
Modelling of Directed Energy Deposition with the Particle Finite Element Method
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Directed Energy Deposition with a Laser Beam (DED-LB) is able to produce high-strength steel parts with complex geometries enabling new concepts for the manufacturing of forming tools as presented in [1]. Computational modelling of DED-LB using a finite element based approach represents a compromise between accuracy and computational efficiency. Conventional models require a predefined geometry of the deposited material, which is then sequentially activated during the simulation to approximate the real interactions during deposition. However, this approach does not allow the simulation of process limits where the desired geometry cannot be produced, for example in the manufacturing of thin-walled structures. The Particle Finite Element Method (PFEM) is a Lagrangian finite element method enhanced by frequent remeshing of the mostly unchanged set of node points. This allows the simulation of very large material flows while retaining the strength of Lagrangian FE in accurately modelling history dependent material behaviour. This contribution presents a thermo-mechanical modelling approach for DED-LB by adapting PFEM, which allows the simulation of melt flow and bonding to the substrate. Melt flow and solidification are governed by a large strain constitutive model describing the phase transition from a Maxwell-type viscous model in the melt to an elastic model in the solid. The model is based on phase fractions, which makes the inclusion of latent heat and transformation strains straightforward. The evolution of the phase fraction is described by a temperature dependent hyperbolic function. This model has been published in [2], while the present contribution also discusses the extension to 3d space with the required developments of the remeshing methods to account for the much higher mesh complexity. The examples are referred to experimental measurements of a single weld bead as part of the joint DFG project 504955789. [1] Dardaei Joghan, H., Hölker-Jäger, R., Komodromos, A., Tekkaya, A. E. Hybrid Additive Manufacturing of Forming Tools. Automot. Innov. 6, 311–323 (2023). doi:10.1007/s42154-023-00239-y. [2] Schewe, M., Noll, I., Bartel, T., and Menzel, A. Towards the simulation of metal deposition with the Particle Finite Element Method and a phase transformation model. Comput. Methods Appl. Mech. Eng. (2025) 437:117730. doi:10.1016/j.cma.2025.117730.