Poisson's ratio:

Poisson's ratio can be defined as 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 relative extension strain, to the applied load, or axial strain in the direction of the applied load. Poisson's Ratio can be expressed as υ = - ε_t / ε_l where υ = Poisson's ratio, ε_t = transverse strain, ε_l = longitudinal strain. 

Value of the Poisson's ratio for most materials lies in between 0.25 and 0.33. Ratio of lateral strain to the axial strain in the axial loaded specimen. It is the constant which relates modulus of rigidity to Young's Modulus. Modulus of Rigidity is coefficient of elasticity for the shearing force. It can be defined as the ratio of shear stress to the displacement per unit sample length. Young's modulus, called 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 can be 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 also. Poisson's effect is caused by slight movements among molecules and the stretching of molecular bonds within material lattice to accommodate stress. When bonds elongate in stress direction, they shorten in other directions. This type of 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 at the time of process of stretching and compressing. I t is possible to generate a negative Poisson ratio. Materials displaying this type of quality are known as auxetics. With such type of materials, stretching them in 1 direction will actually cause them to expand in other directions.