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/m^{2}.
E =
stress/stain = σ/ε = σ_{t}/ε_{t }= σ_{c}/ε_{c}
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/m^{2}.
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/m^{2}.
K = p/ε_{v}
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
(12µ)
Relation between E, C and K:
E=9KC/ (3K+C)
