Image‐based analysis of complex microstructures using the finite cell method

Geometry conforming meshing techniques such as the finite element method (FEM) face a big challenge when dealing with complex and heterogeneous microstructures. Therefore, efficient simulation methods are needed combining accurate morphological reproducibility and computational efficiency. For such problems, the finite cell method (FCM) is a promising approach, which uses a Cartesian grid – independent of the geometry – leading to a fast and efficient mesh generation. However, to handle complex microstructures such as cemented sands the FCM is not sufficient anymore. Therefore, three different versions of the FCM are presented: first, the FCM, which is directly applied to CT scans (denoted as “VoxelFCM”). Second, the FCM combined with a global L² -projection, leading to a smooth geometry description (denoted as “FCM”). And finally, the FCM with L² -projection, which is extended by a local enrichment to capture weak discontinuities at the interfaces between the different phases (denoted as “FCM-Enrichment”). First, in a numerical study, the different versions of the FCM are investigated. Then, these methods are verified against the FEM. Finally, these methods are used to gain a deeper insight into the micromechanical phenomena of cemented sands under compressive loading.