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On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Della Porta, Francesco; Rüland, Angkana; Taylor, Jamie M.; Zillinger, Christian

Abstract:
Building on the work in [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 [BCH15, CH18, TIVP17] 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 implemenation of the scheme and compare it to the numerical results in [BCH15, CH18, TIVP17].

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Volltext §
DOI: 10.5445/IR/1000125687
Veröffentlicht am 05.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 10.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000125687
Verlag KIT, Karlsruhe
Umfang 43 S.
Serie CRC 1173 Preprint ; 2020/31
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter convex integration, higher Sobolev regularity, solid-solid phase transformation, avalanches, nucelation
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