Poisson ratio

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Poisson effect

When a certain material is stretched in one direction, it tends to contract in the other two directions perpendicular to the direction of stretch. Conversely, when a sample of material is compressed in one direction, it tends to expand in the other two directions. This phenomenon is called the Poisson effect.

Definition

Assuming that the material is compressed along the axial direction:

<math>\nu = -\frac{\varepsilon_\mathrm{trans}}{\varepsilon_\mathrm{axial}} = -\frac{\varepsilon_\mathrm{x}}{\varepsilon_\mathrm{y}} </math>

where

<math>\nu</math> is the resulting Poisson's ratio,
<math>\varepsilon_\mathrm{trans}</math> is transverse strain (negative for axial tension, positive for axial compression)
<math>\varepsilon_\mathrm{axial}</math> is axial strain (positive for axial tension, negative for axial compression).

Phenomena Related to Poisson effect

In a highly pressured pipe, a stress pointing to the wall of the pipe is exerted by the flow inside. Due to Poisson effect, the diameter will increase while the length will decrease.

Reference

[1]