18.13 : Poisson's Ratio

Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign ensures a positive value for the ratio, as the two strains typically have opposite signs. The value of Poisson's ratio significantly influences how a material behaves under stress.

Materials with high Poisson's ratios, such as rubber, which has a Poisson's ratio near 0.5, contract laterally nearly as much as they elongate axially. Knowing this ratio can predict how much a material will compress in the lateral direction when subjected to an axial load. This information helps design structures to withstand expected stresses and avoid failures. In summary, Poisson's ratio is a key characteristic of materials essential for predicting their behavior under stress. The anisotropic materials have different Poisson's ratios in different directions, and cork is known to have a zero Poisson ratio in one direction.