Question

An elastic material of youngs modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is

Answer 1

the answer is s²÷2Y

As energy per unit volume = 1/2 x stress x strain

                                             =1/2 x stress x stress/Y

                                           Y=S²÷2Y

Answer 2

Strain energy per unit volume = 1÷2 F × e / A l

Strain energy per unit volume = 1÷2 (F÷A × e÷l )

Stress = F÷A

Strain = e÷l

So......

Strain energy per unit volume = 1÷2 (stress × strain )

We know that :-

Y = stress ÷ strain

Strain = stress ÷ Y

So.......

Strain energy per unit volume = 1 ÷ 2 (stress × stress÷Y)

Strain energy per unit volume = 1÷2 Stress^2÷Y

According to question Stress = S

So......

Strain energy per unit volume =1÷2 S^2÷Y

[This is the area under stress strain graph ]


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