Termination of the starting problem of dynamic expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium

Perhaps the simplest non-trivial problem in small deformation dynamic plasticity is expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium. Here, example problems are considered with two boundary conditions at the cavity's surface: constant velocity and constant pressure. Attempts to obtain analytical solutions are complicated by the fact that, in general, the elastic-plastic boundary propagates with variable speed. However, it is known that the elastic-plastic boundary propagates at constant speed for the starting problem when the shocks due to the applied loads are large enough to cause inelastic response at the instant they are applied. When the value of the applied pressure equals the shock pressure due to the applied velocity the solutions of the two boundary value problems are initially identical and can be compared. The objective of this paper is to review the literature and to examine the termination conditions for the starting problem. Specifically, the starting problem terminates when either the jump in radial stress at the elastic-plastic boundary or the loading condition for plasticity vanishes there. These termination conditions depend on the applied load and on Poisson's ratio.