First slide

Elastic behaviour of solids

Question

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

Moderate

A

$\frac{SY}{2}$
B

$\frac{S^{2}}{2 Y}$
C

$\frac{S}{2 Y}$
D

$\frac{2 S}{Y}$

Solution

Energy per unit volume $= \frac{1}{2} \times Stress \times Strain$
$= \frac{1}{2} \times Stress \times \frac{Stress}{Y} [Y = \frac{Stress}{Strain}] = \frac{S^{2}}{2 Y}$

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