Steinmann, Paul and Schmidt, Ina and Pivonka, Peter and Papastavrou, Areti (2024) A computational two-scale approach to cancellous bone remodelling. Advanced Modeling and Simulation in Engineering Sciences, 11: 13. ISSN 2213-7467

Abstract

We propose a novel two-scale (meso-macro-scale) approach to computationally capture cancellous bone remodelling allowing for efficient and effective numerical implementation. Therein, the macro-scale is governed by the well-established kinematics and kinetics of one-scale continuum bone remodelling. However, the constitutive behaviour is not postulated phenomenologically at the macro-scale, but rather follows from the meso-scale. There, for the sake of computational efficiency, the trabecular architecture is idealised as a truss network with the cross-sectional area of the trabeculae adapting to mechanical loading. Then, the meso- and the macro-scale are coupled through up- and down-scaling. Computational results on benchmark problems from bio-mechanics demonstrate that the proposed two-scale approach is effective from a modelling perspective and efficient from a computational perspective. In particular, it automatically captures anisotropy resulting from the irregular trabecular architecture at the meso-scale, and, most importantly, enables the direct investigation of different trabecular structures at the meso-scale, thereby serving as a virtual “magnifiying glass”. As an outlook, the proposed two-scale approach to cancellous bone remodelling provides an excellent launch pad for further extension, e.g., by considering more complex trabecular architectures and/or through inclusion of micro-scale bone cellular activities.

People
Steinmann, P.
Author

Greiner, Alexander and Reiter, Nina and Hinrichsen, Jan and Kainz, Manuel P. and Sommer, Gerhard and Holzapfel, Gerhard A. and Steinmann, Paul and Comellas, Ester and Budday, Silvia (2024) Model-driven exploration of poro-viscoelasticity in human brain tissue: be careful with the parameters! Interface Focus, 14 (6): 20240026. ISSN 2042-8901

Steinmann, Paul and Schmidt, Ina and Pivonka, Peter and Papastavrou, Areti (2024) A computational two-scale approach to cancellous bone remodelling. Advanced Modeling and Simulation in Engineering Sciences, 11: 13. ISSN 2213-7467

Moreno-Mateos, Miguel Angel and Steinmann, Paul (2024) Configurational force method enables fracture assessment in soft materials. Journal of the Mechanics and Physics of Solids, 186: 105602. ISSN 0022-5096

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Schmidt, Ina
Author

Steinmann, Paul and Schmidt, Ina and Pivonka, Peter and Papastavrou, Areti (2024) A computational two-scale approach to cancellous bone remodelling. Advanced Modeling and Simulation in Engineering Sciences, 11: 13. ISSN 2213-7467

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Pivonka, Peter
Author

Steinmann, Paul and Schmidt, Ina and Pivonka, Peter and Papastavrou, Areti (2024) A computational two-scale approach to cancellous bone remodelling. Advanced Modeling and Simulation in Engineering Sciences, 11: 13. ISSN 2213-7467

See full publications list
Papastavrou, Areti
Author

Steinmann, Paul and Schmidt, Ina and Pivonka, Peter and Papastavrou, Areti (2024) A computational two-scale approach to cancellous bone remodelling. Advanced Modeling and Simulation in Engineering Sciences, 11: 13. ISSN 2213-7467

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