# What is Poisson’s Ratio : Strength of Material

When an external force is applied to a body. It’s length changes in the direction and perpendicular to the direction of the applied force. This effect is known as the Poisson effect. Poisson’s Ratio is a property of a material that is used to calculate Lateral or Longitudinal Mechanical Stress. In this article we will discuss what is Poisson’s ratio? and how to calculate it?

## What is Poisson's Ratio?

Mathematically Poisson’s Ratio is equal to the negative of the ratio of Lateral Strain and Longitudinal Strain within Elastic Limits. It is a unit less quantity and denoted by a symbol “ν“. It’s Value remains constant within the elastic limit.

## Poisson's Ratio Formula

When a tensile force is applied to a metal bar. It’s Length increases in the direction of applied force and width decreases in the direction perpendicular to applied force. This relationship between change in length and width is represented by Poisson’s ratio.

Mathematically Poisson’s Ratio is equal to the negative of the ratio of lateral strain and longitudinal strain.

Negative sign is used because compressive deformation is considered negative and tensile deformation is considered positive. Any one of the  lateral or Longitudinal strain will be compressive. Click this link!! for more details on Lateral or Longitudinal mechanical strain.

## Poisson Ratio Calculation Example

###### Problem:

Consider a steel bar of 100 mm length and 50 mm width. If after the application of 50 newton force, steel bar length is increased to 102 mm. What will be the change in width?

###### Solution:

Let’s consider steel bar width is reduced by dW mm

Poisson Ratio for Steel = 0.3

Longitudinal Strain = (102-100) / 100 = 0.02

According to poisson ratio formula:

0.3 = (dW / 50) /0 .02

(dW / 50) = 0.3 x 0.02 = 0.006

dW = 0.3

Therefore we can conclude that. For the above example, Metal bar width will reduced by 0.3 mm.

## Poisson's Ratio Values For commonly used Materials

Value of Poisson ratio for stable, isotropic materials should lie in between -1.0 to 0.5. Because it has a direct impact on the values of Young Modulus, Bulk Modulus and Shear modulus and their value can not be negative. But for most of the materials Poisson Ratio value varies in the range of 0 to +0.5. It is a scalar and unit less quantity.

MaterialPoisson's Ratio (indicative Purpose Only)
Cork0
Polystyrene Foam0.3
Steel0.27-0.3
Brass0.33
Copper0.35
Rubber0.499

## What is Positive Poisson Ratio?

If material length increases in the direction of applied tensile force. Whereas it reduces in the direction perpendicular to applied force. This type of material behavior indicates a positive Poisson Ratio. Most engineering materials available in the market exhibit this behavior.

## What is Negative Poisson Ratio?

If material length increases in the direction perpendicular to applied external force. This type of material behavior indicates a negative Poisson Ratio. Negative Poisson ratio materials are called Auxetics. They exhibit high energy absorption and resistance to fracture properties. They have applications in packing material, medical knee pads, footwear industry etc.

## Commonly Asked Questions on Poisson's Ratio

It is used to determine the impact of stress in a direction perpendicular to applied force. For example, Gas or liquid in a pipe exhibits hoop stresses inside the pipe.

Due to the poisson ratio these hoop stresses cause the longitudinal stress in the pipe. Which results in change in pipe length as well. Therefore pipe designers need to consider this impact during pipe joint design.

Yes, Cork has zero poisson’s Ratio.

Poisson ratio 0.5 indicates that the volume of the material will remain constant.

For compressive deformation.

Yes, Poisson ratio is a property of a material. It’s value is constant within the elastic limit of a material.

Yes, without this forces acting in the direction perpendicular to applied force can cause product failure.

To sum up, Poisson’s ratio is very useful while selecting material for an application. It’s Value is unit-less and constant within the elastic limit. For perfectly isotropic material, the value of Poisson ratio is equal to 0.25. We suggest you also read this article on Degree of Freedom in Mechanics.

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