MIND GROW Magazine

Properties of Matter – Stage 1 (Page 9)

Poisson’s Ratio & Elastic Constants (JEE Core)

1. Poisson’s Ratio (μ or σ)

When a material is stretched longitudinally, it contracts laterally. The ratio of lateral strain to longitudinal strain is called Poisson’s ratio.

Poisson’s Ratio (μ) = − (Lateral Strain / Longitudinal Strain)

Sign Convention:
Negative sign indicates opposite nature of strains.

2. Range of Poisson’s Ratio

Material Type	Poisson’s Ratio
Ideal Rigid Body	0
Most Solids	0.25 – 0.35
Rubber	≈ 0.5
Auxetic Materials	Negative

IIT Note:
Poisson’s ratio lies between −1 and 0.5

3. Elastic Moduli (Important)

Young’s Modulus (Y) → Stretching
Bulk Modulus (K) → Volume change
Shear Modulus (G) → Shape change

4. Relations Between Elastic Constants

Relation	Formula
Y, K, μ	Y = 3K(1 − 2μ)
Y, G, μ	Y = 2G(1 + μ)
K, G, Y	Y = 9KG / (3K + G)

5. Special Poisson’s Ratio Cases

μ Value	Physical Meaning
μ = 0	No lateral contraction
μ = 0.25	Common metals
μ = 0.5	Perfectly incompressible

6. Numerical Shortcuts (JEE)

If μ = 0.5:
Bulk modulus → ∞
Material is incompressible

Fast Conversion:
Given Y and μ → Find G using:
G = Y / [2(1 + μ)]

7. JEE Frequently Asked Points

Rubber → μ ≈ 0.5
Steel → μ ≈ 0.3
Negative μ → auxetic materials
All three elastic constants are interrelated

Stage 1 – Page 9 Summary

Poisson’s ratio definition & range
Elastic constants relations
Special limiting cases
Direct numerical formulas

Stage 1 – Page 9 Completed ✅
Next: Elastic Energy & Stress–Strain Graph – Page 10

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