Compressible isotropic strain energies that support universal irrotational finite deformations

Analysis of the condition for universal deformations in compressible finite elasticity leads to the identification of two classes of strain energies that support universal irrotational deformations. These classes represent a significant generalization of the classes of strain energies for which universal deformation solutions have been hitherto available. Closed form solutions are presented for cylindrically and spherically radial irrotational deformation for all of these strain energies. Some questions about maximality of some classes of strain energies that support cylindrically radial universal deformations are resolved.