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

By Philip J. Mott, C. Roland. 2009

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The lower bound customarily cited for Poisson's ratio ν, −1, is derived from the relationship between ν 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 ν ⩾ 0.2. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ν for isotropic materials from this theory is actually . 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 that for classical linear elasticity to be applicable. Of course, a few materials exist for which ν < 0.2, thus deviating from this bound; accurate analysis of their mechanical behavior requires more sophisticated elasticity models.

Subfields: Biomedical Engineering, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/545cc45faa2bb5c118857d49268e5f54cf09fd57