Question

define elastic constant and obtain relation among them 6000 words answer​

Answer 1

Explanation:

Young’s modulus, bulk modulus, and Rigidity modulus of an elastic solid are together called as 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=9KGG+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(1+μ) N/m2 or pascal(Pa)

The relation between Young’s modulus and bulk modulus E=3K(1−2μ) 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 –

E=3K(1−2μ)

• Similarly, Young’s modulus can also be expressed using rigidity modulus and Poisson’s ratio as-E=2G(1+2μ)
• 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=9KGG+3K

Hope you understood the relation between Young’s modulus and bulk modulus k and modulus of rigidity.

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Answer 2

define elastic constant and obtain relation among them