Poisson’s Ratio Formula

As stated in its definition, Poisson Ratio is given as the negative of the ratio of the transversal strain to the longitudinal strain its formula is mentioned below:

ν = -ε_t/ε_l

Where,

• ν is Poisson’s Ratio
• ε_t is Transversal Strain, and
• ε_l is Longitudinal Strain.

The negative sign in the ratio is used to make the ratio positive because the numerator i.e. transversal strain is generally negative due to a decrease in breadth. Thus Poisson’s Ratio is generally positive in nature, however in the case of material whose thickness increases on applying tensile stress such as polymers then that material will have a negative Poisson Ratio. Poisson Ratio is an scalar quantity.

Unit of Poisson Ratio: Since the Poisson Ratio is a ratio change in the length along transversal and longitudinal directions it has no unit.

Dimension of Poisson Ratio: Since there is no unit of Poisson Ration, there is no dimension of Poisson Ratio.

Poisson Effect

The Poisson effect is a phenomenon in which a material expands in directions perpendicular to the direction of compression. Poisson’s ratio is a measure of this phenomenon. When a material is stretched rather than crushed, it tends to contract in directions that are transverse to the stretching direction.

Poisson’s Ratio is the negative ratio of transversal strain or lateral strain to the longitudinal strain of a material under stress. When a material particularly a rubber-like material undergoes stress the deformation is not limited to only one direction, rather it happens along both transversal and longitudinal directions. In this situation, material scientists are curious to know the ratio of transversal and longitudinal deformation that occurred in the object to know about the strength of the material.

In this article, we will learn about the longitudinal and transversal strain, the calculation of the Poisson Ratio, and other related aspects in detail.