Continuous space-time multi-level hp Galerkin-Petrov finite elements for the direct numerical simulation of laser power bed fusion processes

• Applicant: Professor Dr.-Ing. Stefan Kollmannsberger
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441506233

This project aims at developing a new discretizational technology for the thermomechanical analysis of laser powder bed fusion (PBF-LB/M). PBF-LB/M is the most important additive manufacturing technology to produce complex shaped load bearing parts. PBF-LB/M is driven by the localized heat input that causes selective melting of powder and subsequent solidification, inducing rapid localized temperature changes. This process covers multiple scales in both space and time, while being multi-physical in nature. The thermomechanical behavior can be modeled by a non-linear transient heat equation involving phase changes coupled with small strain elastoplasticity. The first phase of the project introduced a space-time Galerkin-Petrov finite element formulation on hierarchical grids to capture efficiently both spatial and temporal scales. The combination with the Finite Cell Method (FCM) allows resolving complex geometric shapes in an immersed setting, which would otherwise not be feasible for a boundary-conforming discretization in 4D. The computational framework was verified using several benchmark examples to demonstrate its accuracy and efficiency. The subsequent validation of the nonlinear transient thermal heat model revealed that its range of validity is much larger than initially expected. This provided the starting point for an inverse framework to compute optimal profiles for beam shaping, a practically relevant technology to increase efficiency or improve other process characteristics. The second phase of the project expands the space-time methods developed in the first phase to plasticity. Addressing plasticity is crucial, as the rapid and non-uniform heating and cooling of the part creates undesired residual stresses during the built process. The multi-scale nature of the process demands for a local tracking of the evolution of plastic internal variables. This scientific challenge will be addressed by developing a space-time multi-field elastoplastic formulation. The proposed approach elevates local plastic variables to global solution fields, which not only allows for a holistic numerical treatment of the process, but also bears the exciting new possibility of an adaptive treatment of the evolution of plastic variables in space and time. The impact of the methodological development could exceed PBF-LB/M, as many industrial production processes undergo a similar evolution. The verification and validation of the developed methods will continue with partners from the Professorship of Laser-based Additive Manufacturing at TUM and the US National Institute of Standards and Technology (NIST). The specifically designed benchmarks will be available to the benefit of the entire scientific community through the NIST AM-Bench initiative as open-access data publications.

• DFG Programme: Research Grants
• Co-Investigator: Dr.-Ing. Philipp Kopp