A dual-parametric finite element method for cavitation in nonlinear elasticity

A dual-parametric finite element method is introduced in this paper for the computation of singular minimizers in the two dimensional cavitation problem in nonlinear elasticity. The method overcomes the difficulties, such as the mesh entanglement and material interpenetration, generally encountered in the finite element approximation of problems with extremely large expansionary deformation. Numerical experiments show that the method is highly efficient in the computation of cavitation problems. Numerical experiments are also conducted on discrete problems without the radial symmetry to show the validity of the method to more general settings and the potential of its application to the study of mechanism of cavity nucleation in nonlinear elastic materials.