1.
Deformation: If an applied force causes a change in the
distance between the particles of a material body, it results in a
change in size or shape or both. Such a change in size or shape is
called deformation.
2. Deforming Force: A force causing deformation of a material
body is called a deforming force.
3. Elasticity: The property possessed by a material body due
to which it offers a resistance to the deforming forces and recovers
its original size and shape after the deforming forces are removed is
called elasticity.
4. Perfectly Elastic Body: A material body which completely
recovers its original size and shape upon removal of deforming forces
is called a perfectly elastic body. Example: Quartz fibre (almost perfectly elastic).
5. Plasticity: The property possessed by a material body due
to which it offers no resistance to the deforming forces and remains
in the deformed state even after removal of the deforming forces is
called plasticity.
6. Perfectly Plastic Body: A material body that does not
recover its original shape or size at all even after removal of the
deforming forces is called a perfectly plastic body. Example: Clay.
7. Internal Restoring Force: When deforming forces are applied
to an elastic body, internal opposing forces are set up which tend to
restore the body to its original size and shape. These forces are
called internal restoring forces.
Generally, Internal restoring force = Applied force.
8. Stress: The internal restoring force per unit area of the
body is called the stress.
\ Stress =

Internal restoring force

=

Applied restoring force


Area



Area

Units of Stress:
S I
Units  newton / metre^{2} (N
/ m^{2} )
CGS Units  dyne / centimetre^{2} (dyne / cm^{2})
Dimensions of Stress: [M^{1} L^{}^{1} T^{}^{2} ]
9. Types of Stress:
There are three types of stress.
 Longitudinal Stress or Tensile Stress: If the applied
forces cause a change in the length of a body, the stress is
called longitudinal or tensile stress.
If a mass M is attached at the free end of a wire of length l
and radius r suspended from a rigid support,

Longitudinal stress =

Applied
force

=

Mg



Area of
cross section

pr^{2}


 Volume Stress or Bulk Stress: If the applied
forces cause a change in the volume of a
body, the stress is called volume stress or bulk stress.
Volume stress is represented by the increase in pressure
resulting from the
application of compressive forces normally on all sides of the
body.
\ Volume stress

= Change in pressure = D P
= Applied force per unit area.
= Normal force / surface area.



 Shearing Stress: If the applied
forces produce a change in the shape of the body, the
stress is called shearing stress.
Consider a tangential force F applied to the upper surface of a
solid cube.
Let A be the area of the surface.
\ Shearing stress =

Tangential
force

=

F



Surface
area

A


10.
Strain: The ratio of the change in dimensions of the body to
the original dimensions is called the strain.
Since strain is the ratio of two similar quantities, it has no unit
and no dimensions.
There are three types of strain corresponding to the three types of
stress.
11.
Types of Strain
 Longitudinal or Tensile Strain: It is defined as
the ratio of the change in length to the original length.
Longitudinal strain =

Change in
Length

=

l



Original
Length

L

Where l is the increase in
length of a wire of length L due to the applied force.
 Volume Strain or Bulk Strain: It is defined as
the ratio of the change in volume to the original volume.
\ Volume strain =

Change in
volume

=

dV



Original
volume

V

 where dV is the change in the volume
of a body of volume V due to a pressure change dP.
 Shearing Strain or Shear: When a tangential
force is applied to a body, there is a lateral displacement of
the different layers of the body.

Shearing strain =

Lateral
displacement of a layer


its
distance from a fixed layer


=

AA'

= tan q = q (Since q is very
small and in radian)


AB

12. Elastic Limit: The
internal restoring force comes into play only when a deforming force
acts on a body. It opposes and balances the deforming force. However,
the internal restoring forces can only balance the deforming forces upto a certain limit. If the deforming force is
increased beyond this limit, the internal restoring forces cannot
balance the deforming forces and the body loses its elasticity.
Definition: The maximum value of stress upto
which the body shows elastic behaviour is
called the elastic limit.
13. Hooke's Law of Elasticity:
Within the elastic limit, the stress developed in a body is directly
proportional to the strain produced in it.
\ Stress µ strain.
Stress = E(strain), The constant of
proportionality E is called the modulus of elasticity
or the coefficient of elasticity.
Modulus of elasticity, E =

stress


strain

14. Modulus
of Elasticity:
The modulus of elasticity is defined as the ratio of the stress to
the corresponding strain within the elastic limit.
Units of Modulus of Elasticity (E):
E =

stress

.
Since strain has no units, the units of E are the same as that of
stress 


strain

Unit:
N/m^{2} in the SI system and dyne / cm^{2} in the CGS
system.
15. Elastic Constants (Moduli of
Elasticity):
There are three kinds of moduli of
elasticity corresponding to the three types of stress and strain.
 Young's Modulus (Y): It is defined as
the ratio of longitudinal stress to longitudinal strain within
elastic limit.
Consider a mass M attached to the free end of a wire of length L
and radius r attached to a rigid support. Let the
elongation of the wire due to the force Mg active downward be l.
\ Longitudinal stress =

Mg


pr^{2}

and
Longitudinal strain =

l


L


Young's modulus, Y =

Longitudinal
stress

=

Mg

/

l




Longitudinal
strain

pr^{2}

L


i.e.

Y =

M g L


p r^{2}l




 Bulk Modulus (K): It is defined as
the ratio of the volume stress to the volume strain within
elastic limit.
\ K =

Volume
stress


Volume
strain


Volume stress = Change in pressure, D P.
Volume strain = D
v/v where D v is
the change in the original volume v due to a
change in pressure D P.
\ K =

 DP

=

 VDP



DV/V

DV


\

K =

 VDP


DV



[The negative sign is introduced to make K positive. An
increase in pressure always causes a decrease in volume. Thus, if D P is
positive, D V will be negative.]
Modulus of Rigidity (h): It is
defined as the ratio of the shearing stress to the shearing strain
within elastic limit.
\ h =

shearing
stress


shearing
strain

Shearing stress =

F

, where F is the tangential force applied to a
surface of area A.


A

Shearing strain = q.
Hence, h =

F / A

=

F



q

A.q

\

h =

F


A.q



