Singular limiting induced from continuum solutions and the problem of dynamic cavitation
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1815 | |
dc.contributor.author | Giesselmann, Jan | |
dc.contributor.author | Tzavaras, Athanasios E. | |
dc.date.accessioned | 2016-03-24T17:37:44Z | |
dc.date.available | 2019-06-28T08:19:04Z | |
dc.date.issued | 2013 | |
dc.description.abstract | In the works of K.A. Pericak-Spector and S. Spector [9, 10] a class of self-similar solutions are constructed for the equations of radial isotropic lastodynamics that describe cavitating solutions. Cavitating solutions decrease the total mechanical energy and provide a striking example of non-uniqueness of entropy weak solutions (for polyconvex energies) due to point-singularities at the cavity. To resolve this paradox, we introduce the concept of singular limiting induced from continuum solution (or slic-solution), according to which a discontinuous motion is a slic-solution if its averages form a family of smooth approximate solutions to the problem. It turns out that there is an energetic cost for creating the cavity, which is captured by the notion of slic-solution but neglected by the usual entropic weak solutions. Once this cost is accounted for, the total mechanical energy of the cavitating solution is in fact larger than that of the homogeneously deformed state. We also apply the notion of slic-solutions to a one-dimensional example describing the onset of fracture, and to gas dynamics in Langrangean coordinates with Riemann data inducing vacuum in the wave fan. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/3187 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3197 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Nonlinear elasticity | eng |
dc.subject.other | cavitation | eng |
dc.subject.other | singular solutions | eng |
dc.subject.other | Anfangswertproblem | eng |
dc.title | Singular limiting induced from continuum solutions and the problem of dynamic cavitation | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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