A simple formula for dynamic spherical cavity expansion in a compressible elastic perfectly plastic material with large deformations

Abstract

Simple analytical expressions are obtained for the contact pressure applied to a spherical cavity that is expanding with constant velocity in an infinite compressible elastic perfectly plastic material with large deformations. The solution is obtained by using the kinematics of isochoric flow with a modified value of the shear modulus and with a physical boundary condition on the radial stress at the location of the precursor wave associated with compressible response. Comparison of the predictions with those of full numerical simulations and non-linear similarity solutions indicates that this modified incompressible solution predicts reasonably accurate results for the transient decay of the contact pressure from its shocked value to its asymptotic value.