Poission’s ratio

When material is loaded within elastic limit the ratio of lateral strain to the linear strain is constant and this called as "Poisson's Ratio".

And it denoted by µ (greek letter mu) or ¹ / _m.
The value of Poison's ratio varies from 0.1 to 0.5. The extreme values for concrete and rubber are 0.1 and 0.5 respectively.
Mathematically,

Poisson's Ratio = ^{Lateral strain} / _{Linear strain}

µ or ¹ / _m = ^{Lateral strain} / _e

For rectangular bar -

Consider a bar as shown in fig. bar having length(L), width(b) and thickness(t) subjected to pulling force(P) Due to this loading length of bar increases while decrease in width and thickness take place. Therefore linear strain is positive and lateral strain is negative. In this case,
Linear Strain = e = ^+δL / _L
Lateral Strain = ^-δb / _b or ^-δt / _t
∴ form Poisson's ratio, µ or ¹ / _m = ^{Lateral strain} / _e

Lateral strain = -µ X e