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What is stress? What is strain? What is the relation between them? What are the types of stress and strain?

  In physic, stress may be defined as the restoring force acting on a unit area of a material or object. In maximum cases, this restoring force is equal to the external force. So stress may also define as an external force per unit area of an object. 

If we consider a rod, which is tight on a wall as shown in the figure below



and apply stress or deforming force to it, then the rode opposes this deforming force by producing a restoring force because the rode is in static equilibrium that means the net force is zero. In this case,

Restoring force = Deforming force

It is a tensor quantity (in simple words, tensor quantity means we easily calculate its value by using simple mathematics.)

   The Formula of stress is Ïƒ = F/A

   Dimension of stress is [ML^-1T^-2] {Force=mass x acceleration = mass x (velocity/time)

    =kg x (meter/second/second) = kg x (meter/second^2) = kg meter second^-2= [MLT^-2]}

{Area = meter^2 = [L^2] }

{F/A = [MLT^-2]/ [L^2] = [ML^-1T^-2]}

Unit of stress is N/m^2 or Pascal (Pa).

Stress may be divided into the following types:

1)     1) Longitudinal stress: It is a force per unit area, which is related to the length of an object. It is further divided into two types-

 

a)     a) Tensile stress: It is the force applied per unit area, which results in an increase in length (or area) of a body. The object under tensile stress becomes thinner and longer.

 


b)     b) Compressive stress: It is the force applied per unit area, which results in a decrease in the length (or area) of a body. The object under compressive stress becomes thicker and shorter.

 


2)     2) Shear stress: The deforming force, which is applied tangentially on a crossectional area of an object, object shows some deformation or some minor changes can be obtained on that object, such deforming force is called shear stress.


3) Volumetric stress: If a solid object is present under the water, it experiences some deforming force due to liquid pressure, due to which the solid object starts to reduce its volume. As a result, the object becomes smaller than its original size and shape. This deforming force is called volumetric stress. In this case, the deforming force or stress is equal to the liquid pressure.



                                            Strain

Strain may be defined as the amount of deformation experienced by a body in the direction of applied force, divided by the initial dimension of the body.

The formula of strain in terms of length is ∂L/L (here ∂L = change in length and L = original length of the material

The strain has no dimension as well as the S.I. unit.

Depending on the stress application, strain experienced in a body can be of three types:

1)     1) Longitudinal strain: Longitudinal strain may be defined as the ratio of change in length of an object to the original length of that object due to longitudinal stress.

       2) Volumetric strain: Volumetric strain may be defined as the ratio of change in volume of an object to the original volume of that object due to volumetric stress.

       3) Shear strain: Shear strain may be defined as the ratio of total displacement or shifting to the length along which this shifting causes. This type of strain is obtained due to shear stress. 


that means, Strain = X/L

       Here, X = total displacement

                 L = the length along which this displacement occurs

     

     The relation between the stress and the strain: Up to elastic limit (It is a point in the stress-strain graph, from which object shows plastic deformation), the applied force or stress is directly proportional to the strain.

                        that means, stress ∝ strain

m                                         stress = E strain

                                            E = stress/strain, where E is a proportionality constant and it is called Modulus of Elasticity.


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