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On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Della Porta, Francesco; Rüland, Angkana; Taylor, Jamie M.; Zillinger, Christian ORCID iD icon 1
1 Karlsruher Institut für Technologie (KIT)

Abstract:

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. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000136165
Veröffentlicht am 04.08.2021
Originalveröffentlichung
DOI: 10.1088/1361-6544/abfca9
Scopus
Zitationen: 1
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Zitationen: 2
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 07.2021
Sprache Englisch
Identifikator ISSN: 0951-7715, 1361-6544
KITopen-ID: 1000136165
Erschienen in Nonlinearity
Verlag Institute of Physics Publishing Ltd (IOP Publishing Ltd)
Band 34
Heft 7
Seiten 4844–4896
Vorab online veröffentlicht am 30.06.2021
Schlagwörter convex integration, avalanches, mechanical compatibility, shape-memory alloys, probabilistic, geometrically constrained nucleation
Nachgewiesen in Web of Science
Scopus
Dimensions
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