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arXiv · 2008.00416

On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Francesco Della Porta·Angkana Rüland·Jamie M Taylor·Christian Zillinger
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Abstract

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}.

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Francesco Della Porta, Angkana Rüland, Jamie M Taylor, Christian Zillinger. 2020-08-02. On a probabilistic model for martensitic avalanches incorporating mechanical compatibility. https://doi.org/10.1088/1361-6544/abfca9

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