Berdichevsky and Le have recently found the analytical solution of the anti-plane constrained shear problem within the continuum dislocation theory (CMT, Contin. Mech. Thermodyn. 18:455-467, 2007). Interesting features of this solution are the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. In this paper an analytical solution of the plane constrained shear problem for single crystals exhibiting similar features is obtained and the comparison with the discrete dislocation simulation is provided.

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