  We rigorously derive a strain-gradient model of plasticity as a
$\Gamma$-limit of continuum bodies containing finitely-many edge-dislocations
(in two dimensions). The key difference from previous such derivations is the
elemental notion of a dislocation: we work in a continuum framework in which
the lattice structure is represented by a smooth frame field, and the presence
of a dislocation manifests in a circulation condition on that frame field; the
resulting model is a Lagrangian approach with a multiplicative strain
decomposition. The multiplicative nature of the geometric incompatibility
generates many technical challenges, which require a systematic study of the
geometry of bodies containing multiple dislocations, the definition of new
notions of convergence, and the derivation of new geometric rigidity estimates
pertinent to dislocated bodies. Our approach places the strain-gradient limit
in a unified framework with other models of dislocations, which cannot be
addressed within the "admissible strain" approach used in previous works.
