# What is Poisson’s Ratio?

Poisson’s ratio is the correlation between lateral strain and axial strain. The figure denotes the negative of the ratio of lateral (or transverse) compression to axial extension .

The value measures the manifestation of the Poisson effect, an occurrence in which the material exhibits a compression response that is perpendicular to an axial stretching force. The best visualisation of this phenomenon is the rubber band. When stretched, the material becomes thinner than its relaxed state.

The parameter is named after Simeon Poisson, a French mathematician who used molecular theory in order to come up with the figure.

The theoretical framework behind this characteristic has something to do with the material’s structure. The deformation caused by the stretching force may be attributed to the realignment of bonds between atoms .

Poisson’s ratio is a dimensionless parameter, and is usually represented by ν (Greek lowercase nu). It is also referred to as the Poisson Coefficient.

## How is it measured?

Since Poisson’s ratio deals with minor changes in axial strain, the right equipment needs to be used in order to measure it. A strain measuring device, such as an extensometer, records minute amounts of deformation, from which the value of the material’s Poisson’s ratio may be calculated.

To start the measurement, a test specimen with a predetermined length and width is placed in a strain measuring tool. A stretching force of a known amount is applied to the material, and its changes in length and width are measured.

From this data, the amounts of strain for both axial and lateral orientations are calculated by dividing the change in measurement by its original measurement. Poisson’s ratio is then computed by getting the negative of the ratio of lateral strain to axial (or longitudinal) strain.

A high Poisson’s ratio denotes that the material exhibits large elastic deformation, even when exposed to small amounts of strain. Meanwhile, a material of which the Poisson’s ratio is near to zero does not elastically deform regardless of the magnitude of the strain.

## Poisson’s ratio of materials

This characteristic may differ from material to material, depending on how each one reacts to strain.

Rubber has one of the highest values of Poisson’s ratio at 0.4999, which is evident in its physically noticeable reaction to axial stretching.

Cork is measured to have a Poisson’s ratio of close to zero. Even when exposed to compression or pull, the material’s width or diameter remains the same.

Here are the Poisson’s ratio values for some of the most commonly used materials :

• Gold: ν = 0.44
• Magnesium: ν = 0.35
• Copper: ν = 0.33
• Clay: ν = 0.45
• Steel: ν = 0.30
• Concrete: ν = 0.20
• Foam: ν = 0.10 – 0.40

A special class of materials known as auxetics  are unique in the sense that they exhibit a negative Poisson’s ratio. When a pulling or stretching force is applied, the material increases in thickness. Materials that belong to this classification include graphene , alpha-Cristobalite , and selected polytetrafluorethylene polymers .

## Applications where Poisson’s ratio is important

Cork as bottle stopper

The near-zero Poisson’s ratio for cork makes it an ideal material as a bottle stopper. This is because cork almost does not expand even when compressed on either side. In contrast, a rubber stopper will expand laterally when exposed to axial compression. This causes the rubber material to get jammed in the bottle’s neck.

Fluid pipelines

Materials used in handling pipe flow should have a minimal Poisson’s ratio to prevent deformation. When exposed to high fluid pressure, the internal walls of the pipe receive a substantial amount of force that may cause a slight increase in the interior diameter and a minor shortening of the pipe length. When these phenomena occur, the risk of leaking and disconnection may increase.

Material strength

In the case of metals and alloys, the parameter holds importance in determining the effect of tensile and compressive stresses on the material. An alloy or metal with a high Poisson’s ratio may not bode well in high-stress environments where material integrity is essential, despite the presence of stretching or compression forces.

## Sources

 Gere, J.M. and Goodno, B.J. (2008) Linear Elasticity, Hooke’s Law and Possion’s Ratio. In Mechanics of Materials, Seventh Edition. (pp. 27-29). Boston, MA: Cengage Learning

 (n.d.) Poisson’s Ratio Metals Material Chart. Engineers Edge. Retrieved from: https://www.engineersedge.com/materials/poissons_ratio_metals_materials_chart_13160.htm

 Ren, X. et al. (2018) Auxetic Metamaterials and Structures: A Review. Smart Mater. Struct. 27 023001

 Grima, J. N. et al. (2018) Giant Auxetic Behaviour in Engineered Graphene. Ann. Phys. (Berlin) 1700330

 Yeganeh-Haeri, A. et al. (1992) Elasticity of alpha-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio. Science 257 (5070), 650-652.

 Caddock, B.D. and Evans, K. E. (1989) Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties. J. Phys. D: Appl. Phys. 22 1877-1882.

### Did you know?

Rubber has one of the highest values of Poisson’s ratio at 0.4999, which is evident in its physically noticeable reaction to axial stretching.