Considering 3 different types of stress for solids, we have 3 different types of elasticity modulus.
These are (a) Young’s Modulus (2) Shear Modulus (3) Bulk modulus
Young’s Modulus is the ratio of Longitudinal Stress and Longitudinal Strain. If it’s designated with Y then
Y = Longitudinal Stress / Longitudinal Strain = (F/A)/(l/L) = (FL)/(Al)
Its unit is N/m2 or Pascal. Please note that Strain is dimensionless. [see the derivation of the longitudinal modulus formula]
Also, see the numerical problem based on Young’s modulus.
Shear Modulus | Modulus of Rigidity
Shear Modulus is the ratio of Shear Stress and Shear Strain. This is also known as the Modulus of Rigidity.
If it’s designated as G then
G = (F/A)/(x/L) = (F/A)/θ = F/(Aθ). [see the derivation of the shear modulus formula]
Bulk Modulus (B)is the ratio of Hydraulic Stress and Volume Strain.
B = (F/A)/(Δv / V) = – P /(Δv / V)
Here P is the pressure. As the change in volume is indirectly proportional to the pressure applied, that’s why the negative sign is used.
[see the derivation of the bulk modulus formula]