Expansion of a spherical cavity in an infinite porous rigid/plastic medium

An expanding spherical cavity of a zero initial radius surrounded by an infinite porous rigid/plastic medium is considered. The material is assumed to obey the flow theory of plasticity based on a yield criterion and its associated flow rule. The yield criterion depends on the linear and quadratic stress invariants. No restriction is imposed on this dependence, except for the standard requirements imposed on the yield criteria. It is shown that the solution can be extended into the rigid region. The yield criterion approaches the von Mises yield criterion as the relative density approaches unity. Some equations contain the expression 0/0 at the rigid/plastic boundary. In this respect, the present solution is qualitatively different from available elastic/plastic solutions. However, the solution does not provide the solution for the von Mises yield criterion as a particular case. Numerical results are presented for Green’s yield criterion. These results follow physical expectations concerning the distributions of the relative density, the radial velocity, and the radial stress. The solution is adapted for expanding a cavity of a non-zero initial radius. The pressure required for expanding the cavity is calculated.