When a deforming force acts on a body, the body experiences a change in its dimensions (i.e., shape and size).
The ratio of the change ¡n dimension of the body to its original dimension is known as strain.
strain \( = \frac{\text{Changeindimension}}{ \text{Original} \ \text{dimension}}\)
Since, strain is a ratio of two similar quantities. Therefore, it has no units and dimensions. Strain is thus a dimensionless physical quantity.
Types of Strain
Under the influence of a deforming force, a body experiences change in its dimensions. It could be change in length, volume or shape of the body. Hence, there are three types of strains as classified below:
(a) Longitudinal strain: As the name suggests, under the influence of a deforming force, if there is a change in the length of the body, then the ratio of the change in length to the original length is called the longitudinal strain.
Longitudinal strain = \(\frac{ \text{Change}\ \text{in} \ \text{length} }{ \text{Original} \ \text{length}}\)
\( = \frac{\Delta L}{L}\)
where, ∆V is change in volume and; V is the original volume of the body.
(b) Volumetric strain: If a deforming force is applied, due to which there is change in the volume of the body, then the ratio of the change in volume to the original volume is called as the volumetric strain.
Volumetric strain = \(\frac{ \text{Change}\ \text{in} \ \text{volume} }{ \text{Original} \ \text{volume }}\)
\( = \frac{\Delta V}{V}\)
(c) Shear strain: Shearing strain is defined as the angle θ (in radian) through which a face originally perpendicular to the fixed face gets turned on applying tangential deforming force.
Shear strain = θ = tan θ
\(= \frac{\text{Relative} \ \text{displacement}\ \text{between}\ \text{ two}\ \text{ parallel}\ \text{ planes} }{ \text{Distance}\ \text{ between}\ \text{ parallel}\ \text{ planes} }\)
