There is a continuum contradiction between the Wigner-Seitz model and the volume infinitesimal. By analyzing the attractive force and the repulsive force of the bcc and fcc double Wigner-Seitz model with the classical Lennard-Jones potential, the conclusion that the relative error satisfies the engineering analysis is established even if double Wigner-Seitz models superpose. By comparing the single atom Al sphere-surface force of the Wigner-Seitz model with the discrete simulation, a satisfactory result is obtained. Based on the Wigner-Seitz model, the dynamic equation of the digital micro-mirror device （DMD）, including the sticking effect, is found. The DMD simulation result is compared with the measurement result. The conclusion that the Wigner-Seitz model satisfies the micro-continuum requirement of the micro- and nano-engineering is arrivedat.