SYMMETRY GROUPS FOR RADIAL MOTIONS OF COMPRESSIBLE HYPERELASTIC SPHERES AND CYLINDERS

The exhaustive treatment of symmetry groups for radial motions of compressible homogeneous hyperelastic spheres and cylinders is provided and the special forms of the strain energy function which give rise to different groups are investigated in detail. A class of similarity solutions which are invariant under one of the symmetry group is determined and corresponding field equations associated with motion are reduced to nonlinear ordinary differential equations in a similarity variable.