Elastic constants & their relation

Elastic limit - The maximum stress which can be applied on a body without permanent deformation is called elastic limit.

Hook's law - Within the elastic limit stress developed in a body is directly proportional to strain produced in it.

Elastic constants & their relation

Corresponding to three different types of stress & strain; there are three different modulus of elasticity.

(i) Young's Modulus (Y) 

(ii) Bulk Modulus (K)

(iii) Modulus of rigidity (η) 

Young's Modulus (Y)

Within the elastic limits, ratio of longitudinal stress to longitudinal strain is called as Young's Modulus denoted by "Y".

Bulk Modulus (K)

Within the elastic limits, ratio of volume stress to volume strain is called as Bulk Modulus denoted by "K".

^{Negative sign indicates that when pressure increase volume decrease and vice versa.}

Compressibility

Reciprocal of bulk modulus of elasticity is known as compressibility.

    Compressibility is defined as fractional change in volume per unit increase in pressure.

Modulus of rigidity or Shear modulus (η)

Within the elastic limits, ratio of shearing stress to shearing strain is called as modulus of rigidity or shear modulus denoted by "η".

Poisson's ratio (δ)

When a wire is subjected to a load, it elongates so there is increase in length of wire but decrease in diameter of wire.

    longitudinal strain produces lateral strain in wire.

Definition of Poisson's ratio:

Within the elastic limits, ratio of lateral strain to longitudinal strain is called as Poisson's ratio denoted by "δ".

                          

it is a unit-less quantity.

Negative sign indicates that when pressure increase volume decrease and vice versa.

Relation between Y,K & η