What is strain? Define different types of strains.

Whenever a deforming force is applied on a body, the shape of the body changes. Strain is defined as the ratio of change in configuration to the original configuration.

Different types of strain are:

(i) Longitudinal strain: The deformation produced in the length of the body as a result of the deforming force is longitudnal strain. 
So, longitudinal strain is defined as the ratio of change in length (∆L) of body to its original length L.

$\mathrm{Longitudinal} \mathrm{strain} = \frac{\mathrm{\Delta L}}{\mathrm{L}}$

(ii) Volumetric strain: When the deforming force produces a change in volume only then the strain produced in the body is called volumetric strain. The volumetric strain is defined as the ratio of change in volume (∆V) of the body to its original volume V.

         $\mathrm{Volumetric} \mathrm{strain} = \frac{\mathrm{\Delta V}}{\mathrm{V}}$

(iii) Shearing strain: When only the shape of the body deforms without any change in it's volume, it is shear strain.
So, shearing strain is defined as the ratio of the relative displacement of the opposite faces of the body to the length of the cylinder L.

                $\mathrm{shearing} \mathrm{strain} = \frac{∆\mathrm{x}}{\mathrm{L}}$

All types of strains are dimensionless.