Poisson’s Ratio

When a rubber tube is stretched along its length, there is a contraction in its diameter. While the length increases in the direction of forces, a contraction occurs in the perpendicular direction.

The strain perpendicular to the applied force is called lateral strain. Poisson pointed out that within elastic limit, lateral strain is directly proportional to longitudinal strain i.e. the ratio of lateral strain to longitudinal strain is constant for a material body and is known as Poisson’s ratio. It is denoted by a Greek letter σ (sigma).

If α and β are the longitudinal strain and lateral strain respectively, then Poisson’s ratio is

σ = β/α

If a wire (rod or tube) of length L and diameter d is elongated by applying a stretching force by an amount ∆L and its diameter decreases by ∆d, then

Longitudinal strain, α = ∆L/L

Lateral strain, β = ∆d/d

Possion’s ratio, σ = L/d x ∆d/∆L

Since Poisson’s ratio is a ratio of two strains, it is a pure number. The value of Poisson’s ratio depends only on the nature of material and for most of the substances, it lies between 0.2 and 0.4.

When a body under tension suffers no change in volume, i.e. the body is perfectly incompressible, the value of Poisson’s ratio is maximum i.e. 0.5. Theoretically, the limiting values of Poisson’s ratio are –1 and 0.5.