Elastic Constant

 

Elastic Limit:

When an external force acts on a body, the body tends to undergo some deformation. If the external force is removed and the body comes back to its original shape and size, the body is known as an elastic body. This property, by virtue of which certain materials return back to their original position after the removal of the external force, is called elasticity.

The body will regain its previous shape and size only when the deformation caused by the external force, is within a certain limit. Thus there is a limiting value of force up to and within which, the deformation completely disappears on the removal of the force. The value of stress corresponding to this limiting force is known as the elastic limit of the material.

 

Hooke’s law:

It states that when a material is loaded within the elastic limit, the stress is proportional to the strain produced by the stress. This means the ratio of the stress to the corresponding strain is a constant within the elastic limit.

 

Stress /Strain = Constant

 

This constant is known as elastic constant.

 

 

Types of Elastic Constants:

There are three elastic constants;

Young’smodulus or Modulus of elasticity (E) = Normal stress/ Normal strain      

 

Shear modulus or Modulus of Rigidity (G) = (Shear stress/ Shear strain) 

 

Bulk modulus (K) = (Direct stress/ Volumetric strain)        


Young’s Modulus or Modulus of elasticity (E):

It is defined as the ratio of normal stress (σ) to the longitudinal strain (e).

E = (σn) / (e)

 

Modulus of Rigidity or Shear Modulus (G or C):

It is the ratio between shear stress (τ) and shear strain (es). It is denoted by G or C. G=τ/es

 

Bulk Modulus or Volume Modulus of Elasticity (K):

It may be defined as the ratio of normal stress (on each face of a solid cube) to volumetric strain. It is denoted by K. Bulk modulus is a measure of the resistance of a material to change of volume without change of shape or form.

K = (Direct Stress / Volumetric strain0

= σ/ev

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