  A consistent, small scale description of plastic motion in a crystalline
solid is presented based on a phase field description. By allowing for
independent mass motion given by the phase field, and lattice distortion, the
solid can remain in mechanical equilibrium on the timescale of plastic motion.
Singular (incompatible) strains are determined by the phase field, to which
smooth distortions are added to satisfy mechanical equilibrium. A numerical
implementation of the model is presented, and used to study a benchmark
problem: the motion of an edge dislocation dipole in a hexagonal lattice. The
time dependence of the dipole separation agrees with classical elasticity
without any adjustable parameters.
