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Documentation

Poisson’s Ratio

When a material is compressed or elongated in one direction, it causes deformation in the other two perpendicular directions. This phenomenon is called Poisson’s effect.

Poisson’s ratio describes the relationship between the deformation along one axis to the deformation along the other two perpendicular axes. It is a dimensionless ratio given by:

$$\nu= – \frac {\epsilon_t}{\epsilon_a}$$

Where:

  • \(\nu\) is the Poisson’s ratio,
  • \(\epsilon_t\) and \(\epsilon_a\) are the strains in the transverse and axial directions, respectively, with the load being applied only in the axial direction.
poisson's ratio effect in a material
Figure 1: Poisson effect in a material on application of an axial load

In SimScale, this ratio is specified in the materials tab. It is possible to edit the values in case your material is not present in the materials library.

poisson's ratio specification in SimScale
Figure 2: Specifying the Poisson’s ratio for a material

The Poisson’s ratio ranges from -1 to 0.5. The material is called auxetic when the value is less than 0. Most of the metals, such as steel and aluminum, have values between 0.2 to 0.35 and are considered compressible. Materials such as rubber and some foams have a value of 0.5 and are considered incompressible.

Note

Please avoid setting the Poisson’s ratio value to 0.5, as it will lead to convergence problems. In this case, use 0.499 instead.

Last updated: September 16th, 2020

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