Poisson's ratio:

 Poisson's ratio is the ratio of transverse contraction strain to longitudinal expansion strain. Poisson's ratio is the ratio of the relative contraction strain, or transverse strain normal to the applied load, to the relative extension strain, or axial strain in the direction of the applied load.

Poisson's Ratio can be expressed as ν = ξ _t / ξ _l 

where ν = Poisson's ratio

ξ _t = transverse strain

ξ _l = longitudinal strain.

Value of the Poisson's ratio for most materials lies between 0.25 and 0.33. Ratio of lateral strain to axial strain in an axial loaded specimen. It is the constant that relates modulus of rigidity to Young's Modulus. Modulus of Rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force. It is defined as the ratio of shear stress to the displacement per unit sample length (shear strain). Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an isotropic elastic material. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. Poisson's ratio is also defined as the ratio of the transverse contracting strain to the elongation strain when a rod is stretched by forces which are applied at its ends and which are parallel to the rod's axis. Poisson's effect is caused by slight movements between molecules and the stretching of molecular bonds within the material lattice to accommodate the stress. When the bonds elongate in the stress direction, they shorten in the other directions. This behavior multiplied millions of times throughout the material lattice is what drives the phenomenon. Poisson's ratio in most cases is positive which means that a material stretches in one direction by a greater degree than it contracts in other directions. The bonds between the atoms in the structure become realigned during the process of stretching and compressing. I t is possible to have a negative Poisson ratio. Materials displaying this quality are known as auxetics. With such materials, stretching them in one direction will actually cause them to expand in other directions.