On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation

Handle URI:
http://hdl.handle.net/10754/344585
Title:
On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation
Authors:
Miroshnikov, Alexey; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
We 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.
KAUST Department:
Division fo Computer, Electrical, Mathematical Sciences & Engineering
Citation:
On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation 2014, 118 (2):141 Journal of Elasticity
Publisher:
Springer Netherlands
Journal:
Journal of Elasticity
Issue Date:
21-Aug-2014
DOI:
10.1007/s10659-014-9488-z
Type:
Article
ISSN:
0374-3535; 1573-2681
Additional Links:
http://dx.doi.org/10.1007/s10659-014-9488-z
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorMiroshnikov, Alexeyen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2015-02-19T11:25:41Zen
dc.date.available2015-02-19T11:25:41Zen
dc.date.issued2014-08-21en
dc.identifier.citationOn the Construction and Properties of Weak Solutions Describing Dynamic Cavitation 2014, 118 (2):141 Journal of Elasticityen
dc.identifier.issn0374-3535en
dc.identifier.issn1573-2681en
dc.identifier.doi10.1007/s10659-014-9488-zen
dc.identifier.urihttp://hdl.handle.net/10754/344585en
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.en
dc.publisherSpringer Netherlandsen
dc.relation.urlhttp://dx.doi.org/10.1007/s10659-014-9488-zen
dc.rightsPost-print version of article publicly available 12 months after official publication.en
dc.subjectCavitationen
dc.subjectshock wavesen
dc.subjectPolyconvex elasticityen
dc.subject35L67en
dc.subject35L70en
dc.subject74B20en
dc.subject74H20en
dc.subject74Hen
dc.titleOn the Construction and Properties of Weak Solutions Describing Dynamic Cavitationen
dc.typeArticleen
dc.contributor.departmentDivision fo Computer, Electrical, Mathematical Sciences & Engineeringen
dc.identifier.journalJournal of Elasticityen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Massachusets, Amherst, USAen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorTzavaras, Athanasiosen
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