  Dislocations are the main carriers of the permanent deformation of crystals.
For simulations of engineering applications, continuum models where material
microstructures are represented by continuous density distributions of
dislocations are preferred. It is challenging to capture in the continuum model
the short-range dislocation interactions, which vanish after the standard
averaging procedure from discrete dislocation models. In this study, we
consider systems of parallel straight dislocation walls and develop continuum
descriptions for the short-range interactions of dislocations by using
asymptotic analysis. The obtained continuum short-range interaction formulas
are incorporated in the continuum model for dislocation dynamics based on a
pair of dislocation density potential functions that represent continuous
distributions of dislocations. This derived continuum model is able to describe
the anisotropic dislocation interaction and motion. Mathematically, these
short-range interaction terms ensure strong stability property of the continuum
model that is possessed by the discrete dislocation dynamics model. The derived
continuum model is validated by comparisons with the discrete dislocation
dynamical simulation results.
