  This work introduces a model for large-strain, geometrically nonlinear
elasto-plastic dynamics in single crystals. The key feature of our model is
that the plastic dynamics are entirely driven by the movement of dislocations,
that is, $1$-dimensional topological defects in the crystal lattice. It is well
known that glide motion of dislocations is the dominant microscopic mechanism
for plastic deformation in many crystalline materials, most notably in metals.
We propose a novel geometric language, built on the concepts of space-time
"slip trajectories" and the "crystal scaffold" to describe the movement of
(discrete) dislocations and to couple this movement to plastic flow. The
energetics and dissipation relationships in our model are derived from first
principles drawing on the theories of crystal modeling, elasticity, and
thermodynamics. The resulting force balances involve a new configurational
stress tensor describing the forces acting against slip. In order to place our
model into context, we further show that it recovers several laws that were
known in special cases before, most notably the equation for the Peach-Koehler
force (linearized configurational force) and the fact that the combination of
all dislocations yields the curl of the plastic distortion field. Finally, we
also include a brief discussion on how a number of other effects, such as
hardening, softening, dislocation climb, and coarse-graining, could be
incorporated into our model.
