Bulk Modulus is defined as the ratio of

By Mandeep Kumar|Updated : September 27th, 2022

(a) Shear strain to shear stress

(b) Volumetric stress to volumetric strain

(c) Shear stress to shear strain

(d) Volumetric strain to volumetric stress

Bulk Modulus is defined as the ratio of volumetric strain to volumetric stress. It describes volumetric elasticity, or an object's propensity to deform when loaded evenly from all sides.

Ratio of Bulk Modulus

Bulk modulus of elasticity (K):

  • It is the opposite of compressibility and is defined as volumetric stress over volumetric strain.
  • The bulk modulus is a three-dimensional extension of Young's modulus.
  • Bulk modulus is represented by the letter K. (it is valid within the elastic limit).

i.e., K = -p/ ΔV/V

Unit of K is N/m² or Pa (Pascal) since 1 N/m² = 1 Pa

Hooke's law:

According to Hooke's law, a body's created stress will be precisely proportional to the change it undergoes within the elastic limit.

i.e., stress ∝ strain

∴ stress = E × Strain

Here, E is the proportionality constant, also referred to as the elasticity modulus.

Young’s Modulus of elasticity (E):

Young's modulus is the proportion of longitudinal (tensile or compressive) stress to longitudinal strain.

It is represented by the symbol E. (Its validity is within the elastic limit)

i.e., E = Longitudinal stress (σ)/ Longitudinal strain (ϵ) = F/A/ ΔL/L

Summary:

Bulk Modulus is defined as the ratio of (a) Shear strain to shear stress (b) Volumetric stress to volumetric strain (c) Shear stress to shear strain (d) Volumetric strain to volumetric stress

The volumetric stress to volumetric strain ratio is known as the bulk modulus. It explains the volumetric elasticity. The bulk modulus is also defined as the relative change in the volume of a body developed by a unit of tensile stress acting uniformly over its surface.

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