Explanation:
Realation between Elastic constants :
- Young’s modulus, bulk modulus and Rigidity modulus of an elastic solid are together called Elastic constants. When a deforming force is acting on a solid, it results in the change in its original dimension. In such cases, we can use the relation between elastic constants to understand the magnitude of deformation.
Elastic Constant Formula
E = 9KG/G + 3K
Where,
- G is shear modulus or modulus of rigidity.
- E is Young’s modulus or modulus of Elasticity
Derivation of Relation Between Elastic Constants
We can derive the elastic constant’s relation by combining the mathematical expressions relating terms individually.
- Young modulus can be expressed using Bulk modulus and Poisson’s ratio as –
E = 3K ( 1 - 2u)
- Similarly, Young’s modulus can also be expressed using rigidity modulus and Poisson’s ratio as-
E = 2G (1 + 2u)
- Combining the above two-equation and solving them to eliminate Poisson’s ratio we can get a relation between Young’s modulus and bulk modulus k and modulus of rigidity as -
E = 9KG/G + 3K
Hope you have understood the relation between Young’s modulus and bulk modulus k and modulus of rigidity.
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