Gorji, MahanMahanGorjiHosseini, Seyed FarhadSeyed FarhadHosseiniSartorti, RomanRomanSartortiRadtke, LarsLarsRadtkeDüster, AlexanderAlexanderDüster2024-09-302024-09-302024-0394th Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2024https://hdl.handle.net/11420/49271Numerical methods play an important role when predicting structural failure in industrial applications. Among various methods, the phase‐field modeling (PFM) seems to be a very promising approach. By introducing an additional phase‐field variable, it can account for crack initiation, crack propagation, dynamic crack branching and more. However, it needs a very fine mesh especially along the propagating crack path. When utilizing boundary‐fitted methods such as the finite element method, this can lead to a large amount of elements and thus, results in huge systems of equations. In order to overcome this issue, immersed methods like the finite cell method (FCM) have been developed, where the mesh is independent of the geometry, which results in a fast and simple pre‐processing. In this work, the FCM is applied to the PFM in order to simulate quasi‐static brittle fracture of structures with complex geometries. Furthermore, the non‐negative moment fitting (NNMF) is employed in order to accelerate the finite cell computations. The proposed methods are tested on a numerical example in order to demonstrate the strength of the NNMF.en1617-70612024Wileyhttps://creativecommons.org/licenses/by/4.0/Technology::620: EngineeringNatural Sciences and Mathematics::518: Numerical AnalysisTechnology::624: Civil Engineering, Environmental EngineeringConference Paper10.15480/882.1333610.1002/pamm.20240009410.15480/882.13336Conference Paper