Application of higher-order tensor theory for formulating enhanced continuum models

In this paper attention is focussed on the derivation of higher-order isotropic tensors and their application in the formulation of enhanced continuum models. A mathematical theory will be discussed which relates formal orthogonal invariant polynomial functions to isotropic tensors. Using this theory, the second-order to the sixth-order isotropic tensor will be derived. When the tensor order increases, the derivation procedure clearly reveals a repeatable character. Thereafter, an example will be given of how the higher-order isotropic tensors can be used in the formulation of an enhanced continuum model. It will be demonstrated that symmetry conditions significantly reduce the number of material parameters.