Elastic Constant (Modulus of Elasticity/Modulus of Rigidity)

Hook's Law states that, when a material is loaded within elastic limit, the stress is proportional to the strain produced by the stress.

Stress ∝ Strain 

This constant is known as Modulus of Elasticity or Modulus of Rigidity. 

Modulus of Elasticity:

The ratio between tensile stress and tensile strain or compressive stress and compressive strain is called Modulus of Elasticity or Young’s Modulus. It is denoted by E. 

σ α ϵ 

σ =E.ϵ 

Modulus of Rigidity:

The ratio between Shear Stress and Shear strain is called modulus of rigidity or shearing modulus of elasticity or modulus of transverse rigidity. It is denoted by G.

r ∝ γ 

r = G.γ