Poisson Ratio (ν)

Poisson's ratio: ν = -ε_lateral/ε_axial

Poisson's ratio ν = -ε_lateral/ε_axial captures how much a material spreads out sideways when you pull on it lengthwise (or how much it bulges when you squeeze it). The number is dimensionless and is a property of the material itself. A few typical values: steel ≈ 0.30, aluminum 0.33, concrete 0.15–0.20, rubber ≈ 0.49 (almost incompressible), and cork ≈ 0. That last one is a real quirk, and it's exactly why cork slides into a wine bottle without expanding outward. Auxetic materials sit below zero (rare ones that get fatter when stretched). For isotropic materials the thermodynamic bounds are -1 ≤ ν ≤ 0.5. The ratio also ties the elastic moduli together through E = 2G(1+ν), where E is Young's modulus and G the shear modulus. As an example, pulling a steel bar axially by ε_axial = 0.002 gives ε_lateral ≈ -0.0006, so ν = 0.30.

Applications

It shows up across structural engineering, finite-element analysis (FEM in Ansys/Abaqus wants ν for every material you define), pressurized pipeline design, geotechnics such as soil and rock mechanics, biomechanics and prosthetic selection, the design of seals and O-rings, and the modeling of foams and auxetic metamaterials built to absorb impact.

FAQ

Why does ν have an upper limit of 0.5? At ν = 0.5 the material is incompressible, holding its volume constant. Anything higher would mean the volume grows when you squeeze it hydrostatically, which thermodynamics simply doesn't allow.

Can ν be negative? It can. Auxetic materials, including some foams and certain metamaterials, have ν < 0 and grow wider as you stretch them. That behavior makes them useful for absorbing impact and energy.

Does ν vary with temperature? A little. Most metals barely budge across their normal service ranges. Polymers and rubbers are another story, shifting more noticeably around the glass transition.