Propagation of converging spherical deformation waves in a heteromodular elastic medium

Abstract

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions.