Spherical Cavity Expansion in a Drucker-Prager Solid

Abstract

A finite strain analysis is presented for the pressurized spherical cavity embedded in a Drucker-Prager medium. Material behavior is modeled by a nonassociated deformation theory which accounts for arbitrary strain-hardening. The governing equations of spherically symmetric response are reduced to a single differential equation with the effective stress as the independent variable. Some related topics are discussed including the elastic-perfectly plastic solid, the thin-walled shell, and the Mohr-Coulomb material. Spontaneous growth (cavitation limit) of an internally pressurized cavity is treated as a self-similar process and a few numerical examples are presented. These illustrate, for different hardening characteristics, the pressure sensitivity of material response and that deviations from normality always reduce the caviation pressure.