A Study of Combined Asymmetric and Cavitated Bifurcations in Neo-Hookean Material Under Symmetric Dead Loading

Abstract

A study is given of the deformations of an incompressible body composed of a neo-Hookean material subjected to a uniform, spherically symmetric, tensile dead load. It is based on the energy minimization method using a constructed kinematically admissible deformation field. It brings together the pure homogeneous asymmetric deformations explored by Rivlin (1948, 1974) and the spherically symmetric cavitated deformations analyzed by Ball (1982) in one setting, and, in addition, Hallows nonsymmetric cavitated deformations to compete for a minimum. Many solutions are found and their stabilities examined; especially, the stabilities of the aforementioned asymmetric and cavitated solutions are reassessed in this work, which shows that a cavitated deformation which is stable against the virtual displacements in the spherical form may lose its stability against a wider class of virtual displacements involving nonspherical forms.