B. Svendsen, ON THE REPRESENTATION OF CONSTITUTIVE RELATIONS USING STRUCTURE TENSORS, International journal of engineering science, 32(12), 1994, pp. 1889-1892
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.