  Due to recent successes of a statistical-based nonlocal continuum crystal
plasticity theory for single-glide in explaining various aspects such as
dislocation patterning and size-dependent plasticity, several attempts have
been made to extend the theory to describe crystals with multiple slip systems
using ad-hoc assumptions. We present here a mesoscale continuum theory of
plasticity for multiple slip systems of parallel edge dislocations. We begin by
constructing the Bogolyubov-Born-Green-Yvon-Kirkwood (BBGYK) integral equations
relating different orders of dislocation correlation functions in a grand
canonical ensemble. Approximate pair correlation functions are obtained for
single-slip systems with two types of dislocations and, subsequently, for
general multiple-slip systems of both charges. The effect of the correlations
manifests itself in the form of an entropic force in addition to the external
stress and the self-consistent internal stress. Comparisons with a previous
multiple-slip theory based on phenomenological considerations shall be
discussed.
