Abstract 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 ,… Click to show full abstract
Abstract 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.
               
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