Adaptive capture-based cellular automata for addressing challenges in modeling grain growth competition in additive manufacturing

Abstract

Cellular automata (CA) models are widely used to predict microstructure evolution during solidification in additive manufacturing (AM). However, conventional time-stepping CA frameworks often require fine temporal resolution to mitigate multiple grain assignment errors and discretization inaccuracies—particularly under steep thermal gradients and rapid solidification conditions. To address these challenges, an adaptive capture (AC) algorithm is introduced within the conventional time-stepping framework. This algorithm dynamically computes precise capture times for each competing grain and reconstructs grain envelope evolution based on the local undercooling of newly captured cells. As a result, accurate grain structure prediction can be achieved even under coarse time-step conditions, with accuracy comparable to that of fine-resolution CA models, while significantly improving computational efficiency. The AC-CA framework is systematically evaluated under both idealized and practical AM conditions to quantify the impact of time-step size and mesh resolution on grain growth prediction. By coupling with finite element (FE)-derived thermal fields, the model is validated in laser powder bed fusion (LPBF) simulations, demonstrating high scalability and fidelity in multiscale microstructure prediction. Additionally, the AC-CA model incorporates accelerating strategies, such as the simplified thermal unit method, which significantly improve computational efficiency. This enables the simulation of larger domains with billions of computational cells while maintaining high fidelity. In summary, the AC-CA approach effectively addresses long-standing challenges associated with time resolution in time-stepping CA models and provides a robust, efficient solution for microstructure simulation in additive manufacturing.