Question

Give the theoretical and practical value of Poisson's ratio for all substances.

Answer 1

Answer:

The Poisson's ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. Most materials have Poisson's ratio values ranging between 0.0 and 0.5.

Answer 2

The lateral strain is proportional to longitudinal strain within the elastic limit and the ratio of two strains is called Poisson's ratio.

Longitudinal strain = $\rm \dfrac{\Delta l}{l}$

Lateral strain = $\rm -\dfrac{\Delta R}{R}$

Poisson's ratio:

$\rm \sigma = \dfrac{Lateral \: strain}{Longitudinal \: strain} \\ \\ \rm \sigma = \dfrac{ - \dfrac{\Delta R}{R}}{\dfrac{\Delta l}{l}} \\ \\ \rm \sigma = - \dfrac{\Delta R}{R} \times \dfrac{l}{\Delta l}$

• Poisson's ratio is a unitless & dimensionless quantity.
• Theoretical value of Poisson's ratio for all substance lies between -1 and +0.5
• Partical value of Poisson's ratio for all the substance lies between 0 and +0.5