# Poisson ratio

From Soft-Matter

## 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.