Boolean finite cell method for multi-material problems including local enrichment of the Ansatz space

The Finite Cell Method (FCM) allows for an efficient and accurate simulation of complex geometries by utilizing an unfitted discretization based on rectangular elements equipped with higher-order shape functions. Since the mesh is not aligned to the geometric features, cut elements arise that are intersected by domain boundaries or internal material interfaces. Hence, for an accurate simulation of multi-material problems, several challenges have to be solved to handle cut elements. On the one hand, special integration schemes have to be used for computing the discontinuous integrands and on the other hand, the weak discontinuity of the displacement field along the material interfaces has to be captured accurately. While for the first issue, a space-tree decomposition is often employed, the latter issue can be solved by utilizing a local enrichment approach, adopted from the extended finite element method. In our contribution, a novel integration scheme for multi-material problems is introduced that, based on the B-FCM formulation for porous media, originally proposed by Abedian and Duster (Comput Mech 59(5):877-886, 2017), extends the standard space-tree decomposition by Boolean operations yielding a significantly reduced computational effort. The proposed multi-material B-FCM approach is combined with the local enrichment technique and tested for several problems involving material interfaces in 2D and 3D. The results show that the number of integration points and the computational time can be reduced by a significant amount, while maintaining the same accuracy as the standard FCM.

Automated summary

The Finite Cell Method (FCM) is an efficient and accurate simulation method for complex geometries. It uses rectangular elements with higher-order shape functions and handles cut elements at domain boundaries or material interfaces. This study introduces a novel integration scheme for multi-material problems that extends the standard space-tree decomposition and combines it with a local enrichment technique. The results show significant reductions in the number of integration points and computational time while maintaining accuracy.