Remarks on isotropic extension of anisotropic constitutive functions via structural tensors

In their original formulation of the method of isotropic extension via structural tensors, which is meant for applications to the derivation of coordinate-free representation formulas for anisotropic constitutive functions, both Boehler and Liu start with the assumption that the invariance group of structural tensors is the symmetry group that defines the anisotropy of the constitutive function in question. As a result, the method (with structural tensors of order not higher than two) is applicable only when the anisotropy is characterized by a cylindrical group or belongs to the triclinic, monoclinic, or rhombic crystal classes. In this note we present a reformulation of the method in which the aforementioned assumption of Boehler and of Liu is relaxed, and we show by examples in finite elasticity and anisotropic linear elasticity that the method of isotropic extension via structural tensors could be applicable beyond the original limitations.