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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 rankone convex hulls of three-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T 3 s and show that its intersection with the boundary of the symmetrised rank-one convex hull is fourdimensional. 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.

Soil is essential for sustaining life on land. Plant roots play a crucial role in stabilising soil and minimising erosion, although these mechanisms are still not completely understood. Consequently, identifying and breeding for plant traits to enhance erosion resistance is challenging. Root hair mutants in Arabidopsis thaliana were studied using three different quantitative methods to isolate their effect on root-soil cohesion. We present compelling evidence that micro-scale interactions of root hairs with surrounding soil increase soil cohesion and reduce erosion. Arabidopsis seedlings with root hairs were more difficult to detach from soil, compost and sterile gel media than those with hairless roots, and it was 10-times harder to erode soil from roots with than without hairs. We also developed a model that can consistently predict the impact root hairs make to soil erosion resistance. Our study thus provides new insight into the mechanisms by which roots maintain soil stability.

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