A steel wire of length 2 m and Young's modulus $2.0 \times {10^{11}}N{m^{ - 2}}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and ${10^{-3}}$ respectively, then the elastic potential energy density of the wire is ______ $ \times {10^5}$ (in SI units).