Poisson’s Ratio is the ratio of lateral strain to longitudinal strain is a constant for a material body …
Poisson’s Ratio is the ratio of lateral strain to longitudinal strain is a constant for a material body. It is denoted by Greek Letter σ (sigma). If α and β be the longitudinal and lateral strains respectively, then the Poisson’s Ratio,
σ = β/α
If a wire (rod or tube) of length l and diameter d is elongated om applying a stretching force by an amount Δl and its diameter is decreased by amount Δd, then
longitudinal strain = Δl/l
lateral strain = Δd/d
∴ Poisson’s Ratio, σ = Δd / d/δl / l = l Δd/d Δl
Since, Poisson’s Ratio is a ratio of two strains, it is dimensionless quantity and is purely a number. The value of Poisson’s Ratio depends only upon 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 volume, i.e., the body is perfectly incompressible, the value of Poisson’s Ratio is greatest, i.e., 0.5.