The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity

@article{Sivaloganathan2006TheCO,
  title={The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity},
  author={Jeyabal Sivaloganathan and Scott J. Spector and Viveka Tilakraj},
  journal={SIAM Journal of Applied Mathematics},
  year={2006},
  volume={66},
  pages={736-757}
}
Abstract. Consider a nonlinearly elastic body which occupies the region Ω ⊂ Rm (m = 2, 3) in its reference state and which is held in tension under prescribed boundary displacements on ∂Ω. Let x0 ∈ Ω be any fixed point in the body. It is known from variational arguments that, for sufficiently large boundary displacements, there may exist discontinuous weak solutions of the equilibrium equations corresponding to a hole forming at x0 in the deformed body (this is the phenomenon of cavitation… CONTINUE READING

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