Poisson's Ratio
ν = −ε_T/ε_L — rod extends axially, contracts laterally. See the grid deform.
Key Notes
Poisson's ratio σ_p (often ν) measures lateral contraction during axial stretching: σ_p = −(lateral strain)/(longitudinal strain).
When you stretch a rod axially, it gets THINNER laterally — both effects related by σ_p.
Range: 0 ≤ σ_p ≤ 0.5 for isotropic materials. Most metals: 0.25-0.35. Cork: ~0. Rubber: ~0.5 (essentially incompressible).
σ_p = 0.5: material is incompressible (volume unchanged when stretched). Rubber, soft tissues approach this.
σ_p = 0: no lateral contraction at all. Cork has ~0.04 — useful for bottle stoppers.
Some special materials (auxetics) have NEGATIVE Poisson's ratio — they expand laterally when stretched.
Links Young's modulus, bulk modulus, and shear modulus: B = Y/[3(1−2σ_p)], G = Y/[2(1+σ_p)].
Dimensionless quantity — pure number.
Formulas
Poisson's ratio (definition)
D = diameter; positive value because lateral strain is opposite to longitudinal.
Relation to Y, B
Bulk modulus rises sharply as σ_p → 0.5.
Relation to Y, G
Shear modulus depends on Y and σ_p.
Volume change
Becomes zero for σ_p = 0.5 ⇒ incompressible.
Important Points
σ_p is dimensionless and bounded between 0 and 0.5 for stable isotropic materials.
σ_p = 0.5 ⇒ incompressible (like rubber). At σ_p = 0.5, B → ∞.
When you stretch a wire, it gets thinner. Poisson's ratio quantifies how much.
Cork's near-zero σ_p makes it perfect for bottle stoppers — no lateral expansion when squeezed in.
Auxetic materials (negative σ_p) are man-made — used in protective equipment, exotic foams.
Two independent elastic constants describe an isotropic material — choose any two of {Y, B, G, σ_p}.
Poisson's Ratio notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.