hull structures of monoclinic-I martensite strains, revealing new geometric properties and predicting a novel variant with different semi-convex hulls not yet observed experimentally.

Contribution

It constructs explicit symmetrised rank-one convex hulls and T3 sets for monoclinic-I martensite, and predicts a new martensitic variant with unique convex hull characteristics.

Findings

Constructed sets of T3s for monoclinic-I martensite.

Identified a five-dimensional continuum of T3s.

Predicted a new martensite variant with different semi-convex hulls.

Abstract

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 T3s, which are (non-trivial) symmetrised rank-one convex hulls of three-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. We also 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.