On symmetries of elasticity tensors and Christoffel matrices

TL;DR

This paper demonstrates that the symmetry group of an elasticity tensor is identical to that of its associated Christoffel matrix, providing a fundamental link between these two mathematical objects in elasticity theory.

Contribution

It establishes the equivalence of symmetry groups for elasticity tensors and Christoffel matrices, a novel theoretical result in elasticity and tensor analysis.

Findings

Proves the equality of symmetry groups for elasticity tensors and Christoffel matrices

Provides a new theoretical foundation linking tensor symmetries and matrix symmetries

Enhances understanding of symmetry properties in elasticity theory

Abstract

We prove that the symmetry group of an elasticity tensor is equal to the symmetry group of the corresponding Christoffel matrix.