Bulk or Volume modulus (k) is defined as the ratio of volume stress to volume strain within elastic limit. In other words if the Hooke’s Law is followed,  a small change in pressure produces a proportional change in volume. Bulk modulus of material indicates its resistance to change in volume. It corresponds to volumetric strain.

A body subjected to a uniform compressive force has its volume decreased and the resultant strain is a bulk or volume strain. Consider Δv as the change in volume and V is the original volume, then If F is the total compressive force acting on a total area A, then

Bulk stress = Force / Area = Pressure (P)

Bulk modulus (k) = Bulk Stress/ Bulk strain

If Pressure (P)  is the stress applied i.e. (force/unit area) then,

Bulk strain = Δv / V

The formula for Bulk or Volume modulus (k) is given as,

The unit for bulk modulus is ‘newton metre-2 (N m-2). The single term unit which is widely used for bulk modulus is ‘pascal’ with symbol ‘Pa’.

Tensile Modulus , Modulus of Elasticity, Young modulus is defined as the stress required to cause a unit strain in the material. It is the ratio of linear stress to linear strain. In other words Young modulus is used to measure the elasticity of an elastic material. It corresponds to linear or tensile strain.

Let a wire of initial length L and cross-sectional area ‘ A’, undergo an extension l, when a stretching force ‘F’, is applied in the direction of its length.

Young’s modulus (modulus of elasticity) is given by-

Formula of Young’s modulus  = Linear Stress / Linear Strain.
Longitudinal or linear stress = Force / Area. = F/A
Longitudinal or linear strain = Change in length / Original length = l / L

Using the above formula we get,

The unit for Young’s modulus is newton metre-2 with symbol N m-2.
The single term unit normally used for Young’s modulus is ‘pascal’ with symbol ‘Pa’.

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.