A multi-physics material point method for thermo-fluid-solid coupling problems in metal additive manufacturing processes

The metal additive manufacturing (AM) process involves complex multi-physics coupling phenomena associated with the heat transfer, fluid flow, and solid mechanics that bring challenge to the current numerical methods. In this study, a multi-physics material point method is proposed for solving thermo-fluid–solid coupling problems in metal additive manufacturing processes. In this method, the material domain is discretized by a structured grid and a set of particles with corresponding variants for the heat transfer, fluid flow, and thermal stress evolution, under both Eulerian and Lagrangian descriptions. The interaction between these fields is naturally handled by the same structured grid and particles. Moreover, a semi-implicit local iteration technique is proposed to efficiently solve heat transfer with solid–liquid phase change, an improved Chorin’s projection method is introduced to handle Darcy’s damping, and a staggered derivation scheme with a sub-cell occupation technique is proposed to solve surface tension and Marangoni forces. A set of numerical examples, including the benchmark problems and the selective laser melting AM problems, is presented to validate the proposed method, where good agreements have been achieved with the analytical, numerical, and experimental data available in the literature. It is demonstrated that the proposed method is a powerful tool for thermo-fluid–solid coupling problems in metal additive manufacturing and other multi-physics problems.