Nonmonotonic cavity growth in finite, compressible elasticity

Abstract

We obtain closed form solutions to the problems of cylindrical and spherical cavitation when a stretch is prescribed on the outer boundary for a compressible elastic material. The strain energy function is quite general and contains an arbitrary function of a linear combination of the principal stretch invariants. The cavitating solution is shown to be preferred to the corresponding homogeneous deformation. Three modes of cavitation are identified for the spherical problem whereas only one is possible in the cylindrical case. The most general strain energy function for which the cavitating solution is possible is briefly discussed.