Harmonic factorization and reconstruction of the elasticity tensor

TL;DR

This paper introduces a method to factorize harmonic fourth-order tensors into second-order tensors and provides explicit formulas for reconstructing specific tensor symmetries, enhancing understanding of material anisotropy.

Contribution

The paper presents a novel harmonic tensor factorization approach and explicit equivariant reconstruction formulas for various tensor symmetries, advancing tensor analysis in elasticity.

Findings

Explicit factorization formulas for harmonic tensors.

Reconstruction formulas for transverse isotropic and orthotropic tensors.

Approximate reconstruction for trigonal and tetragonal tensors.

Abstract

In this paper, we propose a factorization of a fourth-order harmonic tensor into second-order tensors. We obtain moreover explicit equivariant reconstruction formulas, using second-order covariants, for transverse isotropic and orthotropic harmonic fourth-order tensors, and for trigonal and tetragonal harmonic fourth-order tensors up to a cubic fourth order covariant remainder.