Tailoring cellular automata for physically-based generation of periodic microstructures in powder bed fusion processes

Abstract Accurate representation of periodic microstructures is essential for predicting faster the effective mechanical response of additively manufactured metals through computational homogenization. While geometrically-based microstructure generation approaches can readily enforce periodicity, achieving periodic domains within physically-based models remains challenging due to the inherently directional and history-dependent nature of solidification. This work introduces a cellular automata (CA) framework specifically tailored to generate periodic microstructures in laser-based powder bed fusion (PBF) of 316 L stainless steel. By leveraging the spatial invariance along the scanning direction of the temperature field in the reference frame moving with the laser, where the melt pool reaches a quasi-steady state condition, periodic microstructures can be constructed despite the intrinsically non-periodic evolution of the process in time. Building on this observation, classical deterministic CA formulations for solidification are augmented with virtual orientation fields to enforce periodicity along the in-plane directions of two-dimensional domains. The methodology is benchmarked against experimentally validated thermal fields obtained from high-fidelity multiphysics computational fluid dynamics simulations. Results demonstrate that the proposed framework eliminates artificial edge effects and yields microstructures governed solely by competitive grain growth, thereby providing domains compatible with periodic boundary conditions. This enables their direct use in fast Fourier transform-based micromechanical solvers, reducing computational cost compared to conventional finite element methods. Challenges associated with enforcing periodicity along the build direction are highlighted, underscoring the need for fully three-dimensional CA formulations. The presented study thus establishes a methodology for the physically-based generation of periodic representative volume elements, forming the basis for integrated process–structure–property modeling of PBF components.