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

The lower bound customarily cited for Poisson's ratio ?, ?1, is derived from the relationship between ? 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 ????0.2. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ? for isotropic materials from this theory is actually . Herein we generalize this result, first by analyzing expressions for ? in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate that for classical linear elasticity to be applicable. Of course, a few materials exist for which ??<?0.2, thus deviating from this bound; accurate analysis of their mechanical behavior requires more sophisticated elasticity models.

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