A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon

verfasst von: Fynn Bensel, Marlis Reiber, Elise Foulatier, Philipp Junker, Udo Nackenhorst
Abstract: Numerical simulation of bone remodelling enables the investigation of short- and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90’s, and these models have been continuously refined since then. However, one issue which has been under discussion since those early days concerns a numerical instability known as checkerboarding. A literature review of recent approaches guided us to adopt a technique established in damage mechanics and topology optimisation, where similar mesh dependencies and instabilities occur. In our investigations, the so-called gradient enhancement is used to regularise the internal variable field, representing the evolution of the bone mass density. For this, a well-established mathematical model for load-adaptive bone remodelling is employed. A description of the constitutive model, the gradient enhancement extension and the implementation into an open-access Abaqus user element subroutine is provided. Parametric studies on the robustness of the approach are demonstrated using two benchmark examples. Finally, the presented approach is used to simulate a detailed femur model.
Organisationseinheit(en): Institut für Baumechanik und Numerische Mechanik
Internationales GRK 2657: Methoden der Numerischen Mechanik in höheren Dimensionen
SFB/Transregio 298: Sicherheitsintegrierte und infektionsreaktive Implantate (SIIRI)
Institut für Kontinuumsmechanik
Externe Organisation(en): Universität Paris-Saclay
Typ: Artikel
Journal: Computational mechanics
ISSN: 0178-7675
Publikationsdatum: 28.11.2023
Publikationsstatus: Elektronisch veröffentlicht (E-Pub)
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1007/s00466-023-02413-9 (Zugang: Offen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{94e6ed07937d4d79842cc08934a4857c,
title = "A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon",
abstract = "Numerical simulation of bone remodelling enables the investigation of short- and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90{\textquoteright}s, and these models have been continuously refined since then. However, one issue which has been under discussion since those early days concerns a numerical instability known as checkerboarding. A literature review of recent approaches guided us to adopt a technique established in damage mechanics and topology optimisation, where similar mesh dependencies and instabilities occur. In our investigations, the so-called gradient enhancement is used to regularise the internal variable field, representing the evolution of the bone mass density. For this, a well-established mathematical model for load-adaptive bone remodelling is employed. A description of the constitutive model, the gradient enhancement extension and the implementation into an open-access Abaqus user element subroutine is provided. Parametric studies on the robustness of the approach are demonstrated using two benchmark examples. Finally, the presented approach is used to simulate a detailed femur model.",
keywords = "Abaqus user element, Bone remodelling, Checkerboarding, Finite element method, Gradient enhancement",
author = "Fynn Bensel and Marlis Reiber and Elise Foulatier and Philipp Junker and Udo Nackenhorst",
note = "Funding information: The funding of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) of the International Research Training Group IRTG 2657 grant 433082294 and the SFB/TRR-298-SIIRI - Project-ID 426335750 is gratefully acknowledged. This work was supported by the compute cluster, which is funded by the Leibniz University of Hannover, the Lower Saxony Ministry of Science and Culture (MWK) and the DFG. Open Access funding enabled and organized by Projekt DEAL. F. Bensel is funded by the DFG through the IRTG 2657 grant 433082294. M. Reiber is funded by the DFG through the SFB/TRR-298-SIIRI - Project-ID 426335750. ",
year = "2023",
month = nov,
day = "28",
doi = "10.1007/s00466-023-02413-9",
language = "English",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
}