The bulk modulus and Poissonʹs ratio of “incompressible” materials

Poissonʹs ratio, ν, is a fundamental parameter characterizing the mechanical behavior of a material. Because the ratio of the bulk to the shear modulus, B/G, becomes infinite when ν = 1 / 2 , it is often assumed that the bulk modulus becomes very large as a material approaches “incompressibility.” This is incorrect; experimental results for viscoelastic materials show that changes in the bulk modulus are actually negligible as ν approaches 1/2. An analysis is performed to clarify the apparent conflict between the classic elastic equations and the experiments. At ν = 1 / 2 , the bulk modulus is shown to exhibit a singularity, but this is irrelevant to real materials.