Elastic Constants

Mechanical Engineering

Elastic Constants:

Young’s Modulus or Modulus of Elasticity: It is the ratio between compressive stress and compressive strain or tensile stress and tensile strain. It is denoted by ‘E’. Its units are GN/m2.

E = stress/stain = σ/ε = σt= σcc

Modulus of Rigidity or Shear Modulus of Elasticity: It is the ratio of shear stress (τ) to shear strain (γ). It is represented by ‘C’, ‘N’ or ‘G’. Its units are GN/m2.

C, N or G = τ/γ

Bulk Modulus or Volume Modulus of elasticity:  It is defined as the ratio of applied pressure (on each face of solid cube) to volumetric strain. It is represented by ‘K’. Its units are GN/m2.

K = p/εv

Poisson’s ratio: The ratio of lateral strain to linear strain is called Poisson’s ratio. It is denoted by ‘µ’ or ‘ν’ or ‘1/m’.

µ = lateral strain/linear strain = 1/m

The value of ‘µ’ varies from 1/3 to 1/4 depending upon the material.

Relation between the Elastic constants:

Relation between E and C: E = 2C [1+ µ]

Relation between E and K: 3K (1-2µ)

Relation between E, C and K: E=9KC/ (3K+C)