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 B1,∞2/3-estimate for the characteristic functions of twins, which heuristically suggests that the larger-scale interfaces can cluster on a set of Hausdorff-dimension 3−32. 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.
@article{arxiv.1801.01338,
title = {Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures},
author = {Thilo M. Simon},
journal= {arXiv preprint arXiv:1801.01338},
year = {2018}
}