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Modulus of elasticity is the measure of the tendency of an object or a substance to get deformed when force is applied to it. Let us know how to calculate modulus of elasticity and what the various types of elasticity modulus are. The modulus of elasticity is graphically represented as the slope of stress-strain. It is represented by the symbol “λ” and measured in the units of stress i.e. Pascal’s.

Modulus of elasticity of a substance is given as,

There are basically three types of modulus of elasticity, viz. Young’s modulus of elasticity, shear modulus of elasticity, and bulk modulus of elasticity.

Young’s modulus of elasticity

• Young’s modulus of elasticity describes the tendency of an object to get deformed along its axis. It is sometimes simply called as modulus of elasticity.
• Young’s modulus of elasticity is represented as E and it can be found out by dividing tensile stress by tensile strain.
• The formula for calculating Young’s modulus is given as,

E =

E = ρ/є

E = (F/A₀) / (∆L/L₀)

Simplifying the above equation,

E = (FL₀)/A₀ ∆L

In the above equation,

• E = Young’s modulus
• F = force applied to the object
• A₀ = cross section area through which the force is applied
• ∆L =  length through which the object is elongated
• L₀ = original length of object

Shear modulus of elasticity

• Shear modulus of elasticity is the deformation of an object at constant volume. It describes the shear tendency of an object.
• Here, the forces act only from the opposite direction.
• It is represented by the symbol G or μ and is calculated as the ratio of shear stress to shear strain.
• It is also called as modulus of rigidity.
• The formula for calculating shear modulus of elasticity is given as,

G =

G =

G = (F/A)/ (∆x/I)

This can be simplified as,

G = (FI)/ (A ∆x)

In the above formula,

• T_xy = shear stress

• 
• = shear strain which is equal to tan

• F = net force acting on the object
• A = area of the object on which the force acts
• ∆x = transverse displacement
• I = initial length

Bulk modulus of elasticity

• Bulk modulus is the measure of the substance’s resistance to uniform compression.
• In this, the forces act in all directions and the object is deformed in all directions.
• It is defined as volumetric stress over volumetric strain.
• It is basically the extension of Young’s modulus in all directions.
• Bulk modulus of elasticity is represented by the symbol K.
• The formula for calculating bulk modulus of elasticity is given as,

In the above formula,

• K = bulk modulus of elasticity
• V = volume of the object
• ∂P/∂V = partial derivative of pressure with respect to volume of the substance

These are the most used modulus of elasticity of the substances. There are three more moduli of elasticity viz. P-wave modulus, Poisson’s ratio and Lame’s first parameter.

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