Question

define elastic constants and obtain relation amit
them​

Answer 1

Explanation:

Elastic constants :

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 :

$e \: = \: \frac{9kg}{g \: + \: 3k}$

Where,

• K is the Bulk modulus
• G is shear modulus or modulus of rigidity.
• E is Young’s modulus or modulus of Elasticity.

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.