Introduction to Elasticity:

• Elasticity is a branch of Physics which deals with the elastic property of materials.
• When an external force is applied to a body, there will be some change in its length shape and volume.
• When this external force is removed, and if the body regains its original shape and size, then the body is said to be a Perfectly Elastic body.
• If the body does not regain its original shape or size after removal of the applied force, then it is said to be perfectly plastic body.

Stress and Strain:

Stress:

• A body is said to be rigid body, if the distance between any two points in a body is unaltered due to application of the force. In practice no body is perfectly rigid.
• When a body is subjected to some external forces the body will offer some resistance to the deforming forces, as a result some work is done on the body and this work is stored as the elastic potential energy.
• Now if the deforming forces are re-removed the energy stored brings back the body to its original condition.

Tensile or Longitudinal Stress:

When the force is applied parallel to the surface of the body, then the stress is called as longitudinal stress or tensile stress.

Tangential or Shearing :

When the force is applied along the surface of the body hence the corresponding stress exerted is called as tangential stress or shearing stress.

Hydrostatic Stress :

When a body is subjected to a uniform force from all sides, then the corresponding stress is called as Hydrostatic Stress .

Strain:

• Strain is defined as the change in dimension (fractional deformation)produced by the external force of the body.
• In other way it can also be defined as the ratio of the change in dimension to the original dimension .It is a dimensionless quantity as it is a ratio between two quantities of same dimension.

Types of Strain:

Strain are classified into three types as follows :

Longitudinal Strain :

• Longitudinal strain of a deformed body is defined as the ratio of the change in length of the body due to the deformation to its original length in the direction of the force.
• If l is the original length and dl the change in length occurred due to the deformation, the Longitudinal strain

Longitudinal strain = $$\frac{Change in length }{Original length }$$ = $$\frac{\Delta l}{l}$$

Volumetric Strain :

• Volumetric strain of a deformed body is defined as the ratio of the change in volume of the body to the deformation to its original volume. If V is the original volume and ΔV the change in volume occurred due to the deformation, the volumetric strain is given by

Volumetric Strain = $$\frac{change in Volume }{Original volume}$$ =$$ \frac{\Delta V}{V}$$

• When a force is applied uniformly and normally to the entire surface of the body, then there will be a change in volume of the body, without any change in its shape. This strain is called ‘bulk strain or volumetric strain'.

Shear Strain :

Shear strain is defined as the strain accompanying a shearing action. It is the angle in radian measure through which the body gets distorted when subjected to an external shearing action. It is denoted by $$\theta$$ .

Hooke’s Law:

Hooke’s law states that stress is proportional to strain upto elastic limit

Stress $$\alpha$$ Strain

Stress = $$E \times$$ Strain

Modulus of elasticity (E) = $$\frac{Stress}{ Strain}$$