Poisson’s Ratio Origin

When the force is applied to a body, it undergoes certain deformations because of that force. Under the effect of that force, the object can contract and expand. And it is the study of the Poisson ratio of a material that will determine its characteristics under an applied force.

Calculation of the degree to which there will be a change in the material’s shape (contraction and expansion) is also a characteristic of the Poisson’s ratio. Calculating the Poisson ratio for the material makes it easier to predict how other objects made of the same material will react to force.

Poisson’s ratio

Lateral Strain

Lateral strain is the measure of change in the radius of a circular body when force is applied over it. This is given as the ratio of change in the radius of the circular body to the original radius of the body. This physical quantity is dimensionless because of the comparison between two entities of the same dimension. 

Lateral or transverse strain = (Change in the radius of the spherical body) / Initial diameter of the body

Longitudinal Strain

The longitudinal strain of a body refers to the change in the length of the body that is brought about because of the application of force on that body. Longitudinal strain for a body is given as the ratio of the change in length of the body to the original length. In its entirety, longitudinal strain happens to be a dimensionless or unitless physical entity. 

Longitudinal strain = (Change in the length of the body) / Initial length of the body

Poisson Ratio

Poisson ratio for a body is the physical entity that is negative of the ratio of the lateral strain on a body to its longitudinal strain. This is a scalar and unitless quantity, always acting in the direction perpendicular to that of the applied force. 

Poisson ratio of a body = -(Lateral or transverse strain) / longitudinal strain

This quantity tells us about the changes brought about in the material because of the exertion of force over it. It tells us about the degree to which the material will contract or expand under the action of applied force.

Poisson’s Ratio Formula

v = -(ϵt) / ϵl

where ϵt stands for the transverse or maternal strain over a body,

ϵl stands for the longitudinal strain that the body is currently going through; and

(-)ve sign denotes the direction of the Poisson ratio for the body, i.e., the direction of the Poisson ratio is perpendicular to the direction of applied force.

Poisson’s ratio stands for how a body can undergo deformation and strain before reaching its yielding or breaking point. The Poisson ratio at that yielding point gives the tensile strength of the given material.

The positive or negative sign over the value of the Poisson ratio determines whether the given material will shrink or expand under the application of stress and strain.

A body that has a negative Poisson ratio is most likely to shrink under the action of stress and strain. On the other hand, if a body has a Poisson ratio as positive, it will expand under the action of the applied force.

Poisson’s Ratio for Steel

The average value of the Poisson’s ratio for steel happens to be between 0.27 and 0.30. Because of the high longitudinal strain that steel can withstand, it has a relatively higher malleability and ductility. 

The Poisson’s ratio for steel means that this is the limit to which steel can be deformed while keeping it in its partial elastic character. Any more strain beyond that is enough to push the material over to its breaking point.

Poisson’s ratio is important to understand the properties of a given material under the effect of stress and strain. This physical quantity gives a good measure of the physical characteristics of the material.

Conclusion

Poisson’s ratio compares the expansion of a material to the compression when it is under the effect of a force. And because of the action of such force, that material changes shape. The Poisson ratio deals with the after-effects brought into the body after applying a force.