When a wire is subjected to a longitudinal strain, its elongation is naturally accompanied by a contraction in its diameter. Usually, under the influence of an external force, when a body elongates in any direction, it also undergoes contraction in a perpendicular direction. Conversely, when a body contracts in any direction under the influence of an external force.
It also elongates at the same time in perpendicular directions. So, longitudinal strain and maternal strain occur simultaneously in a body. If the lateral strain is low, then it is proportional to its longitudinal strain. The ratio of maternal strain to longitudinal strain is called Poisson’s ratio.
Poisson’s ratio = lateral strain / longitudinal strain
Let us consider a wire of initial length L and initial diameter D. If the increase in the length of the wire under the influence of the external force is l and the decrease in its diameter is d, then lateral strain = d/D, longitudinal strain = l/L
∴ Poisson’s ratio = d/D / l/L
Poisson’s ratio depends only on the nature of the material of a body. Since it is a pure number, it has no unit. It applies only to solids. In the case of liquids and gases, Poisson’s ratio is meaningless. Poisson’s ratio isn’t the ratio of stress to strain. It is an elastic constant.