• Novel pseudo-periodic boundary condition accounts for sintering shrinkage. • Surface artifacts are eliminated in phase-field simulations on a fixed grid. • Bulk behavior is reproduced with ∼300 particles, vs 7000 conventionally. • High-accuracy microstructure prediction is achieved at low computational cost. Numerical simulation of sintering is essential for predicting microstructures and defects. However, applying periodic boundary conditions remains a challenge because sintering involves volumetric shrinkage due to densification. As a result, conventional methods require large-scale simulations to mitigate surface effects and capture bulk behavior, posing significant challenges in terms of computational cost and accuracy. In this study, we propose a novel pseudo-periodic boundary condition (PPBC) that simultaneously accounts for shrinkage and eliminates surface artifacts in multi-phase-field sintering simulations. By applying this approach to particles regularly arranged in one- and three-dimensional arrays, we demonstrate that the PPBC successfully reproduces bulk behavior independent of the boundary constraints. Furthermore, simulations with varying domain sizes reveal that the PPBC is highly effective in reducing the computational cost required to predict key microstructural parameters. The proposed method is expected to significantly contribute to the accurate prediction and control of sintered microstructures.
Nakazawa et al. (Sun,) studied this question.