Building on the work in \cite{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 \cite{BCH15,CH18,TIVP17} we include \emph{mechanical compatibility}. The mechanical compatibility here is guaranteed by using \emph{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 \cite{BCH15,CH18,TIVP17}.
Cite
@article{arxiv.2008.00416,
title = {On a probabilistic model for martensitic avalanches incorporating mechanical compatibility},
author = {Francesco Della Porta and Angkana Rüland and Jamie M Taylor and Christian Zillinger},
journal= {arXiv preprint arXiv:2008.00416},
year = {2021}
}