Explain the different types of modulus of elasticity.

Explanation

There are three types of modulus of elasticity. They are:
(i) Young's modulus
(ii) Bulk modulus
(iii) Rigidity modulus.
Young's modulus: When a wire is stretched or compressed, then the ratio between tensile stress (or compressive stress) and tensile strain (or compressive strain) is defined as Young's modulus.
Young modulus of a material `=("Tensile stress or compressive stress")/("Tensile strain or compressive strain")`
`Y=(sigma_i)/(epsilon_i)orY=(sigma_c)/(epsilon_c)`
SI unit of Young's modulus is `Nm^(-2)` or pascal.
Bulk modulus: Bulk modulus is defined as the ratio of volume stress to the volume strain.
Bulk modulus,
`K=("Normal(perpendicular)stress or pressure")/("Volume strain")`
The normal stress or pressure is
`sigma_(n)=(F_n)/(DeltaA)=Deltap`
The volume strain is
`epsilon_(v)=(DeltaV)/(V)`
Therefore, Bulk modulus is `K=-(sigma_n)/(epsilon_v)=-(Deltap)/(DeltaV//V)" "...(1)`
The negative sign in the equation (1) means that when pressure is applied on the body, its volume decreases.
The rigidity modulus or shear modulus: It is defined as rigidity modulus or Shear modulus,
`eta_(R)=("shearing stress")/("angle of shear or shearing strain")`
The shearing stress is
`sigma_(s)=("tangential force")/("area over which it is applied")=(F_i)/(DeltaA)`
The angle of shear or shearing strain
`epsilon_(s)=(x)/(h)=theta`
Therefore, Rigidity modulus is,
`eta_(R)=(sigma_s)/(epsilon_s)=(F_(1)//DeltaA)/(x//h)=(F_(1)//DeltaA)/(theta)`