Cavitation, Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity
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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).
KeywordsCavitation Invertibility Convergence Regular minimizers Singular minimizers Multiple cavities
Mathematics Subject Classification (2000)74G20 74G65 74G10 49J45
- 2.Ball, J.M.: Constitutive inequalities and existence theorems in nonlinear elastostatics. In: Knops, R.J. (ed.) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. I, pp. 187–241. Pitman, London (1977) Google Scholar