Bulk Modulus of Elasticity

The bulk modulus is a numerical constant that characterizes the elastic properties of a solid or fluid when it is subjected to pressure on all sides. When pressure is applied to a material, its volume decreases, but it returns to its normal volume when the pressure is released. The bulk modulus is also known as incompressibility, which is a measure of the capacity of a substance to sustain changes in volume, when it is compressed on all sides. Bulk modulus is calculated as the quotient of the applied pressure divided by the relative deformation.

Bulk Modulus vs Elastic Properties

Elastic moduli are used to describe the properties of elastic materials.

Moduli of Elasticity

The elastic modulus is a material parameter that characterises the stiffness of a material and is one of the most essential qualities of solid materials. When deformation is elastic, it is the stress-to-strain ratio. When a deforming force is applied to a material until it reaches static equilibrium, a resistive force develops inside the material to fight the external force. The resistive force per unit area is referred to as stress (Force/Area). The length of the material will alter as a result of the application of deforming force.

Strain (ΔL/L) is the change in length of a material per unit length. This modulus may be thought of as the resistance of a material to elastic deformation. Moduli are classified into three categories, which are as follows:

1. Young’s Modulus of Elasticity (Y)
2. Bulk Modulus of Elasticity (B)
3. Modulus of Rigidity (η)

Bulk Modulus

The bulk modulus is a constant that describes how compressible a substance is. It is defined as the ratio of an increase in pressure to a reduction in the volume of a substance. The bulk modulus, together with Young’s modulus, shear modulus, and Hooke’s law, characterises a material’s reaction to stress or strain.

In equations and tables, bulk modulus is usually denoted by K or B. While it can be applied to any substance, it is most commonly used to explain the behaviour of fluids. It can be used to determine compression, compute density, and identify the types of chemical bonding inside a substance indirectly.

Because a compressed material returns to its original volume once the pressure is removed, the bulk modulus is considered a descriptor of elastic characteristics.

Pascals (Pa) or newtons per square metre (N/m2) in the metric system, or pounds per square inch (PSI) in the English system, are the units for the bulk modulus.

Elasticity

Elasticity is a material feature that allows the body to resist changes in shape or size when deforming forces are applied to it and to return to its original condition once the deforming forces are withdrawn. Rubber, steel, quartz fibre, and phosphor bronze are all examples of elasticity.

Formulas for Bulk Modulus

Powder diffraction can be used to determine a material’s bulk modulus by directing x-rays, neutrons, or electrons at a powdered or microcrystalline sample. the bulk modulus can be calculated by using the formula:

K = Volumetric stress / Volumetric strain

Where, K = Bulk Modulus

This is equivalent to saying it equals the difference in pressure divided by the change in volume divided by the original volume:

Bulk Modulus is given by:

K = (p1 – p0) / [(V1 – V0) / V0]

In this equation, p0 and V0 represent the starting pressure and volume, respectively, while p1 and V1 represent the pressure and volume observed after compression.

Bulk modulus elasticity can also be described in pressure and density terms:

K = (p1 – p0) / [(ρ1 – ρ0) / ρ0]

The initial and final density values are 0 and 1, respectively.

It is important to note that a material’s compressibility is an indirect measure of its bulk modulus; they are the reciprocal of each other. Thus, a material or particle with a high bulk bulk modulus can’t be compressed easily and vice versa.

Compressibility: According to the compressive modulus definition, “the reciprocal of the material’s bulk modulus of elasticity is called the material’s compressibility.” It is represented by the symbol β. Thus,

Compressibility, β = 1/K 

Compressibility is measured in metre2/newton and has the dimensional formula [M-1 L T-2].

Uses of Bulk Modulus

Bulk modulus is used to measure the solid’s incompressibility. Furthermore, the higher the value of K for a material, the greater its tendency to be incompressible. For instance, the value of K for steel is 1.6×1011 N/m2, while the value of K for glass is 4×1010 N/m2. In this case, K for steel is more than three times that of K for glass. As a result, glass is more compressible than steel.

Conclusion 

The bulk modulus is a numerical constant that characterizes the elastic properties of a solid or fluid when it is subjected to pressure on all sides. The bulk modulus is also known as incompressibility, which is a measure of the capacity of a substance to sustain changes in volume, when it is compressed on all sides. Bulk modulus is calculated as the quotient of the applied pressure divided by the relative deformation. The elastic modulus is a material parameter that characterises the stiffness of a material and is one of the most essential qualities of solid materials. It is important to note that a material’s compressibility is an indirect measure of its bulk modulus; they are the reciprocal of each other.