A NUMERICAL STUDY ON CAVITATION IN NONLINEAR ELASTICITY — DEFECTS AND CONFIGURATIONAL FORCES

Abstract

An iso-parametric finite element method is introduced in this paper to study cavitations and configurational forces in nonlinear elasticity. The method is shown to be highly efficient in capturing the cavitation phenomenon, especially in dealing with multiple cavities of various sizes and shapes. Our numerical experiments verified and extended, for a class of nonlinear elasticity materials, the theory of Sivaloganathan and Spector on the configurational forces of cavities, as well as justified a crucial hypothesis of the theory on the cavities. Numerical experiments on configurational forces indicate that, in the case of a round reference configuration with radially symmetric stretch on the boundary, the cavitation centered at the origin is the unique energy minimizer. Numerical experiments also reveal an interesting size effect phenomenon: for macro-scale pre-existing-defects, the cavitation process is dominated by the relatively larger pre-existing-defects, and the cavitation tendency of much smaller pre-existing-defects is significantly suppressed.