18.13 : 泊松比

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.