Plane Strain Expansion of a Cylindrical Cavity in an Infinite Porous Rigid/Plastic Medium Obeying a General Yield Criterion

Abstract

A semi-analytical plane-strain solution for an expanding cylindrical cavity surrounded by an infinite porous rigid/plastic medium is presented. The constitutive equations are a general yield criterion and its associated flow rule. The yield criterion depends on the relative density and the linear and quadratic stress invariants. No restriction is imposed on this dependence, except for the standard requirements imposed on the yield criteria. The boundary value problem reduces to a Cauchy problem for three ordinary differential equations. This system of equations must be solved numerically. Numerical results are presented for Green’s yield criterion. This yield criterion involves two functions of the relative density. The influence of the choice of these functions on the distributions of the relative density, the radial velocity, and the stress components is revealed.