Further remarks on isotropic extension of anisotropic constitutive functions via structural tensors

For the original method of isotropic extension of anisotropic constitutive function via structural tensors to work, a necessary condition is that the symmetry group G of the anisotropic solid can be characterized as the intersection of stabilizers of specific tensors (called structural tensors) under the action of O(3) on the tensor spaces in question. Here we strengthen the method by replacing “structural tensor” in the characterization of G with “set of structural tensors”, thereby broadening the range of subgroups of O(3) covered when the structural tensors are restricted to be of order not higher than two. Mathematical theorems are proved to support our strengthened method of isotropic extension via structural tensors, and a procedure is formalized for using the method to find a representation formula for the anisotropic constitutive function when the structural tensors involved are restricted to be of order not higher than two. As illustration, we consider the constitutive function in anisotropic nonlinear Cauchy elasticity and examine the cases where the anisotropic symmetry group does not satisfy the characterization required by the original method.