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dc.contributor.authorRüland, A.
dc.contributor.authorTaylor, J.M. 
dc.contributor.authorZillinger, C.
dc.date.accessioned2019-04-03T09:56:30Z
dc.date.available2019-04-03T09:56:30Z
dc.date.issued2019-03-30
dc.identifier.issn0938-8974
dc.identifier.urihttp://hdl.handle.net/20.500.11824/964
dc.description.abstractWe study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal regularity of convex integration solutions to the presence of lower bounds in variational models with surface energy. Hence, variational models with surface energy could be viewed as a selection mechanism allowing for or excluding convex integration solutions. Secondly, we present the first numerical implementations of convex integration schemes for the model problem of the geomet- rically linearised two-dimensional hexagonal-to-rhombic phase transformation. We discuss and compare the two algorithms from Rüland et al. (J Elast. 2019. https://doi. org/10.1007/s10659-018-09719-3; SIAM J Math Anal 50(4):3791–3841, 2018) and give a numerical estimate of the regularity attained.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectConvex integrationen_US
dc.subjectHigher Sobolev regularityen_US
dc.subjectScaling Lawsen_US
dc.subjectSolid-solid phase transformationsen_US
dc.titleConvex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementationsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/s00332-019-09540-9
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s00332-019-09540-9?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst&utm_source=ArticleAuthorOnlineFirst&utm_medium=email&utm_content=AA_en_06082018&ArticleAuthorOnlineFirst_20190402en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//MTM2017-82184-Ren_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleJournal of Nonlinear Scienceen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España