  Continuum dislocation dynamics models of mesoscale plasticity consist of
dislocation transport-reaction equations coupled with crystal mechanics
equations. The coupling between these two sets of equations is such that
dislocation transport gives rise to the evolution of plastic distortion
(strain), while the evolution of the latter fixes the stress from which the
dislocation velocity field is found via a mobility law. Earlier solutions of
these equations employed a staggered solution scheme for the two sets of
equations in which the plastic distortion was updated via time integration of
its rate, as found from Orowan's law. In this work, we show that such a direct
time integration scheme can suffer from accumulation of numerical errors. We
introduce an alternative scheme based on field dislocation mechanics that
ensures consistency between the plastic distortion and the dislocation content
in the crystal. The new scheme is based on calculating the compatible and
incompatible parts of the plastic distortion separately, and the incompatible
part is calculated from the current dislocation density field. Stress field and
dislocation transport calculations were implemented within a finite element
based discretization of the governing equations, with the crystal mechanics
part solved by a conventional Galerkin method and the dislocation transport
equations by the least squares method. A simple test is first performed to show
the accuracy of the two schemes for updating the plastic distortion, which
shows that the solution method based on field dislocation mechanics is more
accurate. This method then was used to simulate an austenitic steel crystal
under uniaxial loading and multiple slip conditions.
