Limits to Poisson's ratio in isotropic materials - general result for arbitrary deformation

TL;DR

This paper establishes that the lower bound for Poisson's ratio in isotropic materials under linear elasticity is 1/5, extending previous findings and confirming consistency with experimental data.

Contribution

The paper generalizes the lower bound of Poisson's ratio for isotropic materials using six elastic constants and arbitrary strains, confirming the 1/5 limit.

Findings

Poisson's ratio lower bound is 1/5 for isotropic materials.

The result is consistent with experimental measurements.

The analysis applies to arbitrary strains in linear elasticity.

Abstract

The lower bound usually cited for Poisson's ratio {\nu} is -1, derived from the relationship between {\nu} and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on {\nu} for isotropic materials is actually 1/5, a value also consistent with experimental measurements on real materials. Herein we generalize this result, first by analyzing expressions for {\nu} in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate the prior finding that 1/5 <= {\nu} for linear elasticity to be applicable.