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.
Categories: cond-mat.mtrl-sci cond-mat.other