Details
| Original language | English |
|---|---|
| Pages (from-to) | 853-866 |
| Number of pages | 14 |
| Journal | Computational mechanics |
| Volume | 71 |
| Issue number | 5 |
| Early online date | 13 Feb 2023 |
| Publication status | Published - May 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.
Keywords
- Biomechanics, Bone remodeling, Finite elements, Thermodynamics with internal state variables
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, Vol. 71, No. 5, 05.2023, p. 853-866.
Research output: Contribution to journal › Article › Research › 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 -