A membrane finite element for fast simulation of overlapping beads geometry during direct energy deposition additive manufacturing

The aim of this paper is to propose a fast FEM strategy for simulating molten metal deposition geometry during additive manufacturing for studying the influence of the sequence of deposition on the geometry. The approach is inspired by the algorithm initially proposed by Feulvarch et al. (Eur J Mech A 89:104290, 2021) for coatings. In this article, the membrane finite element is notably improved and extended for simulating of a large stack of deposits in order to study the building of 3D geometries. A constant vertical evolution rate of the surface tension is introduced to adjust the geometry of the free surface of the molten pool which depends on the hydrodynamics of the liquid phase. The simulation is very fast because it is carried out on a 2D mesh composed of linear triangles that corresponds to the sole free surface of the liquid phase at each time step. Moreover, the implicit nonlinear algorithm developed has the advantage of avoiding matrix systems resolution (reduced RAM memory, efficient parallel computing). In addition, a simple and robust remeshing procedure is detailed in order to avoid too large distortions of the triangular elements during the 'inflating' stage of the workpiece. Its interest lies in the fact that it does not require any field projection typically employed in remeshing procedures, as the geometry serves as the only historical data required to resume FEM computations following each remeshing step. Examples are proposed to clearly evidence the efficiency and robustness of the method developed in terms of geometry and CPU time.