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dc.contributor.authorMiroshnikov, Alexey
dc.contributor.authorTzavaras, Athanasios
dc.date.accessioned2015-02-19T11:25:41Z
dc.date.available2015-02-19T11:25:41Z
dc.date.issued2014-08-21
dc.identifier.citationOn the Construction and Properties of Weak Solutions Describing Dynamic Cavitation 2014, 118 (2):141 Journal of Elasticity
dc.identifier.issn0374-3535
dc.identifier.issn1573-2681
dc.identifier.doi10.1007/s10659-014-9488-z
dc.identifier.urihttp://hdl.handle.net/10754/344585
dc.description.abstractWe consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation. For dimensions d=2,3 we show that cavity formation is necessarily associated with a unique precursor shock. We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation as a function of the cavity speed of the self-similar profiles. We show that for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents.
dc.publisherSpringer Nature
dc.relation.urlhttp://dx.doi.org/10.1007/s10659-014-9488-z
dc.rightsPost-print version of article publicly available 12 months after official publication.
dc.subjectCavitation
dc.subjectshock waves
dc.subjectPolyconvex elasticity
dc.subject35L67
dc.subject35L70
dc.subject74B20
dc.subject74H20
dc.subject74H
dc.titleOn the Construction and Properties of Weak Solutions Describing Dynamic Cavitation
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Elasticity
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Massachusets, Amherst, USA
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxividarXiv:1402.3706
kaust.personTzavaras, Athanasios
refterms.dateFOA2015-08-21T00:00:00Z
dc.date.published-online2014-08-21
dc.date.published-print2015-02


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