Depending upon the three of strain, there are three types of elastic moduli, viz.
a) Young’s Modulus(Y) or modulus corresponding to longitudinal strain
b) Bulk modulus(K) or modulus corresponding to the volume strain
c) Rigidity modulus(N) or modulus corresponding to the shearing strain.

**TYPES OF MODULI OF
ELASTICITY**

Depending upon the three of strain, there
are three types of elastic moduli, viz.

a)
Young’s Modulus(Y) or
modulus corresponding to longitudinal strain

b)
Bulk modulus(K) or
modulus corresponding to the volume strain

c)
Rigidity modulus(N) or
modulus corresponding to the shearing strain.

**1
YOUNGS MODULUS(Y)**

**DEFINITION:**
it is defined as the ratio between the longitudinal stress to longitudinal
strain, within the elastic limits,

**i.**e
youngs Modulus(Y)= Logitudnal Stress\ Logitudinal Strain Nm^{-2} or
pascals

**Explanation:
**Let us consider a wire of length ‘L’
with an area of cross section ‘A’. Let one end of the wire is fixed and the
other end is loaded or stretched as shown in the figure.

Let ‘I’ be the change
in length due to the action of the force, then

**2
BULK MODULUS**

**DEFINITION:**
it is defined as the ration between the volume stress or bulk strain with in
the elastic limits

**Bulk
Modulus (K) =Bulk Stress\Bulk Strain Nm ^{-2}**

**Explanation:**
Let us consider a body of volume ‘V’ with an area of cross section ‘A’. Let
three equal forces act on the body in mutually perpendicular directions as
shown in the figure. Let ‘V’ be the change in volume, due to the action of
forces, then

**The
volume stress or bulk stress=F\A**

**The
volume strain or bulk strain=v\V**

**Bulk
Modulus (K) = (F\A)\(v\V)=FV\vA**

**K=PV\v
Nm ^{-2}**

Where,

**P=F\A**

**3
RIGIDITY MODULUS**

**Definition:**
it is defined as the ratio between the tangential stress to the shearing strain
within the elastic limit.

**Rigidity
Modulus (n)=Tangential Stress\Tangential Strain Nm ^{-2}**

**Explanation:**
Let us consider a solid cube ABCDEFGH wherein lower CDHG is fixed as applied
over the figure. A tangential force ‘F’ is applied over the upper face ABEF.
The result is that the cube gets deformed into rhombus shape A’B’CDE’F’GH i.e
the lines joining the two faces are shifted to an angle ø. If ‘L’ is the
original ‘l’ is the relative displacement of the upper face of the cube with
respect to the lower fixed face, then

We can write the
tangential stress=F\A

The shearing stress ø
cam be defined as the ration of the relative displacement between the two
layers in the direction of the stress, to the distance measured perpendicular
to the layer.

**Rigidity
Modulus (n)=tangential stress\Shearing strain=F\AøNm ^{-2}**

**4
POISSONS RARIO**

**DEFINITION:**
It is defined as the ratio between the lateral strain per unit stress (β) to
the longitudinal strain per unit stress (α), within the elastic limits.

**Explanation:**
Let us consider a wire, fixed at one end and is stretched alomg the other end
as shown in the figure.

Due to force applied
the wire becomes longer but it also becomes thinner i.e although there is an
increase in its length, there is a decrease in its diameter as shown in the
figure. Therefore the wire elongates freely in the direction of tensile force
and contracts laterally in the direction perpendicular to the force. Let ‘L’ be
the original length and ‘D’ be the original diameter of the wire after the application
of force, let the length increase from L to L+l and the diameter decrease from
D and d, then

Longitudinal Strain=l\L

And Lateral
Strain=(D-d)\D

The negative sign
indicates that longitudinal strain and lateral strain are opposite to each
other.

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