Wilmanski's Anniversary Volume, WIAS
Cavitation, Deformations (Mechanics), Inhomogeneous materials, Symmetric functions
A class of non-spherically symmetric deformations of a neo-Hookean incompressible elastic ball is considered. It is shown that the only possible solution, the cavitated radially symmetric solution and the deformation of radial inflation and polar stretching. These are the same solutions as found by Polignone-Warne and Warne  for a smaller class of deformations. This fact shows once again that the radial deformations are the only deformations, at least within the class considered, which may support a formation of a cavity in the center of an incompressible, isotropic, elastic sphere.
Marek Elźanowski. (2000). "About Non-Spherically Symmetric Deformations of an Incompressible Neo-Hookean Sphere" Wilmanski's Anniversary Volume, WIAS, 68-72.