A continuum theory of screw dislocation equilibrium

Large ensembles of screw dislocations can be described by a continuum theory. One such theory was derived from homogenization reasoning by Berdichevsky (International Journal of Engineering Science, 106, 10-28, 2016). In the paper, this theory is refined by including the corrections of order 1/N, N being the number of dislocations. The correcting terms are needed for a more accurate computation of energy, which is a small functional of order 1/N, and in the leading approximation energy is zero. The correcting terms reflect a detailed description of the microstructure and depend on mutual dislocation positions. Comparison with numerical simulations confirms that the improved theory provides correct values of energy of the system.