Elastic Constants: Stress produces a strain, but how much strain is produced depends on the solid itself. The solid is then characterised by anelastic modulus that relates strain to stress.>
Different types of stresses and their corresponding strains within elastic limit are related which are referred to as elastic constants. The three types of elastic constants (moduli) are:
Modulus of elasticity or Young’s modulus (E),Bulk modulus (K) andModulus of rigidity or shear modulus (M, C or G).Young’s modulus
Rigidity modulus
Bulk modulus
Poisson’s Ratio (µ): is defined as ratio of lateral strain to axial or longitudinal strain
Poisson Ratio=-(Transverse Strain/Axial Strain)
(Under unidirectional stress in x-direction)
Young’s modulus or Modulus of elasticity (E) = (PL /Aδ)= σ/∈ Modulus of rigidity or Shear modulus of elasticity (G) =τ/γ= PL /Aδ Bulk Modulus or Volume modulus of elasticity (K) = -(Δ p/p)/(Δv/v) =(Δp)/(ΔR/R )
Relationship between the elastic constants E, G, K, µ :
where K = Bulk Modulus, μ= Poisson’s Ratio, E= Young’s modulus, G= Modulus of rigidity
Hooke's Law (Linear elasticity)
Hooke's Law stated that within elastic limit, the linear relationship between simple stress and strain for a bar is expressed by equations.
Where, E = Young's modulus of elasticity
P = Applied load across a cross-sectional area
Δl = Change in length
l = Original length
Free expansion of 1 due to temperature rise
Free expansion of 2 due to temperature rise
Expansion of 1 due to temperature stress (tensile)
Compression of 2 due to temperature stress (compression)
