  We present a mathematical framework within which Discrete Dislocation
Dynamics in three dimensions is well-posed. By considering smooth distributions
of slip, we derive a regularised energy for curved dislocations, and rigorously
derive the Peach-Koehler force on the dislocation network via an inner
variation. We propose a dissipative evolution law which is cast as a
generalised gradient flow, and using a discrete-in-time approximation scheme,
existence and regularity results are obtained for the evolution, up until the
first time at which an infinite density of dislocation lines forms.
