Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium

Abstract

The self-similar elastoplastic field induced by dynamic expansion of a pressurized spherical cavity is investigated for pressure sensitive solids. Material behavior is described by the hypoelastic model of the Drucker–Prager material with a non-associated flow rule, with arbitrary strain-hardening. We examine in detail the external elastic field, which is expected to develop at a distance from the cavity prior to plastic yielding. A new observation that emerges from that elastic solution is the possible existence of a compressive elastic zone where yielding is prevented since the effective stress remains negative. Simple analytical solutions are given for the fully incompressible elastic/perfectly plastic material with a non-associated flow rule. In particular, we study the influence of plastic pressure sensitivity on the dynamic cavitation pressure. A few useful relations are derived for the cavitation pressure which reveal the coupled effect of plastic pressure sensitivity and material inertia. A separate numerical analysis is given for the fully incompressible strain-hardening solid with a non-associated flow rule. Several numerical illustrations are presented for the solid with an associated flow rule along with a plastic boundary layer analysis for the thin singular zone near the cavity wall.