  This work rigorously implements a recent model of large-strain elasto-plastic
evolution in single crystals where the plastic flow is driven by the movement
of discrete dislocation lines. The model is geometrically and elastically
nonlinear, that is, the total deformation gradient splits multiplicatively into
elastic and plastic parts, and the elastic energy density is polyconvex. There
are two internal variables: The system of all dislocations is modeled via
$1$-dimensional boundaryless integral currents, whereas the history of plastic
flow is encoded in a plastic distortion matrix-field. As our main result we
construct an energetic solution in the case of a rate-independent flow rule.
Besides the classical stability and energy balance conditions, our notion of
solution also accounts for the movement of dislocations and the resulting
plastic flow. Because of the path-dependence of plastic flow, a central role is
played by so-called ``slip trajectories'', that is, the surfaces traced out by
moving dislocations, which we represent as integral $2$-currents in space-time.
The proof of our main existence result further crucially rests on careful
a-priori estimates via a nonlinear Gronwall-type lemma and a rescaling of time.
In particular, we have to account for the fact that the plastic flow may cause
the coercivity of the elastic energy functional to decay along the evolution,
and hence the solution may blow up in finite time.
