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
| \(E=\frac{9KG}{G+3K}\) |
Where,
- K is the Bulk modulus
- G is shear modulus or modulus of rigidity.
- E is Young’s modulus or modulus of Elasticity.
Individually Young’s modulus and bulk modulus and modulus of rigidity are related as-
| Formula | SI Units | |
| The relation between modulus of elasticity and modulus of rigidity | \(E=2G\left ( 1+\mu \right )\) | N/m2 or pascal(Pa) |
| The relation between Young’s modulus and bulk modulus | \(E=3K\left ( 1-2\mu \right )\) | N/m2 or pascal(Pa) |
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 –
- Similarly, Young’s modulus can also be expressed using rigidity modulus and Poisson’s ratio as-\(E=2G\left (1+2\mu \right)\)
- 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 -\(E=\frac{9KG}{G+3K}\)
Hope you have understood the relation between Young’s modulus and bulk modulus k and modulus of rigidity.
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