# Poisson's ratio

An elastic parameter: the ratio of transverse contractional strain to longitudinal extensional strain. In other words, a measure of the degree to which a material expands outwards when squeezed, or equivalently contracts when stretched (though some materials, called *auxetic*, do display the opposite behaviour).

## Definition

## Other expressions

Expressed in terms of acoustic velocities, assuming the material is isotropic and homogenous:

In this case, when a material has a positive it will have a ratio greater than 1.42.

Expressed in terms of Lamé's parameters:

## Typical values

For incompressible material, `ν` is approximately 0.5. Cork has a value of about 0, meaning that it does not expand radially as it is compressed. Most rocks have `ν` between about 0.1 and 0.4.

Materials with negative Poisson's ratio, meaning that they get thinner as they are compressed, do exist. They are called *auxetic* and include the mineral α-cristobalite.

**Required:** a table of common (and relevant) values.

## External links

- Poisson's ratio — Wikipedia article

Conversion formulas — edit | |||||||||||
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The elastic properties of homogeneous isotropic linear elastic materials are uniquely determined by any two moduli. Given any two, the others can thus be calculated. Key reference: Mavko, G, T Mukerji and J Dvorkin (2003), The Rock Physics Handbook, Cambridge University Press.
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P-wave velocity |
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S-wave velocity |
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Velocity ratio |
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1st Lamé parameter |
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Shear modulus |
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Young's modulus |
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Bulk modulus |
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Poisson's ratio |
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P-wave modulus |