Young's and shear moduli and Poisson's ratio for elastic media of high and middle symmetry

TL;DR

This paper derives explicit formulas for Young's modulus, shear modulus, and Poisson's ratio in high and medium symmetry elastic media, facilitating analysis of anisotropic and auxetic properties.

Contribution

It introduces tensorial expressions for elastic moduli and Poisson's ratio based on symmetry-adapted bases, enhancing understanding of anisotropic elastic behavior.

Findings

Derived formulas for elastic moduli and Poisson's ratio for symmetric media.

Decomposed elastic characteristics into isotropic and anisotropic parts.

Provided tools for studying auxetic materials.

Abstract

Using bases of fourth rank tensorial bases of complete Voigt's symmetry elaborated by Walpole we obtained expressions for inverse of Young's modulus E, inverse of shear modulus G and Poisson's ratio, which depend on components of the stiffness tensor S, on direction cosines of vectors n of uniaxial load and the vector m of lateral strain with crystalline symmetry axes. Crystalline media of high and medium symmetries are considered. Such representation yields decomposition of the above elastic characteristics to isotropic and anisotropic parts. Expressions for Poisson's coefficient are well suited for studying the property of auxeticity.