Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures

Thilo M. Simon

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arXiv · 1801.01338

Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures

Thilo M. Simon

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Abstract

We quantify the rigidity of branching microstructures in shape memory alloys undergoing cubic-to-tetragonal transformations in the geometrically linearized theory by making use of Tartar's H-measures. The main result is a $B^{2/3}_{1,\infty}$-estimate for the characteristic functions of twins, which heuristically suggests that the larger-scale interfaces can cluster on a set of Hausdorff-dimension $3-\frac{2}{3}$. We provide evidence indicating that the dimension is optimal. Furthermore, we get an essentially local lower bound for the blow-up behavior of the limiting energy density close to a habit plane.

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Thilo M. Simon. 2018-01-04. Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures. https://arxiv.org/abs/1801.01338

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