  In continuum models of dislocations, proper formulations of short-range
elastic interactions of dislocations are crucial for capturing various types of
dislocation patterns formed in crystalline materials. In this article, the
continuum dynamics of straight dislocations distributed on two parallel slip
planes is modelled through upscaling the underlying discrete dislocation
dynamics. Two continuum velocity field quantities are introduced to facilitate
the discrete-to-continuum transition. The first one is the local migration
velocity of dislocation ensembles which is found fully independent of the
short-range dislocation correlations. The second one is the decoupling velocity
of dislocation pairs controlled by a threshold stress value, which is proposed
to be the effective flow stress for single slip systems. Compared to the almost
ubiquitously adopted Taylor relationship, the derived flow stress formula
exhibits two features that are more consistent with the underlying discrete
dislocation dynamics: i) the flow stress increases with the in-plane component
of the dislocation density only up to a certain value, hence the derived
formula admits a minimum inter-dislocation distance within slip planes; ii) the
flow stress smoothly transits to zero when all dislocations become
geometrically necessary dislocations. A regime under which inhomogeneities in
dislocation density grow is identified, and is further validated through
comparison with discrete dislocation dynamical simulation results. Based on the
findings in this article and in our previous works, a general strategy for
incorporating short-range dislocation correlations in continuum models of
dislocations is proposed.
