On the representation of constitutive relations using structure tensors

Abstract The purpose of this paper is to present a general formulation of the representation of constitutive relations for a material with a given (material) symmetry group in terms of functionals that depend on one or more so-called structure tensors. The principal result in this work takes the form of a relation between the symmetry groups of (1), the material constitutive relation, (2), the corresponding structure tensor(s), and (3), the functional depending on these tensors. In particular, this result contains that of the Rychlewski-Zhang representation theorem (e.g. Zhang and Rychlewski [1]) for anisotropic solids as a special case, and as such clarifies, simplifies and generalizes their formulation.