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Cavitation, invertibility, and convergence of regularized minimizers in nonlinear elasticity. (English) Zbl 1159.74322

Summary: 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 \(\epsilon \rightarrow 0\), by introducing micro-voids of radius \(\epsilon \) in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by J. Sivaloganathan, S. J. Spector and V. Tilakraj [SIAM J. Appl. Math. 66, No. 3, 736–757 (2006; Zbl 1104.74016)] to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).

MSC:

74B20 Nonlinear elasticity
74G65 Energy minimization in equilibrium problems in solid mechanics
49J45 Methods involving semicontinuity and convergence; relaxation
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)

Citations:

Zbl 1104.74016
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References:

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