Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 853-866 |
| Seitenumfang | 14 |
| Fachzeitschrift | Computational mechanics |
| Jahrgang | 71 |
| Ausgabenummer | 5 |
| Frühes Online-Datum | 13 Feb. 2023 |
| Publikationsstatus | Veröffentlicht - Mai 2023 |
Abstract
This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Numerische Mechanik
- Ingenieurwesen (insg.)
- Meerestechnik
- Ingenieurwesen (insg.)
- Maschinenbau
- Informatik (insg.)
- Theoretische Informatik und Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Computational mechanics, Jahrgang 71, Nr. 5, 05.2023, S. 853-866.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations
AU - Bittens, Maximilian
AU - Nackenhorst, Udo
N1 - Open Access funding enabled and organized by Projekt DEAL.
PY - 2023/5
Y1 - 2023/5
N2 - This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method.
AB - This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method.
KW - Biomechanics
KW - Bone remodeling
KW - Finite elements
KW - Thermodynamics with internal state variables
UR - http://www.scopus.com/inward/record.url?scp=85147905477&partnerID=8YFLogxK
U2 - 10.1007/s00466-022-02263-x
DO - 10.1007/s00466-022-02263-x
M3 - Article
AN - SCOPUS:85147905477
VL - 71
SP - 853
EP - 866
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 5
ER -