On Isotropic, Frame-Invariant, Polyconvex Strain-Energy Functions

We discuss the problem of generating polyconvex and coercive strain-energy functions for isotropic elastic solids. Such functions meet the main requirements of Ball's fundamental existence theory. We demonstrate that a formulation based on the principal invariants of the right stretch tensor, which has advanced analytical work to a considerable degree, furnishes a natural setting for this purpose. It is shown that this formulation is amenable to numerical treatment in that it does not require explicit polar decompositions or eigenanalysis. We thus adapt to a computational setting a formulation of isotropic finite elasticity theory which has been highly successful in analytical studies.