Quasi-static spherical/cylindrical cavity expansion in a medium with an arbitrary equation of state and a shear strength plasticity envelope

Abstract

This paper presents a new analytical quasi-static spherical/cylindrical cavity-expansion model for a medium that is described by an arbitrary (non-linear) equation of state ("pressure - bulk strain" relationship) and a shear strength plasticity envelope (principal stress difference vs. pressure relationship). The paper presents the formulae for determination of the cavity pressure and the corresponding stresses variations in the radial direction.A unified solution is presented for a general compressible elastic-plastic or an elastic-cracked-plastic medium that is described by any nonlinear equation of state and shear strength plasticity envelope.The solution of the problem is based on an analytical relationship that is developed for the ratio between the elastic-plastic interface coordinate and the cavity radius for the examined problem. The derived formulae for the variation of the stresses with the radial coordinate depend on this ratio. The formulation is characterized by special features, for example the cavity boundary condition is not necessarily pressure but may be the boundary displacement, which is more suitable for the model implementation in interaction problems.From the general present model, different special cases may be obtained, such as linear equation of state and linear shear strength envelope, locked hydrostat, or for an incompressible material.Comparisons of the analytical model with available results and known solutions of particular cases, for both spherical and cylindrical cavity expansion problems, show excellent agreement.