Elastic stress and strain

When a material undergoes loading, deformation takes place. This deformation may be elastic or plastic. So what is elastic and plastic deformation? If the body regains its shape and size after removal of deforming force then that deformation is called elastic deformation and the body is called elastic body. If it does not regain its original shape and size then it’s plastic body. Here deforming force refers to the force responsible for deformation of the body. In this material we focus on elastic deformation. Let’s discuss more about elastic properties and elastic stress and strain.

Elasticity:

Elasticity is a property by virtue of which a body regains its original shape and size after removal of deforming force. And the body having elasticity is called elastic body.

Stress:

Stress is defined as the internal restoring force per unit area. Let us take an example. If we apply a force on a rubber wire, it elongates. After a while when we remove the force then the rubber regains its original shape and size. Now the question is what is the responsible force which drives back the rubber to its original position? It can be explained like this: An internal force is developed when we apply the external force. The magnitude of this restoring force increases as the elongation of wire increases. When we remove the external force, due to that restoring force the rubber wire returns to its original shape and size. So stress is the restoring force per unit area that acts inside the body. 

Unit: Nm-2

Difference between pressure and stress:

Both pressure and stress have the same unit and dimension, But they are not the same physical quantity. Pressure is the external force per unit area where stress is the internal force per unit area. Pressure is an external phenomenon where stress is an internal phenomenon. 

Types of stress:

Various types of stress are described below:

• Tensile and compressive stress: Tensile or compressive stress are simply applied force perpendicular per unit area. Tensile stress is defined for tension force where compressive stress is defined for compressive force. 

Stress =FA 

Where F is the magnitude of the force perpendicular to the area A.

• Shear stress: Shear stress also force per unit area but here the force vector is not perpendicular to the surface, the force vector lies on the plane of area. Or we can define the force as a tangential force to a given surface area.

Shear stress=FA 

Where F is the magnitude of the force acting tangential to the surface having area A.

1. Volumetric Stress: If we applied force on the total volume of a body. Let us take an example that when a body is submerged in water then hydrostatic force acting on the total surface, this is a type pressure force also. So this pressure force per unit area is called volumetric stress. 

Strain

Strain is defined as the change in shape,length or volume per unit shape, length or volume.

Let us consider a rod of length L goes through an elastic deformation by the action of a tensile force. Now, length of the rod is L+L. 

Where the change in length = L and the original length = L

Strain = Change in lengthOriginal length=LL

Strain is a unit less physical quantity. 

Types of strain

Similar to stress, Strain is also classified in a similar manner. 

1. Longitudinal Strain: Longitudinal strain is formed due to the elongation in the direction of length because of tensile or compressive stress. If the length increases after deformation it is called tensile strain, and if the length decreases from its original length after deformation it is called compressive strain.  

Longitudinal strain=Ll

Where L=change in length

And L= Original length

2. Shearing strain: Shearing strain is produced when a shear stress acts over a cross-section. To understand this strain, let us take an example of a body having a square cross-section. Forces are acting parallel to the square section as shown in figure. 

From the figure, we can conclude that the total force and total torque on the cross section is zero. Which implies that the body is in rotational and translational equilibrium.So due to the shear force deformation takes place as marked in fig.

Shearing strain =DD’AD=h 

3. Volume strain: When a volumetric stress acts on a body, then the volume of the body is changed. Volume strain is defined as the change in volume to its original volume. 

Let us consider a body having volume V. After deformation, its volume becomes V+V, then the change in volume is V.

Hence, volumetric strain =VV

Relation between stress and strain:

There is a relation between stress and strain of a body; this is called Hooke’s Law.

According to Hooke’s law, stress is proportional to the strain (up to elastic limit)

    Stress ∝ Strain

      Or Stress/Strain=constant

     This constant is called Young’s modulus of elasticity.

Or FA=LL

Conclusion 

In material engineering and science, there are various studies and applications of elasticity properties of material. When stress on a material increases, various changes take place that are described by various limits. This study material consists of notes on elastic property, definition of stress and strain, types of stress and strain, etc.