Poisson’s ratio in Physics | Longitudinal Strain and Lateral Strain – Elasticity

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Poisson’s Ratio Definition:
When a deforming force is applied at the free end of a suspended wire of length l and radius R, then its length increases by dl but its radius decreases by dR. Now two types of strains are produced by a single force. In the elastic regime, this ratio is a material constant with a value of about 0.3 for most metals.

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Poisson’s Ratio | Longitudinal Strain and Lateral Strain – Elasticity

Poisson’s Ratio Symbol:
v is commonly used as the symbol for the Poisson’s ratio

  1. Longitudinal strain = Δl/l
  2. Lateral strain = – ΔR/R

∴ Poisson’s ratio (v) = \(\frac{\text { Lateral strain }}{\text { Longitudinal strain }}=\frac{-\Delta R / R}{\Delta l / l}\)

Theoretical value of Poisson’s ratio:
The theoretical value of Poisson’s ratio lies between -1 and 0.5.

The practical value of Poisson’s ratio:
Its practical value lies between 0 and 0.5.

Relation Between Y, K, η and σ

(i) Y = 3K (1 – 2σ)
(ii) Y = 2η (1 + σ)
(iii) σ = \(\frac{3 K-2 \eta}{2 \eta+6 K}\)
(iv) \(\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta}\) or Y = \(\frac{9 K \eta}{\eta+3 K}\)

Important Points

  • For the same material, the three coefficients of elasticity γ, η and K have different magnitudes.
  • Isothermal elasticity of a gas Eγ = p where, p = pressure of the gas.
  • Adiabatic elasticity of a gas Es = γp
    where, y = \( \frac{C_{p}}{C_{V}}\), ratio of specific heats at constant pressure and at constant volume.
  • Ratio between isothermal elasticity and adiabatic elasticity \( \frac{E_{s}}{E_{T}}=\gamma=\frac{C_{p}}{C_{V}}\)

Elasticity:
Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity.

Deforming Force Elasticity
Stress Strain
Hooke’s Law Elastic Modulus
Types of Modulus of Elasticity Poisson’s Ratio
Stress and Strain Curve Thermal Stress
Cantilever Beam Torsion of a Cylinder