Poisson's Ratio Explained (Formula and Examples)

Most students are scared by the concept of Poisson's ratio. But you need not fear.

Definition

The Poisson's ratio describes the expansion or contraction of a material in directions perpendicular to the direction of the force applied.

Explaining the concept

Now let's take a minute to draw what this actually means:

In the example above a force is applied to compress a material. Consequently the material expands in the perpendicular direction of the force applied.

In another words, the length is reduced and the width is increased.

If the force was applied in the opposite direction the material would get thinner, like in a "workout elastic rubber".

In another words, the length is increased but the width is increased.

Why is important?

I have worked many years in a pipe laying company and a pipe mill. I can tell you it needs to consider the Poisson's effect when you stack lots of pipes together.

It is specially important in high pressure and temperature environments.

Imagine the combined effect of hundreds of pipes getting shorter because of the high pressure inside them?

So piping design takes this ratio very seriously.

The formula for Poisson's ratio (Equation)

So it is a ratio, but of what?

If a material is stretched or compressed in only one direction:

Symbols

  • 𝑣 is the poisson's ratio symbol.
  • ɛtrans is transverse strain.
  • ɛaxial is the axial strain.

Translating the math to our language:

The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain.

It can also be calculated in many other direction (x, y, z):

As you can see, the Poisson's ratio is a ratio of the transverse strain to the axial strain. And it doesn't matter which axis.

Poisson's ratio, modulus of elasticity, shear modulus and bulk modulus

These properties (Poisson's ratio, modulus of elasticity, shear modulus and bulk modulus) are correlated in the following way:

  • 𝑣 is the Poisson's ratio symbol.
  • E is the modulus of elasticity.
  • G is the shear modulus.
  • K is the bulk modulus.

Typical values

The Poisson's ratio typically lies between -1.0 and +0.5 for stable, isotropic materials. So you may probably be thinking:

Wow... can Poisson's ratio be negative?

Common materials will have positive Poisson's ratio and behave like we expect. But some will have negative numbers. Honeycombs, for instance, can have negative ratio values:

Rod Lakes

They are sometimes called anti rubber.    

Incompressible materials such as rubber, have a ratio near 0.5.

Practical example

Add subtitles if you need it:

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Materials: Poisson's Ratio Explained (Formula and Examples)
Poisson's Ratio Explained (Formula and Examples)
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