Standardized compliance matrixes for general anisotropic materials and a simple measure of anisotropy degree based on shear-extension coupling coefficient

TL;DR

This paper introduces a standardized compliance matrix for anisotropic materials, clarifies elastic constants, and proposes a simple measure of anisotropy degree based on shear-extension coupling, improving material comparison and understanding.

Contribution

It establishes a unique STF-OS compliance matrix for anisotropic materials and proposes a new measure of anisotropy degree based on shear-extension coupling.

Findings

The STF-OS compliance matrix clearly shows 18 independent elastic constants.

A material with isotropic tensile stiffness may not be fully isotropic.

The proposed anisotropy measure is more accurate than the stiffness ratio.

Abstract

The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing elastic properties between different materials. In this paper, a unique stiffest orientation based standardized (STF-OS) compliance matrix is established, and 18 independent elastic material constants are clearly shown. During the searching process for stiffest orientation, it is interesting to find from our theoretical analysis and an example that a material with isotropic tensile stiffness does not definitely possess isotropic elasticity. Therefore the ratio between the maximum and minimum tensile stiffnesses is not a correct measure of anisotropy degree. Alternatively, a simple and correct measure of anisotropy degree based on the maximum shear-extension coupling coefficient in all orientations is proposed.