SIM-AM 2023

Model Reduction for Fast Computation in Additive Manufacturing: QuadWire Approach as an Extended 1D Model

  • Preumont, Laurane (CNRS, LMS)
  • Weisz-Patrault, Daniel (CNRS, LMS)
  • Allaire, Grégoire (CNRS, CMAP)
  • Margerit, Pierre (CNRS, PIMM)

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Directed energy deposition (DED) is a class of additive manufacturing (AM) processes using a moving focused heat source to melt feed-stock material simultaneously deposited by a moving nozzle. Both single and multi-track scanning strategies can be performed to build multilayer thin-walled structures and massive parts alike. Process parameters have a significant influence on microstructure and residual stresses, which mainly depend on temperature history. However, although fast numerical approaches have been developed for thermal analysis and phase transitions [1], efficient computation of residual stresses remains challenging. Indeed, 3D/2D finite elements method (FEM) involves meshing along the layer thickness and/or height, which implies a very fine discretization along the print direction as the elements should not be too elongated to avoid conditioning issues. To avoid such a fine mesh density, an enriched 1D model immersed in the 3D space named QuadWire is proposed. Reducing dimension (e.g., from 3D to 2D/1D) and increasing the number of degrees of freedom (DOF) enables significantly shorter computation time while still capturing complex stress fields in the part and ensuring good accuracy [2]. In the proposed model, layer thickness and layer height are internal parameters independent of mesh size, which in turn can be coarser along print direction. At each material point, 4 displacement vectors are introduced leading to 12 DOFs. Thus, kinematic conditions between a bead and its 4 neighbours (i.e., right, left, top and bottom) may be simply written. The model derivation through the virtual work principle will be broached, and a linear thermo-elastic behaviour will be derived. This contribution focuses on a FE implementation of this extended 1D model, convergence analysis will highlight both single and multi-track scanning strategies. In addition, material parameters will be identified to match 3D computations on various test cases. This extended 1D approach enables part-scale numerical optimization of process parameters to control residual stress.