VOID NUCLEATION AND GROWTH FOR COMPRESSIBLE NONLINEARLY ELASTIC-MATERIALS - AN EXAMPLE

In this paper, we carry out an explicit analysis of a bifurcation problem for a solid sphere. composed of a special class of compressible non-linearly elastic materials, and subjected to prescribed radial stretch lambda > at its boundary. One solution to this problem, for all values of lambda, is that of pure homogeneous stretching in which the sphere expands radially. However, for sufficiently large values of lambda, a second configuration is possible where an internal traction-free spherical cavity forms at the origin. The critical stretch lambda = lambda(cr) at which this solution bifurcates from the trivial homogeneous solution is determined. The trivial solution is shown to become unstable at lambda = lambda(cr). It is also shown how the bifurcation model may be interpreted as describing sudden rapid growth of a pre-existing microvoid. The analogous issues for axisymmetric plane strain deformations of a cylinder are briefly discussed.