THREE-TERM REPRESENTATIONS OF POWER TENSOR SERIES IN THE THEORY OF CONSTITUTIVE RELATIONS

Abstract

A class of power tensor series (constitutive relations) with coefficients (material functions), which 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. The cases of tensor linearity, or quasi-linearity, as well as the independence of material functions from invariants are discussed.