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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. When subjected to positive strain in a longitudinal axis, the transverse strain in the material becomes positive thereby increasing the cross-sectional area.

Most 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.

Poisson’s Ratio for Common Materials

MaterialPoisson’s Ratio
Rubber0.4999
Magnesium0.252–0.289
Titanium0.265–0.34
Copper0.33
Aluminum-alloy0.32
Clay0.3-0.45
Stainless Steel0.3-0.31
Cast Iron0.21–0.26
Concrete0.1–0.2
Glass0.18–0.3
Cork0.0
Foam0.10–0.50
Sand0.20–0.455
Table 1: Commonly used materials with their Poisson’s ratio values

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.

Applications of Poisson’s Ratio

  • Pipelines carrying fluids with high fluid pressure, receive a substantial amount of force on the internal walls that may cause a slight increase in the interior diameter and a minor shortening of the pipe length. This increases the risk of leaking and disconnection.
  • Manufacturing of packing materials like foam for long lasting shock absorption.
  • Using auxetic materials in medical kneepads and footwear for sport purposes.

Last updated: August 4th, 2022

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