Void collapse in an elastic solid

Abstract

Radial deformations of an infinite medium surrounding a traction-free spherical cavity are considered. The body is composed of an isotropic, incompressible elastic material and is subjected to a uniform pressure at infinity. The possibility of void collapse (i.e. the void radius becoming zero at a finite value of the applied stress) is examined. This does not occur in all materials. The class of materials that do exhibit this phenomenon is determined, and for such materials, an explicit expression for the value of the applied pressure at which collapse occurs is derived. The stability of the deformation and the influence of a finite outer radius are also considered. The results are illustrated for a particular class of power-law materials. In certain respects, the present results for void collapse are complementary to Ball (1982)'s results for cavitation in an incompressible elastic material.