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

Answer: 25

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