Multi‐level hp‐finite cell method for embedded interface problems with application in biomechanics

• Published in: International journal for numerical methods in biomedical engineering Vol. 34; no. 4; pp. e2951 - n/a
• Main Authors: Elhaddad, Mohamed, Zander, Nils, Bog, Tino, Kudela, László, Kollmannsberger, Stefan, Kirschke, Jan, Baum, Thomas, Ruess, Martin, Rank, Ernst
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.04.2018
• Subjects: Biomechanical Phenomena; Biomechanics; Computer simulation; Convergence; domain coupling; embedded interface problems; finite cell method; Finite Element Analysis; Finite element method; high‐order finite elements; hp adaptivity; Interfaces; Mathematical models; Mesh generation; Numerical Analysis, Computer-Assisted; Pedicle Screws; Singularity (mathematics); Spine; Spine - surgery; Stress, Mechanical; Vertebrae; vertebra‐implant model; embedded interface problems; vertebra-implant model; high-order finite elements; hp adaptivity; finite cell method; domain coupling
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.2951

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. A numerical discretization technique for solving material interface problems involving complex geometry without mesh generation is presented. The presented technique combines a fictitious domain approach with a domain coupling method and a hierarchical local refinement scheme. A series of numerical benchmarks demonstrates the favorable convergence properties of the suggested technique. Finally, the scheme is applied to simulate a full 3‐dimensional vertebra‐implant model, illustrating the method's potential as an accurate simulation tool for biomechanical problems involving complex geometry.