Stress, Strain and Young's modulus

Stress

in general, a Forces acting on a material per unit area, cause a change in dimensions and the material is said to be in a state of stress (it has units of pressure).
*Stress is the ratio of the applied force (F) to the cross-sectional area (A) of the material. (ie., F/A)
The symbol used for tensile and compressive stress is σ (sigma). 
*The unit of stress is the Pascal, Pa, where 1 Pa = 1 N/m². 

Hence  
N/mm²

Strain

The fractional change in a dimension of a material produced by a force is called the strain.
For a tensile or compressive force, strain is the ratio of the change of length to the original length. 
The symbol used for strain is ε (epsilon). 
*A material of length L metres, which changes to  ΔL metres when subjected to load is called Strain. (Change in length to Original length)

Strain    = ΔL

           L

Young's modulus
It is defined as the ratio if Stress to Strain.
 


where
  E is the Young's modulus (modulus of elasticity)
  F is the force exerted on an object
  A is the actual cross-sectional area where the force is applied;
  ΔL is the amount by which the length of the object changes;
  L₀ is the original length of the object.