On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
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,TIV...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2 Aug 2020
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| In: |
Arxiv
Year: 2020, Pages: 1-43 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2008.00416
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| Author Notes: | Francesco Della Porta, Angkana Rüland, Jamie M. Taylor, and Christian Zillinger |
| Summary: | 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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| Item Description: | Gesehen am 27.05.2021 |
| Physical Description: | Online Resource |