Poisson's ratio.

Explanation

When a wire is axially stretched, its diameter decreases. That is , longitudinal extension causes lateral contraction. Conversely, longitudinal compression of a rod causes lateral extension. Thus, longitudinal strain is accompanied with lateral strain. Lateral is defined as the ratio of the change in diameter to the original diameter of a wire or rod.
Let L and D be the original length and diameter of the wire. When it is axially stretched, let the increase in its length be `DeltaL` and the decrease in its diameter be `DeltaD`.
Longitudinal strain = `("change in length")/("original length") = (DeltaL)/L`
Lateralstrain =`("change in diameter")/("original diameter")= (DeltaD)/D`
Lateral strain `propto` longitudinal strain
` :. ` Lateral strain = `sigma *` longitudinal strain
where the constant of proportionality `sigma` is called Poisson's ratio .
The ratio of the lateral strain to the longitudinal strain is called
Poisson's ratio (`sigma`) .
` :. "Poisson 's ratio," sigma = ("lateral strain")/("longitudinal strain") `
` = (Delta D//D)/(Delta L//L)`
As strain has no unit , Poisson's ratio is a pure number i.e., it has no unit.
For a homogeneous isotropic solid, theoretically, ` - 1 lt sigma lt 0.5`.
For most metals, ` 0.2 lt sigma lt 0.4`.