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

Abstract

The lower bound usually cited for Poisson's ratio ν is -1, derived from the relationship between ν and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ν 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 ν in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate the prior finding that 1/5 <= ν for linear elasticity to be applicable.

15 pages, 3 figures, 1 table