# Poisson's ratio

Poisson's ratio of a material defines the ratio of transverse strain (x direction) to the axial strain (y direction)

In materials science and solid mechanics, Poisson's ratio ${\displaystyle \nu }$ (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, ${\displaystyle \nu }$ is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. Soft materials,[1] such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2-0.3. The ratio is named after the French mathematician and physicist Siméon Poisson.

1. ^ For soft materials, the bulk modulus (K) is typically large compared to the shear modulus (G) so that they can be regarded as incompressible, since it is easier to change shape than to compress. This results in the Young's modulus (E) being ${\displaystyle E=3G}$ and hence ${\displaystyle \nu =0.5}$.Jastrzebski, D. (1959). Nature and Properties of Engineering Materials (Wiley International ed.). John Wiley & Sons, Inc.