Bulk Modulus (B)

The bulk modulus is defined as the measure of decreasing the volume and increasing the pressure. It is used in measuring the mechanical properties of solids and other elastic modulus and the proportion of volumetric stress, which is related to the volumetric strain in a specific material while the material is deforming within the elastic limit.

So basically, the bulk modulus is just a numerical constant used to measure the elastic property of a solid or a fluid material when pressure is applied on all surfaces. Sometimes, the bulk modulus is also referred to as incompressibility. 

Elasticity

Elasticity, known as the ability when a material is deformed, returns to its original shape and size as the material or the object stretches back. Elasticity can be defined as the ability of an object to deform its shape and revert to its former size after being stretched or compressed due to the application of an external force. Most of the materials are known to exhibit elastic behaviour.

The bulk modulus of elasticity

• The bulk modulus of elasticity is also known as one of the measures of mechanical properties of solids.
• The bulk modulus is indicated by K or B in equations as well as in tables. When it is applied to a uniform substance, the compression often shows the elasticity of that substance, and it can be used in predicting the compression, the density, and the types of chemical bonding within the substance.
• The bulk modulus has Pascal (Pa) or Newton per square metre (N/m2) units in the metric system.
• There are different elastic moduli, and formulas are used for finding out the elasticity, such as Young’s modulus and the shear modulus.
• The relative formation is also known as strain, and it is found out by the change volume when it is divided by the original volume.
• The bulk modulus is also a specific form of Hooke’s law of elasticity, and the bulk modulus can also be found out when pressure is divided by strain.

Mathematical representation of bulk modulus of elasticity

This is the result of the relationship between the applied pressure and the resulting decrease in material volume. Mathematically, it is:

K = ΔP / (ΔV / V)

where:

K: bulk modulus

ΔP: Variation in pressure or force acting on a material per unit area.

ΔV: change in material volume due to compression

V: Initial volume of the material (in m3).

Bulk modulus factors

The main factors affecting the mass modulus of a liquid are:

• the temperature and 
• the fluid being entrained.

The volume coefficient decreases with increasing temperature. In other words, the lower the temperature of the liquid, the harder it is to compress it. The entrained gas (mainly air) has a significant influence on the mass modulus of the liquid. The more gas there is in the liquid, the lower the volume ratio. The exception is that the volumetric modulus of elasticity of the liquid is lower than the volumetric modulus of compression of air and vice versa.

The bulk modulus of water

The bulk modulus of water or liquid is closely related to the compressibility and the pressure required to change the volume of the liquid. Since most liquids are incompressible, it requires a large amount of pressure to be applied for any significant volume changes.

The water has a bulk modulus of approximately 300,000 psi (2.1 GPa), giving the compressibility of 3.3 × 10−6 (psi)−1.

Poisson’s ratio

Compressive deformation of cloth is negative, while tensile deformation is taken into account. If you apply a tensile force to a substance, it will develop stress akin to the applied force (P), which will be contracting the cross-section and elongate the length (ΔL). We can express the tensile strain ε as,

                     ε = ΔL/L.

 If you apply a compressive force, the corresponding strain  can be expressed as

                ε = -ΔL/L. 

This supported Hooke’s law. You can express the relation between stress and strain by the below-mentioned formula:

                        σ = Eε,

 where σ – stress

 E – modulus of elasticity 

and ε – strain.

Poisson’s ratio formula

Consider a piece of rubber that has a normal shape of a cuboid. If you start pulling it along its edges, it will start to compress in the middle.

In this case,

=-dB/B(l)=-dL/L

Conclusion

There are different uses and applications of bulk modulus and elasticity in our day-to-day life, such as fishing rods, mattresses, bracelets, and clothes. These all are closely related in describing the elastic properties of any solid or fluid. When the increased pressure has been applied on all the surfaces of the material, there are also many modules such as the Young modulus and Hooke’s law which are being exerted on our day-to-day life, such as in making bridges or in air balloons.