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Γ-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity

Identificadores del recurso

Archive for Rational Mechanics and Analysis 216.15 (2015): 813-879

0003-9527 (print)

1432-0673 (online)

http://hdl.handle.net/10486/665481

10.1007/s00205-014-0820-3

813

879

216

Procedència

(Biblos-e Archivo)

Fitxa

Títol:: Γ-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity
Tema:: Matemáticas
Descripció:: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-014-0820-3; 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; 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
Idioma:: English
Autor/Productor:: Henao, Duvan A.; Mora Corral, Carlos; Xu, Xianmin
Editor:: Springer Verlag
Otros colaboradores/productores:: UAM. Departamento de Matemáticas
Drets:: open access
Data:: 2014-12-05
Tipo de recurso:: journal article; info:eu-repo/semantics/acceptedVersion
Format:: application/pdf

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