Difference between revisions of "Poisson's ratio"

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(Other expressions)
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==Other expressions==
 
==Other expressions==
Expressed in terms of acoustic velocities, assuming the material is isotropic and homogenous:
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Expressed in terms of acoustic velocities, assuming the material is [[isotropic]] and homogenous:
  
 
:<math> \nu = \frac{ \left( \frac{V_\mathrm{P}}{V_\mathrm{S}} \right)^2 - 2}{2\left(\frac{V_\mathrm{P}}{V_\mathrm{S}}\right)^2 - 2}</math>
 
:<math> \nu = \frac{ \left( \frac{V_\mathrm{P}}{V_\mathrm{S}} \right)^2 - 2}{2\left(\frac{V_\mathrm{P}}{V_\mathrm{S}}\right)^2 - 2}</math>
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In this case, when a material has a positive <math>\nu</math> it will have a <math>V_\mathrm{P}/V_\mathrm{S}</math> ratio greater than 1.42.
 
In this case, when a material has a positive <math>\nu</math> it will have a <math>V_\mathrm{P}/V_\mathrm{S}</math> ratio greater than 1.42.
  
Expressed in terms of Lamé's parameters:
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Expressed in terms of [[Lamé's parameters]]:
  
 
:<math> \nu = \frac{\lambda}{2\,(\lambda + \mu)}</math>
 
:<math> \nu = \frac{\lambda}{2\,(\lambda + \mu)}</math>

Revision as of 12:40, 31 March 2012

Dictionary entry for Poisson's ratio (edit)

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  1. REDIRECT Dictionary:Poisson’s_ratio

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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.

External links