TY - JOUR A1 - Elhaddad, Mohamed A1 - Zander, Nils A1 - Bog, Tino A1 - Kudela, László A1 - Kollmannsberger, Stefan A1 - Kirschke, Jan A1 - Baum, Thomas A1 - Ruess, Martin A1 - Rank, Ernst T1 - Multi-level hp-finite cell method for embedded interface problems with application in biomechanics JF - International Journal for Numerical Methods in Biomedical Engineering N2 - This work presents a numerical discretization technique for solving 3-dimensional material interface problems involving complex geometry without conforming mesh generation. The finite cell method (FCM), which is a high-order fictitious domain approach, is used for the numerical approximation of the solution without a boundary-conforming mesh. Weak discontinuities at material interfaces are resolved by using separate FCM meshes for each material sub-domain and weakly enforcing the interface conditions between the different meshes. Additionally, a recently developed hierarchical hp-refinement scheme is used to locally refine the FCM meshes to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for nonsmooth problems. A series of numerical experiments with 2- and 3-dimensional benchmark problems is presented, showing that the proposed hp-refinement scheme in conjunction with the weak enforcement of the interface conditions leads to a significant improvement of the convergence rates, even in the presence of singularities. Finally, the proposed technique is applied to simulate a vertebra-implant model. The application showcases the method's potential as an accurate simulation tool for biomechanical problems involving complex geometry, and it demonstrates its flexibility in dealing with different types of geometric description. Y1 - 2018 UR - http://www.ncbi.nlm.nih.gov/pubmed/29265715 U6 - https://doi.org/10.1002/cnm.2951 SN - 2040-7947 VL - 34 IS - 4 PB - Wiley ER - TY - JOUR A1 - Nguyen, Lam H. A1 - Stoter, Stein K.F. A1 - Baum, Thomas A1 - Kirschke, Jan A1 - Ruess, Martin A1 - Yosibash, Zohar A1 - Schillinger, Dominik T1 - Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures JF - International Journal for Numerical Methods in Biomedical Engineering Y1 - 2017 UR - http://www.ncbi.nlm.nih.gov/pubmed/28294574 U6 - https://doi.org/10.1002/cnm.2880 SN - 2040-7947 VL - 33 IS - 12 PB - Wiley ER -