On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

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