Recovering the normal form of an elasticity tensor

TL;DR

This paper introduces a geometric method to transform any elasticity tensor into its normal form based on its symmetry class, using covariants and an algorithm for symmetry detection.

Contribution

It presents a novel geometric approach and an algorithm for recovering the normal form of elasticity tensors across all symmetry classes.

Findings

Effective rotation method for normal form recovery

Algorithm for symmetry class detection

Applicable to tensors in any orthonormal frame

Abstract

We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its components in any orthonormal frame, and this for any tensor of any symmetry class. Our methodology relies on the use of specific covariants and on the geometric characterization of each symmetry class using these covariants. An algorithm to detect the symmetry class of an Elasticity tensor is finally formulated.