Abstract

In this presentation, we will discuss the derivation of a novel closed-form criterion for the onset of cavitation in compressible, isotropic, hyperelastic solids subjected to non- symmetric loading conditions. The criterion is based on the solution of a boundary value problem where a hyperelastic solid, which is infinite in extent and contains a single vacuous inhomogeneity, is subjected to uniform displacement boundary conditions. By making use of a “linear-comparison” variational procedure, we solve this problem approximately and generate variational estimates for the critical stretches applied on the boundary at which the cavity suddenly starts growing. The accuracy of the proposed analytical result will be assessed by comparisons with exact solutions available from the literature for radially symmetric cavitation, as well as with finite element simulations. In addition, applications will be presented for a variety of materials of practical and theoretical interest—including the harmonic, Blatz-Ko, and compressible Neo-Hookean materials—which will provide new insight into the phenomenon of cavitation.