Poisson's Ratio:

 When a wire is stretched along its length, it is elongated and, simultaneously, there is a contraction in its diameter. The length of the wire increases in the direction of the applied force, whereas the contraction in its diameter occurs in the direction perpendicular to the direction of the applied force. This is true not only for wire but also for all other bodies under strain. The strain (change in the dimensions of the body) perpendicular to the applied force is called lateral strain. Poisson pointed out that within elastic limit, lateral strain is directly proportional to longitudinal strain. In other words, the ratio of lateral strain to longitudinal strain is a constant for a material body and is known as Poisson's ratio. It is denoted by P_R.

If α and β be the longitudinal and lateral strains respectively of a material body, its Poisson's ratio is given by:

P_R = β/ α

Let, due to an applied stretching force, the length l of a wire (rod or tube) increased by an amount Δ l and its diameter d is decreases by an amount Δ d. Thus, longitudinal strain is Δ l/l , and lateral strain is Δ d/d . And, the Poisson's ratio is given as :

PR = (Δ d/d)/( Δ l/l)

= l/d(Δ d/ Δ l)

Since Poisson's ratio is a ratio of two strains, it is a dimensionless quantity. The value of Poisson's ratio depends on the nature of the material and for most of the substances; it lies between 0.2 and 0.4. When a body under tension suffers no change in its volume, i.e. the body is perfectly incompressible, the value of Poisson's ratio is the highest (i.e. 0.5).