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
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 | N/m2 or pascal(Pa) | |
The Relation Between Young’s Modulus and Bulk Modulus | 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-
- 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 -
Hope you have understood the relation between Young’s modulus and bulk modulus k and modulus of rigidity.
Physics Related Topics:
Tensile stress |
Longitudinal strain |
Bulk modulus |
Shearing Stress |
See the video below to learn about the elastic property of matter.
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