Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

TL;DR

This paper presents a method to approximate anisotropic elastic constants with higher symmetry moduli by minimizing differences in acoustical tensors, aiding in modeling complex materials acoustically.

Contribution

It introduces a tensor projection approach to find optimal higher symmetry elastic moduli that best fit the acoustical properties of anisotropic materials.

Findings

Optimal moduli minimize mean squared differences in acoustical tensors.

Projection method aligns elastic stiffness tensors with higher symmetry.

Implications for improved acoustic modeling of complex materials.

Abstract

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance function, or equivalently, projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.