Using Shield's inverse theorem, new families of solutions describing spherical inflation for isotropic, homogeneous, compressible elasticity are found. Cavitation is shown to be possible for each of the solutions and each family shares a common simple mathematical description of cavitation. The set of solutions includes the solution for the Varga material. Cavitation is also shown to be preferred energetically over the corresponding homogeneous deformation. Finally some features of the cavitation solutions are explored.
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