What is Strain

Elasticity

Elasticity is defined as the property of an object under which it resists any kind of change in its dimensions such as size and shape when any deforming force is exerted on it and regains its shape and size after the removal of the applied deforming force.

Stress 

When the deforming force is applied to a body within the range of its elastic limit, there are changes either in length or in the volume of the body. Due to the property of elasticity, an internal reaction force is generated in the body, which withstands any change and tends to bring the body back to its initial state. This internal reaction force is known as the restoring force. At equilibrium, the restoring force is exactly equal and opposite to the deforming force which is being exerted.  This restoring force acting on the unit area of the cross-section of a body is defined as Stress.

If the area of cross-section of a body is denoted by A and the external deforming force applied on the body is denoted by F, so the restoring force will also be equal to F, and hence, 

Stress = restoring force/ Area = F/A

The unit of stress is  Newton per metre square N/m2 and its dimensional formula is given as [ML-1T-2]

Types of stress:

1.  Longitudinal or tensile stress:  When the deforming force is applied over the length of the body the stress produced in the body is called longitudinal or tensile stress. 

2. Normal stress:  When the deforming force is applied normally to the surface of the body, the stress produced is called normal stress. The stress is expansive if there is an expansion in the volume of the body and the stress is compressive if the volume of the body decreases. 

3. Tangential or shear stress: When the deforming force is applied along the cross-section of the body, where the opposite face of the body is kept fixed, the stress produced here is known as shear stress.

Strain 

When a body is deformed by the exertion of deforming force, the body is said to be strained i.e. a body is called strained when the length/ volume/ shape of the body alters due to an external force acting on it. This alteration in measurements is directly proportional to the original dimension. Therefore the relative change which is produced in the body by the external force  is defined as Strain.

 Strain is the ratio of change in dimension to the original dimension.

Since strain is a ratio between two quantities of the same direction, it has no unit and no dimension.

Strain = change in dimension / original dimension

 Strain is classified into three different types, which are as follows:

1. Longitudinal strain:  If the application of deforming force exerted on a body across its length cause extension in the length of the body then the ratio of change in length of the body to the actual length is called longitudinal strain.

Longitudinal strain is usually denoted by the Greek letter “𝜺” (epsilon).

Let the original length of the body be L, and change in length by application of deforming force be l, then longitudinal strain can be written as

Longitudinal strain = change in length / original length= l/L

2. Volumetric strain: If the deforming force is applied across a body such that there is a change in the volume of the body, the ratio of change in volume to the initial volume of the body is known as volume strain.

We denote volumetric strain by theta “θ”.

 If V is the original volume and v is the change in volume produced by the applied external force then

Volumetric strain = change in volume / original volume = v/V

3. Shear strain: If the deforming force is applied to a body along its surface in a way where the volume of the body remains constant but an alteration in the shape of the body is observed. This type of strain is known as the shear strain. 

Strain is a dimensionless quantity.

 Hooke’s Law

Hooke’s law was given by British physicist Robert Hooke based on his experimental observations on elastic bodies. Hooke’s law states that –

“Within the limit of elasticity of a body, the strain generated in a body is directly proportional to the stress applied on that body”

i.e. stress ∝ strain

Or stress/strain = E

Where E is defined as the modulus of elasticity or coefficient of elasticity. It depends upon the nature of the substance.

Thus, the modulus of elasticity is defined as the ratio of stress to the corresponding strain produced, within the elastic limit. The unit of modulus of elasticity is N/m2. The dimensional formula for E is [ML-1T-2] which is the same as stress.

Conclusion

Stress is defined as the force per unit area on a body. Stress is a 3 types. On application of the deforming force if there is an alteration in any measurements of the body such as length, volume, or shape then the ratio of change in dimension to the initial dimension of the body is known as strain. Strain is of 3 different tpes. Strain is a dimensionless quantity. Strain  tells us how much an object is deformed when an external deforming force is applied on an object.