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

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.