Derivation of strain-gradient plasticity from a generalized Peierls–Nabarro model

We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in plane. After scaling, the elastic interaction we continuous energy with linear growth depending on measure which characterizes macroscopic dislocation density as well effective representing far-field between dislocations. Relaxation and formation microstructures at intermediate scales are automatically incorporated limiting procedure based $\Gamma$-convergence.