NEW FAMILIES OF EXACT-SOLUTIONS FOR FINITELY DEFORMED INCOMPRESSIBLE ELASTIC-MATERIALS

The governing partial differential equations for static deformations of homogeneous isotropic incompressible elastic materials are highly nonlinear, and consequently only a few exact solutions are known. For these materials, only one general solution involving a single arbitrary function is presently known, which is for plane deformations and is applicable to the so-called Varga strain-energy function. In this paper, new families of exact solutions are derived for plane and axially symmetric deformations of perfectly elastic materials. In the case of plane deformations, a different formulation of the known general solution for the Varga strain-energy function is presented, from which numerous new solutions may be obtained. In the case of axially symmetric deformations, the Varga material again arises as the privileged strain-energy function, and this constitutes the main result of the paper. For this material, a number of new simple exact solutions are derived for axially symmetric deformations. Finally, all the solutions obtained here are shown to also apply to a modified Varga strain-energy function involving the reciprocals of the principal stretches.