Poisson's ratio

A tensile stress in a particular direction causes extension (say $\epsilon_z$) in that direction and contraction in other two directions ($\epsilon_x$ and $\epsilon_y$). For isotropic materials:

$$v=-\frac{\epsilon_x}{\epsilon_z}=-\frac{\epsilon_y}{\epsilon_z}$$

For metals (if not given) can be taken as $v=0.34$. Rubber’s poisson’s ratio is $0.5$ which is the maximum possible value, mathematically.

Isotropic materials

Homogenous materials. $\epsilon_x=\epsilon_y$. $$