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Journal of Elasticity

, 94:55 | Cite as

Cavitation, Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity

  • Duvan HenaoEmail author
Article

Abstract

We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed flaw points can be obtained, in the limit as ε→0, by introducing micro-voids of radius ε in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).

Keywords

Cavitation Invertibility Convergence Regular minimizers Singular minimizers Multiple cavities 

Mathematics Subject Classification (2000)

74G20 74G65 74G10 49J45 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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