The strain energy stored in a body of volume $V$ due to shear strain $\phi$ is (shear modulus is $\eta$ )
Medium
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(d)
Shear modulus $=\frac{\text { Shear } \text { stress }}{\text { Shear } \text { stress }}$
$\eta=\frac{\text { Shear stress }}{\phi}$
$\eta \phi=$ Shear stress
Strain energy per unit volume $=\frac{1}{2} \times$ shear stress $\times$ shear strain $\Rightarrow \frac{\text { Strain energy }}{\text { Volume }}=\frac{1}{2} \times \eta \phi \times \phi \quad$ (Cross multiply volume)
Strain energy $=\frac{1}{2} \eta \phi^2 V$
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