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

authored by: 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.
Organisation(s): Institute of Mechanics and Computational Mechanics
International RTG 2657: Computational Mechanics Techniques in High Dimensions
CRC/Transregio 298: Safety Integrated and Infection Reactive Implants (SIIRI)
Institute of Continuum Mechanics
External Organisation(s): Université Paris-Saclay
Type: Article
Journal: Computational mechanics
Volume: 73
Pages: 1335-1349
No. of pages: 15
ISSN: 0178-7675
Publication date: 06.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-023-02413-9 (Access: Open)
: Details in the research portal "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 = "Publisher Copyright: {\textcopyright} The Author(s) 2023.",
year = "2024",
month = jun,
doi = "10.1007/s00466-023-02413-9",
language = "English",
volume = "73",
pages = "1335--1349",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}