Efficient FFT solver for discrete dislocation dynamics with sharp field description of plastic strain in FCC metals

Discrete Dislocation Dynamics (DDD) is an established mesoscopic numerical method for simulating dislocation motion to determine the plastic behaviour of metals. However, DDD’s reliance on analytical expressions for internal stress fields limits its application to infinite isotropic media. The Discrete-Continuous Model (DCM), which couples DDD with a finite element elastic solver, has been proposed to handle more complex boundary conditions by regularising plastic strain using the eigenstrain formalism. However, this model still relies on analytical solutions for short-range dislocation interactions, making it unsuitable for anisotropic media. In this work, we present an improved DCM framework that replaces the FE solver with a Fast Fourier transform (FFT) solver for improved computational efficiency and full numerical calculation of stress fields, eliminating the need for analytical corrections. The proposed FFT solver employs a discrete theory of Green’s operators and uses a sharp eigenstrain field to describe dislocations. The solver mesh is aligned with the face-centred cubic (fcc) lattice of the DDD, forming an octahedral cell to address symmetry artefacts around {111} slip planes. Our FFT-based approach successfully maintains numerical stability by representing fcc dislocations as sharp fields without generating oscillations. This coupling allows the study of plasticity in anisotropic materials and interactions between dislocations and diffuse inclusions, such as precipitates, without short-range stress corrections.