Question

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is..... $kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.

Answer 1

$y =\frac{\text { stress }}{\text { strain }}=2.0 \times 10^{10}$
Energy density $=\frac{1}{2}$ stress $\times$ strain
$=\frac{1}{2}(\text { strain })^{2} y =\frac{1}{2}\left(5 \times 10^{-4}\right)^{2} \times 20 \times 10^{10}$
$=25 \times 10^{2} \times 10=25 \frac{ kJ }{ m ^{3}}$