Three-Term Representations of Power Tensor Series in the Theory of Constitutive Relations

A class of power tensor series (constitutive relations) with coefficients (material functions) that are functions of three independent invariants is considered in three-dimensional space. Based on the Hamilton–Cayley formula, the exact expressions in the form of matrix series are found for the coefficients of three-term representations of such power series. The relationship of the coefficients of direct and inverse three-term constitutive relations is derived. Cases of tensor linearity, or quasi-linearity, as well as the independence of material functions from invariants, are discussed.