On deformations possible in every compressible elastic body (Q1082867)

Here we show that the constraint of plane strain is a sufficient condition for the existence of nonhomogeneous deformations which are possible in every compressible homogeneous isotropic hyperelastic material. As in the case of incompressible materials, we obtain restrictions on the invariants of the left Cauchy-Green deformation tensor. Specifically we find that the surfaces over which the invariants are constant are necessarily coaxial right circular cylinders or parallel planes. The existence of universal nonhomogeneous deformations allows for general solutions of elastostatic problems involving compressible bodies subject to plane strain.