Zentrum für Technomathematik Fachbereich 3 – Mathematik und Informatik Using the eXtended finite element method for keyhole-based welding processes

This article addresses the modeling and simulation of keyhole-based welding processes using the eXtended finite element method with multiple indicator function. The welding process is modeled by the heat equation where the keyhole geometry and the interface separating molten and solid area are both represented by level set functions. The keyhole shape is computed by an analytical approach based on the idea of Kaplan and remains constant during the process. In contrast to this, the solid-liquid interface is considered as free boundary whose evolution is described by the two-phase Stefan problem. The coupled problem including two discontinuities is solved using miXFEM, an extended finite element method implemented within the FEniCS framework. Numerical results are compared to experimental data for different materials.d.