# Poisson’s Ratio¶

When a material is compressed or elongated in one direction, it causes deformation in other two perpendicular directions. This phenomena is called Poisson’s effect. Poisson ratio describes the relationship between the deformation along one axis to the deformation along other two perpendicular axis.It is given by:

$\nu = \frac {-\epsilon_t}{\epsilon_a}$

where, ‘$$nu$$‘ is the Poisson’s ratio, ‘$$\epsilon_t$$‘ and ‘$$\epsilon_a$$‘ are the strains in transverse and axial direction respectively, when the load applied only in the axial direction.

Poisson Effect in a material

Value of Poisson’s ratio ranges from -1 to 0.5.The material is called auxetic when the value is less than 0. Most of the metals such as steel and almunium have value between 0.2 to 0.35 and are considered compressible while the material such as rubber and some foams have value of 0.5 and are considered incompressible.

Note

1. Please avoid setting the value 0.5 for the Poisson’s ratio as it will lead to convergence problem, use 0.499 instead.
2. Poisson ratio has no units,it is a dimensionless quantity.