An Irreducible Function Basis of Isotropic Invariants of A Third Order Three-Dimensional Symmetric Tensor

TL;DR

This paper establishes an eleven-invariant irreducible function basis for third-order three-dimensional symmetric tensors, simplifying previous bases by removing certain invariants, which aids future tensor research.

Contribution

It introduces a minimal irreducible function basis that is a proper subset of the existing Olive-Auffray basis, excluding higher-degree invariants.

Findings

Reduced the invariant basis to eleven elements.

Dropped the octic and sextic invariants from the previous basis.

Facilitates further research on higher-order tensor invariants.

Abstract

In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity basis of that tensor. The octic invariant and a sextic invariant in the Olive-Auffray integrity basis are dropped out. This result is of significance to the further research of irreducible function bases of higher order tensors.