$15\mathrm{.}3($B$).$ Show that the strain energy per unit volume of a material under a single direct stress is given by $\frac{1}{2}($stress

$$ strain$).$ Hence show that for a material under the action of the principal stresses ${}_1,{}_2$ and ${}_3$ the strain energy per

unit volume becomes

$\frac{1}{2E}[{}_1^2+{}_2^2+{}_3^2-2v({}_1{}_2+{}_1{}_3+{}_2{}_3)]$