Shear modulus or Modulus of Rigidity is by definition
“The ratio of the shear stress to the shear strain is known as shear modulus”
Let’s assume a block as shown in the figure. The bottom face of the block is fixed and on the top face, a force F is acting normally. Then there will be a deformation in the block and the face tend to displace to a new position.
From this, the shear stress will be the force acting per unit cross-section of the face being sheared
Shear strain will be the displacement.
The shear modulus is the elastic modulus we use for the deformation which takes place when a force is applied parallel to one face of the object while the opposite face is held fixed by another equal force.
A material having a bigger shear modulus that means it will have high rigidity. So that why we call it as modulus of rigidity.
This can be denoted by G or S or µ
Units are Pascals
Due to the deformation, There is an approximation that “the is no change in volume in the deformation.