This paper investigates the implementation of Field Dislocation Mechanics theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous elds). In this context, the uniqueness of the stress and elastic distortion elds is established. This allows to propose an e cient numerical scheme based on Fourier transform to compute the internal stress eld, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the Field Dislocation Mechanics theory.
