  A novel implementation of the dislocation flux boundary condition in discrete
dislocation dynamics is presented. The continuity of the individual dislocation
loops in a periodic representative crystal volume (RVE) is enforced across the
boundary of the RVE with the help of a dual topological description for
representing dislocation line kinematics in two equivalent spaces representing
the deforming crystal, the RVE and the unbounded crystal spaces. The former
describes the motion of the dislocations in the simulated crystal RVE whereas
the latter represents the motion of dislocations in an infinite space
containing all replicas of the RVE. A mapping between the two spaces forms the
basis of the implementation of flux boundary condition. The implementation
details are discussed in the context of statistical homogeneity of bulk
crystals undergoing macroscopically homogeneous plastic deformation. Some test
cases are presented and discussed to establish the proposed approach. It has
been observed that the boundary nodes associated with dislocation segments bear
no relevance in the motion of the dislocation segments from the standpoint of
bulk crystal plasticity modeling throughout the deformation history of the
crystal.
