ON THE REPRESENTATION OF CONSTITUTIVE RELATIONS USING STRUCTURE TENSORS

The purpose of this paper is to present a general formulation of the r epresentation of constitutive relations for a material with a given (m aterial) symmetry group in terms of functionals that depend on one or more so-called structure tensors. The principal result in this work ta kes the form of a relation between the symmetry groups of (1), the mat erial consitutive relation, (2), the corresponding structure tensor(s) , and (3), the functional depending on these tensors. In particular, t his result contains that of the Rychlewski-Zhang representation theore m (e.g. Zhang and Rychlewski [1] for anisotropic solids as a special c ase, and as such clarifies, simplifies and generalizes their formulati on.