Using a Radial Point Interpolation Meshless Method for the numerical simulation of the viscoplastic extrusion process

Resumo

In this work, an accurate and efficient meshless technique - the Radial Point Interpolation Method (RPIM) – is used to address the numerical simulation of the viscoplastic extrusion process, which is the initial phase of the Fused Filament Fabrication (FFF), an extrusion-based additive manufacturing (AM) process. Unlike the FEM, in meshless methods, there is no preestablished relationship between the nodes in the nodal mesh. Thus, the concept of ‘element’ is inexistent. In meshless methods, nodal discretization can be straightforwardly modified since nodes can be added or removed from the initial nodal mesh. Hence, mesh-free techniques show a particular relevance if associated with AM processes since the nodes can be distributed to match the layer-by-layer deposition of the printing process. Additionally, meshless methods have shape functions with virtually a higher order, allowing a higher continuity and reproducibility. This work combines, for the first time, the flow formulation and the heat transfer formulation in an RPIM algorithm to simulate the extrusion process of viscoplastic materials like the ones used in the FFF. The proposed algorithm is developed, implemented, and then validated for benchmark examples. The accuracy of the obtained numerical results highlights the importance of using meshless techniques in this field.