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

The lower bound customarily cited for Poisson's ratio nu, -1, is derived from the relationship between nu and the bulk and shear moduli in the classical theory of linear elasticity. However, experimental verification of the theory has been limited to materials having nu >= 0.2. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on nu for isotropic materials from this theory is actually 1/5. 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 that nu > 1/5 for classical linear elasticity to be applicable. Of course, a few materials exist for which nu < 0.2, thus deviating from this bound; accurate analysis of their mechanical behavior requires more sophisticated elasticity models.