Poissons Ratio
Poisson’s ratio, and why metal gets thinner when you pull it
Stretch a rubber band and it gets longer. It also gets thinner — and you already knew that without being told. Poisson’s ratio is just the number that says how much thinner.
The one equation
Strain is simply how much something changed, divided by how big it was to start with. Pull a 100 mm bar to 101 mm and the longitudinal strain is 0.01.
ν = − ( lateral strain / longitudinal strain )
ν (nu) = Poisson’s ratio · lateral = across · longitudinal = along the pull
Why the minus sign? By convention, stretching is positive and shrinking is negative. When you pull a bar, the length grows (+) and the width shrinks (−). Dividing one by the other gives a negative answer, so the minus sign flips it back to positive. It exists purely so that ordinary materials have a positive Poisson’s ratio. Nothing deeper than that.
Typical values
Poisson’s ratio has no units — it is a plain number, and for almost every real material it sits between 0 and 0.5.
| Material | ν | What that means in practice |
|---|---|---|
| Cork | ~0.0 | Barely spreads when squeezed. Precisely why it goes into a wine bottle and stays there. |
| Steel | 0.27 – 0.30 | The working range for most structural and sheet steels. |
| Stainless 304 | ~0.29 | Close to carbon steel. |
| Aluminium | ~0.33 | Spreads more than steel for the same squeeze. |
| Copper | ~0.34 | Similar to aluminium. |
| Concrete | 0.1 – 0.2 | Low. Part of why it behaves so differently from metal. |
| Rubber | ~0.4999 | Effectively incompressible — squeeze it and the volume barely changes, it just moves. |
Where this touches sheet metal
Bend a strip and the outside of the bend has further to travel than the inside. The outer fibre stretches, and because of Poisson’s effect it thins. The inner fibre compresses, and it thickens.
Between them is a layer that does neither — the neutral axis. It never sits exactly in the middle. It shifts toward the inside of the bend, and it shifts further as the radius gets tighter.
It also explains a failure you have probably seen. On a very tight bend, the outer fibre thins so much that it cracks. That is not bad steel. It is the material running out of ability to stretch, and it is why minimum bend radius exists as a rule at all.
The honest limits
Everything above assumes an isotropic material — one that behaves the same in every direction. Rolled sheet is not truly isotropic. Grain direction matters, which is why bending along the rolling direction behaves differently from bending across it.
These figures also describe elastic behaviour, the deformation a material recovers from. Bending takes metal well past that point into plastic deformation, where the relationships get more complicated. Poisson’s ratio explains why the thinning happens; it will not tell you exactly how much on a real press brake.