Question

What is the best definition of elasticity?

Answer 1

Elasticity:

1. Elasticity is an ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed.
2. Hooke's law explains elasticity as if the deformation is small, the stress in a body is proportional to the corresponding strain.
   $\frac{\mathrm{stress}}{\mathrm{strain}}=\mathrm{constant}$
   This constant is known as the modulus of elasticity (or) coefficient of elasticity.
3. Stress: stress is the force acting on the unit area of a material. Stress can deform the body
4. Strain: The effect of stress on a body is named strain.Strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body.
5. There are three types of modulus of elasticity:
   3.1 Young's modulus of elasticity $\text{'}\mathrm{Y}\text{'}$
   3.2 Bulk modulus of elasticity $\text{'}\mathrm{B}\text{'}$
   3.3 Modulus of rigidity

Young's modulus of elasticity:

Within the elastic limit, the ratio of longitudinal stress and longitudinal strain is called Young’s modulus of elasticity $\text{'}\mathrm{Y}\text{'}$.
$\mathrm{Y}=\frac{\mathrm{longitudinal}\mathrm{stress}}{\mathrm{longitudinal}\mathrm{strain}}$

Bulk modulus of elasticity:

Within the elastic limit, the ratio of the volume stress and the volume strain is called the bulk modulus of elasticity $\text{'}\mathrm{B}\text{'}$.

$\mathrm{B}=\frac{\mathrm{change}\mathrm{of}\mathrm{the}\mathrm{pressure}\mathrm{or}\mathrm{force}\mathrm{applied}\mathrm{per}\mathrm{unit}\mathrm{area}\mathrm{on}\mathrm{the}\mathrm{material}}{{\displaystyle -\frac{\mathrm{change}\mathrm{of}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{material}\mathrm{due}\mathrm{to}\mathrm{the}\mathrm{compression}}{\mathrm{Initial}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{material}}}}$

Modulus of rigidity:

Within elastic limit, the ratio of shearing stress (or) tangential stress and shearing strain (or) tangential strain is called the modulus of rigidity $\text{'}\mathrm{\eta }\text{'}$.

$\mathrm{\eta }=\frac{\mathrm{shearing}\mathrm{stress}}{\mathrm{shearing}\mathrm{strain}}$