Nucleation and Growth of a Spherical Void in a Nonlinear Elastic Material

Abstract

Spherically symmetric deformation of a solid sphere under applied uniform radial stretch is considered within the theory of finite elasticity. The sphere is composed of a homogeneous, isotropic, compressible, hyperelastic material called Blatz-Ko material. As a result, there exists, in addition to a trivial homogeneous solution, a solution which contains a spherical cavity when applied stretch exceeds a certain critical value. Since the solution for the microvoid problem converges to the bifurcated solution, this bifurcation phenomenon can be regarded as an idealized model describing the void nucleation and growth in the material.