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What is Poisson's Ratio?

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  • Written By: John Lister
  • Edited By: Bronwyn Harris
  • Last Modified Date: 28 October 2016
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Poisson's ratio deals with the way stretching or compressing an object in one direction causes it to compress or stretch in the other direction. The ratio measures the extent of this effect in a particular substance. This can vary considerably, and the ratio can even be negative, usually in man-made substances.

The technical definition of Poisson's ratio is “the ratio of transverse contraction strain to longitudinal expansion strain.” This sounds complicated, but describes a fairly simple effect. To picture it, imagine a piece of rubber, such as that used in a rubber band. When you stretch the band, it becomes both narrower and longer. The relationship between these two changes is what’s measured by Poisson's ratio.

In reality, Poisson's ratio applies in three dimensions. In the rubber band example, the thickness of the stretched band also decreases – it’s just harder to see. To picture the effect in three dimensions, imagine taking a pet toy in the shape of a cube and squeezing two opposite sides. The cube will get contract in the direction between these two sides, but will expand in the other two directions.

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In most cases, Poisson's ratio is positive, meaning a material stretches in one direction by a greater degree than it contracts in other directions. There are a couple of explanations for this, using different scientific approaches. A simple explanation is that most materials are better able to resist the compression than they are to resist the stretching. A more complicated explanation is that the bonds between the atoms in the structure become realigned during the process of stretching and compressing.

In most cases, a material’s Poisson ratio will range between 0 and 0.5. Among common materials, rubber has a Poisson ratio very close to 0.5, whereas steel has one of 0.3 and cork is much closer to 0. This is why wine corks are made of cork: it can withstand the pressure from the neck of the bottle without stretching vertically and jamming in place.

It is possible to have a negative Poisson ratio. Materials displaying this quality are known as auxetics. With such materials, stretching them in one direction will actually cause them to expand in other directions. It’s suspected that living bone tissue is an auxetic, though this is difficult to prove. There are also several man-made auxetic substances, most notably the polymers used in Gore-Tex waterproof clothing.

Poisson's ratio is used in more complicated ways in several fields of science. When you bend an object in one direction, Poisson's ratio affects the way the object curves in the perpendicular direction. The ratio also affects the way stress waves travel through substances such as rock, meaning it has some important uses in geology.

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