Question

Define strain energy and derive the equation for the same.

Answer 1

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape. It is usually denoted by U.

The strain energy formula is given as,

U = Fδ / 2

Where,

δ = compression,

F = force applied.

When stress σ is proportional to strain ϵ, the strain energy formula is given by,

U = 1 / 2 V σ ϵ

Where,

σ = stress,

ϵ = strain,

V = volume of body

Regarding young’s modulus E, the strain energy formula is given as,

U = σ2 / 2E × V.

Where,

σ = stress,

E = young’s modulus,

V = volume of body.

Answer 2

Hii dear,

◆ Strain Energy-
- Strain energy is the energy stored by a system undergoing deformation.

◆ Derivation-
Consider deformation of body under force,
Y = stress / strain
Y = (F/A) / (x/L)
F = YAx / L

Work done for elongation is given by
W = ∫dW.dx
W = ∫dF.dx
W = ∫d(YAx/L).dx
W = YAl^2 / 2L

Thus strain energy is
W = YAl^2 / 2L

Hope that is useful...