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.

When a slender bar is subjected to an axial load, the bar material undergoes axial strain, causing it to deform in the axial direction.

Simultaneously, the material also experiences a lateral strain, deforming in directions perpendicular to the axial load.

The material is assumed to be homogeneous and isotropic, making its mechanical properties independent of the position and direction. So, the strain in any transverse direction must have the same value.

Poisson's ratio is a fundamental constant defined as the negative ratio of the lateral strain and the axial strain induced by the applied load for a given material.

The negative sign used is to obtain a positive value for Poisson's ratio since axial and lateral strains have opposite signs.

Materials with a high Poisson's ratio tend to experience greater lateral contraction when subjected to axial loads, while those with a low ratio tend to be less affected.

For instance, rubber has a Poisson's ratio close to 0.5, which means it experiences nearly as much lateral contraction as axial elongation.