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).
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Henao, D. Cavitation, Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity. J Elasticity 94, 55–68 (2009). https://doi.org/10.1007/s10659-008-9184-y
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DOI: https://doi.org/10.1007/s10659-008-9184-y