Γ-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity

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dc.contributor.author Henao, Duvan A.
dc.contributor.author Mora-Corral, Carlos
dc.contributor.author Xu, Xianmin
dc.contributor.other UAM. Departamento de Matemáticas es_ES
dc.date.accessioned 2015-04-24T11:07:47Z
dc.date.available 2015-04-24T11:07:47Z
dc.date.issued 2014-12-05
dc.identifier.citation Archive for Rational Mechanics and Analysis 216.15 (2015): 813-879 en_US
dc.identifier.issn 0003-9527 (print) es_ES
dc.identifier.issn 1432-0673 (online) es_ES
dc.identifier.uri http://hdl.handle.net/10486/665481
dc.description The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-014-0820-3 en_US
dc.description.abstract Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (Arch Rational Mech Anal 197:619–655, 2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The expression of the functional involves a volume integral and two surface integrals, and this fact makes the problem numerically intractable. In this paper we propose an approximation (in the sense of Γ-convergence) by functionals involving only volume integrals, which makes a numerical approximation by finite elements feasible. This approximation has some similarities to the Modica–Mortola approximation of the perimeter and the Ambrosio–Tortorelli approximation of the Mumford–Shah functional, but with the added difficulties typical of nonlinear elasticity, in which the deformation is assumed to be one-to-one and orientation-preserving en_US
dc.description.sponsorship D. Henao gratefully acknowledges the Chilean Ministry of Education’s support through the FONDE-CYT Iniciación project no. 11110011. C. Mora-Corral has been supported by Project MTM2011-28198 of the Spanish Ministry of Economy and Competitivity, the ERC Starting grant no. 307179, the “Ramón y Cajal” programme and the European Social Fund. X. Xu acknowledges the funding by NSFC 11001260 en_US
dc.format.extent 67 pag en
dc.format.mimetype application/pdf en
dc.language.iso eng en
dc.publisher Springer Verlag en_US
dc.relation.ispartof Archive for Rational Mechanics and Analysis en_US
dc.rights © 2014 Springer-Verlag Berlin Heidelberg en_US
dc.title Γ-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity en_US
dc.type article en
dc.subject.eciencia Matemáticas es_ES
dc.date.embargoend 2016-07-01
dc.relation.publisherversion http://dx.doi.org/10.1007/s00205-014-0820-3 es_ES
dc.identifier.doi 10.1007/s00205-014-0820-3 es_ES
dc.identifier.publicationfirstpage 813 es_ES
dc.identifier.publicationissue 15 es_ES
dc.identifier.publicationlastpage 879 es_ES
dc.identifier.publicationvolume 216 es_ES
dc.type.version info:eu-repo/semantics/acceptedVersion en
dc.rights.accessRights openAccess en


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