Question

define various elastic constants and establish relation between them ​

Answer 1

Answer:

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

Explanation:

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=9KG / G+3K

I don't study these topics therefore i go ogled it...

hope it will help u...