Details
| Original language | English |
|---|---|
| Journal | Computational mechanics |
| Early online date | 28 Nov 2023 |
| Publication status | E-pub ahead of print - 28 Nov 2023 |
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.
Keywords
- Abaqus user element, Bone remodelling, Checkerboarding, Finite element method, Gradient enhancement
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, 28.11.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A gradient-enhanced bone remodelling approach to avoid the checkerboard phenomenon
AU - Bensel, Fynn
AU - Reiber, Marlis
AU - Foulatier, Elise
AU - Junker, Philipp
AU - Nackenhorst, Udo
N1 - 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.
PY - 2023/11/28
Y1 - 2023/11/28
N2 - 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.
AB - 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.
KW - Abaqus user element
KW - Bone remodelling
KW - Checkerboarding
KW - Finite element method
KW - Gradient enhancement
UR - http://www.scopus.com/inward/record.url?scp=85178354725&partnerID=8YFLogxK
U2 - 10.1007/s00466-023-02413-9
DO - 10.1007/s00466-023-02413-9
M3 - Article
AN - SCOPUS:85178354725
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
ER -