Implications of Shield’s inverse deformation theorem for compressible finite elasticity

Abstract.

Some properties of the Shield transformation on elastic strain energy functions are established. It is reflexive, it preserves objectivity and material symmetry for isotropic materials, and it also preserves infinitesimal strain response, ellipticity and Hadamard stability, and the Baker–Ericksen condition. Two new classes of strain energies for compressible isotropic materials are introduced, one of them being the image under the Shield transformation of the class of harmonic strain energies. In view of Shield’s Inverse Deformation Theorem, these new classes of strain energies will allow solution in closed form of a variety of problems in finite elastostatics.