Question

Poisson's ratio for a perfectly incompressible linear elastic material is

Answer 1

Volumetric strain for linear elastic material is given by
$\text{Volumetric stain} =\frac{\Delta V}{V}= \frac{1-2\mu}{E}(\sigma_x+\sigma_y+\sigma_z)$

where, μ is poisson's ratio , E is Young's modulus of elasticity .
σ is stress.
For incomprehensible material, ∆V = 0
Then, 1 - 2μ = 0 ⇒ μ = 0.5