According to Hooke’s Law  strain is proportional to the stress (under certain circumstances). In other words we can say that under certain conditions  strain is directly proportional to the stress.  This means that when more force is applied to pull the material the more it expands and when more compressed force is applied more it gets compact.

Mathematically ,
Strain α Stress

According to Hooke’s law,
Stress / Strain = E
Where E is a constant known as “Coefficient of elasticity” or “modulus of elasticity” or “Elastic Modulus”

When a deforming force is applied on the body produces change in shape of body then this strain is called the shearing strain. Solids alone can have a shearing strain.

The formula for Shearing (or) Rigidity strain is given as,

Shearing strain = Relative displacement of any layer / Its distance from fixed layer

As the linear strain is ratio of lengths, it has no unit and dimension.

In the above figure  shearing strain = Δx / h.

When there is a change in volume of the body, without any change in its shape because of a force which is applied uniformly and normally it is known as Bulk strain.
Volume strain is defined as change in volume of body per unit original volume is volume strain.

If Δv is the change in volume produced in a body of original volume V,then the formula for bulk or volume strain is given as,

Bulk or Volume strain = Change in volume / Original Volume.

Bulk or Volume strain = Δv / V

As the linear strain is ratio of lengths, it has no unit and dimension.

The linear strain is the ratio of change in length to the original length.
The length is shortened in the direction of the forces when the forces are compressive. This is called the linear strain or Compressive Strain . If the change in length is ‘ l ‘ in a wire or bar of original length L,
the formula for Linear strain or longitudinal strain is given as,

Linear Strain or Compressive Strain = Change in length / Original Length

Linear Strain or Compressive Strain =  Δ l / L

The change in length can be an increase or decrease.
As the linear strain is ratio of lengths,it has no unit and dimension.

When an external deforming force applied on the body it produces change in shape of body which is known as shearing stress.

The formula for shearing stress is given as,

Shearing Stress = tangential applied Force / Area

Shearing Stress = F/A

In the above figure Shearing Force F1 is applied to one face of Square which causes deformity in square known as Shearing Stress