On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Building on the work in [BCH15, CH18, TIVP17], in this article we propose and study a simple, geometrically constrained, probabilistic algorithm geared towards capturing some aspects of the nucleation in shape-memory alloys. As a main novelty with respect to the algorithms in [BCH15, CH18, TIVP17] we include mechanical compatibility. The mechanical compatibility here is guaranteed by using convex integration building blocks in the nucleation steps. We analytically investigate the algorithm’s convergence and the solutions’ regularity, viewing the latter as a measure for the fractality of the resulting microstructure. We complement our analysis with a numerical implemenation of the scheme and compare it to the numerical results in [BCH15, CH18, TIVP17].