On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv: 1810.04380 ), Torrents et al (2017 Phys. Rev. E 95 013001), 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 by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv: 1810.04380 ), Torrents et al (2017 Phys. Rev. E 95 013001) 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 implementation of the scheme and compare it to the numerical results by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv: 1810.04380 ), Torrents et al (2017 Phys. Rev. E 95 013001).