Acoustic Axes in Elasticity

TL;DR

This paper introduces a new tensor-based framework for understanding acoustic axes in elastic anisotropic materials, providing a unified geometric approach and clarifying conditions across various crystal symmetries.

Contribution

It presents a novel tensor formulation for acoustic axes, unifies previous conditions, and applies geometric methods to different crystal symmetries in elasticity.

Findings

All previous degeneracy conditions derive from the new acoustic axis tensor.

Conditions for acoustic axes are reinterpreted for various crystal symmetries.

First-order anisotropy conditions do not always identify true acoustic axes.

Abstract

New results are presented for the degeneracy condition of elastic waves in anisotropic materials. The existence of acoustic axes involves a traceless symmetric third order tensor that must vanish identically. It is shown that all previous representations of the degeneracy condition follow from this acoustic axis tensor. The conditions for existence of acoustic axes in elastic crystals of orthorhombic, tetragonal, hexagonal and cubic (RTHC) symmetry are reinterpreted using the geometrical methods developed here. Application to weakly anisotropic solids is discussed, and it is shown that the satisfaction of the acoustic axes conditions to first order in anisotropy does not in general coincide with true acoustic axes.