A remeshing approach for the finite cell method applied to problems with large deformations

• Applicant: Professor Dr.-Ing. Alexander Düster
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 505137962

The research project aims to advance the finite cell method (FCM), a high-order fictitious domain approach, for large deformation analysis, including elastoplasticity and contact problems. In the project's initial phase, we successfully developed and implemented a robust remeshing procedure within FCM to accommodate large deformations. However, our numerical simulations revealed a limitation in modeling contact and self-contact scenarios, necessitating the second phase of the project. This next phase focuses on enhancing the FCM's capability to handle contact issues by adopting a more sophisticated remeshing strategy. Specifically, we will advance the third medium contact (TMC) approach within the FCM framework. Currently, TMC is utilized with boundary-conforming meshes, but its performance with immersed boundary methods like FCM remains untested. Traditional approaches require meshes to conform to domain boundaries, avoiding material transitions within a single element. To integrate TMC into FCM, we propose using specially designed enrichment functions along the domain interface to effectively capture the weak discontinuity at the immersed contact boundary. We hypothesize that introducing a third medium will enhance FCM results by accurately representing the material interface, especially when combined with suitable enrichment functions. A significant challenge is the stability of TMC, which is known to be problematic without appropriate stabilization methods. The effectiveness of existing stabilization techniques for TMC in immersed boundary methods is uncertain due to the lack of body-conforming meshes, which can exacerbate problem conditioning and lead to instabilities. However, our findings from the first project phase demonstrate that FCM stability can be significantly improved through carefully designed stabilization strategies. Therefore, a key objective of this phase is to develop and thoroughly investigate stabilization methods for TMC within the FCM framework. To evaluate the robustness and effectiveness of the enhanced FCM, particularly regarding remeshing and contact constraint handling, we will use challenging benchmarks, including some recommended by the TMC community.

• DFG Programme: Research Grants