  The aim of this paper is to investigate the numerical implementation of the
Field Dislocation Mechanics (FDM) theory for the simulation of
dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and
Roy (2006) is recalled which permits to express the set of equations under the
form of a static problem, corresponding to the determination of the local
stress field for a given dislocation density distribution, complemented by an
evolution problem, corresponding to the transport of the dislocation density.
The static problem is solved using FFT-based techniques (Brenner et al., 2014).
The main contribution of the present study is an efficient numerical scheme
based on high resolution Godunov-type solvers to solve the evolution problem.
Model problems of dislocation-mediated plasticity are finally considered in a
simplified layer case. First, uncoupled problems with uniform velocity are
considered, which permits to reproduce annihilation of dislocations and
expansion of dislocation loops. Then, the FDM theory is applied to several
problems of dislocation microstructures subjected to a mechanical loading.
