Frame-invariant polyconvex strain-energy functions for some anisotropic solids

We present a set of simple sufficient conditions for the polyconvexity and coercivity of strain-energy functions for transversely isotropic and orthotropic elastic solids. The formulation is based on appropriate function bases for the right stretch tensor in the polar decomposition of the deformation gradient and furnishes numerical analysts with a priori existence criteria for boundary-value problems.