A limit analysis approach for the prediction of the human proximal femur ultimate load

A limit analysis approach for the prediction of the human proximal femur ultimate load

Aurora Angela Pisano, Paolo Fuschi

download PDF

Abstract. A limit analysis numerical procedure for the determination of a lower bound on the ultimate load of the human proximal femur is presented. The procedure, already applied by the authors in different contexts, is based on a simplified 3D geometrical model of the human femur and on the assumption of a few geometric and material data available in the relevant literature. The perfectly plastic behaviour of the human bone, due to phenomena starting at molecular scale, and the orthotropic behaviour of the main human femur tissues, trabecular and cortical, allows to assume a yield surface of Tsai-Wu-type for its constitutive description. The effectiveness of the promoted numerical approach is validated by comparison of the obtained results with experimental findings on in-vitro tests of human femurs.

Keywords
Static Limit Analysis, Human Proximal Femur, Tsai-Wu Constitutive Criterion

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Aurora Angela Pisano, Paolo Fuschi, A limit analysis approach for the prediction of the human proximal femur ultimate load, Materials Research Proceedings, Vol. 26, pp 287-292, 2023

DOI: https://doi.org/10.21741/9781644902431-47

The article was published as article 47 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] A.A. Pisano, P. Fuschi, D. De Domenico. Numerical limit analysis of steel-reinforced concrete walls and slabs, Computers and Structures, 160, 42-55, (2015). https://doi.org/10.1016/j.compstruc.2015.08.004
[2] A.A. Pisano, P. Fuschi. Limit Analysis of Human Proximal Femur. Journal of the Mechanical Behavior of Biomedical Materials. 124, 104844, (2021). https://doi.org/10.1016/j.jmbbm.2021.104844
[3] E. Dall’Ara, B. Luisier , R. Schmidt, M. Pretterklieber, F. Kainberger, P. Zysset , D. Pahr. DXA predictions of human femoral mechanical properties depend on the load configuration, Medical Engineering & Physics, 35, 1564-1572, (2013). https://doi.org/10.1016/j.medengphy.2013.04.008
[4] R.O. Ritchie, M.J. Buehler, P. Hansma. Plasticity and toughness in bone, Physics Today, 62(6), 41-47, (2009). https://doi.org/10.1063/1.3156332
[5] G. Holzer, G. von Skrbensky, L.A. Holzer, W. Pichl. Hip Fractures and the Contribution of Cortical Versus Trabecular Bone to Femoral Neck Strength, Journal of Bone and Mineral Research, 24(3), 468-474, (2009). https://doi.org/10.1359/jbmr.081108
[6] J. Michelotti, J. Clark. Femoral Neck Length and Hip Fracture Risk, Journal of Bone and Mineral Research, 14(10), 1714-1720, (1999). https://doi.org/10.1359/jbmr.1999.14.10.1714
[7] Z. Yang, W. Jian, L. Zhi-han, X. Jun, Z. Liang, Y. Ge, S. Zhan-jun. The Geometry of the Bone Structure Associated with Total Hip Arthroplasty. PLOS ONE, 9(3):e91058, doi: 10.1371/journal.pone. 0091058, (2014). https://doi.org/10.1371/journal.pone.0091058
[8] D.C. Wirtz, N. Schiffers, T. Pandorf, K. Radermacher, D. Weichert, R. Forst. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of proximal femur, Journal of Biomechanics, 33, 1325-1330, (2000). https://doi.org/10.1016/S0021-9290(00)00069-5
[9] J.C. Lotz, T.N. Gerhart, W.C. Hayes. Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study, Journal of Computer Assisted Tomography, 14, 107-114, (1990). https://doi.org/10.1097/00004728-199001000-00020
[10] J.C. Lotz, T.N. Gerhart, W.C. Hayes. Mechanical properties of metaphyseal bone in the proximal femur, Journal of Biomechanics, 24, 317-329, (1991). https://doi.org/10.1016/0021-9290(91)90350-V
[11] J. Currey. Cortical Bone. In: Handbook of Biomaterial Properties, (Chapter A1) Springer Science + Business Media New York 2016, W. Murphy et al. (eds.), (2016).
[12] M. Doblaré, J.M. García, M.J. Gómez. Modelling bone tissue fracture and healing: a review, Engineering Fracture Mechanics, 71, 1809-1840, (2004). https://doi.org/10.1016/j.engfracmech.2003.08.003
[13] L. Rincón-Kohli, P.K. Zysset. Multi-axial mechanical properties of human trabecular bone. Biomechanics and Modeling in Mechanobiology, 8(3), 195-208, (2009). https://doi.org/10.1007/s10237-008-0128-z
[14] C.H. Turner, T. Wang, D.B. Burr. Shear Strength and Fatigue Properties of Human Cortical Bone Determined from Pure Shear Tests, Calcified Tissue International, 69, 373-378, (2001). https://doi.org/10.1007/s00223-001-1006-1
[15] A. Sanyal, A. Gupta, H.H. Bayraktar, R.Y. Kwon, T.M. Keaveny. Shear strength behavior of human trabecular bone. Journal of Biomechanics, 45, 2513-2519, (2012). https://doi.org/10.1016/j.jbiomech.2012.07.023
[16] S.P. Väänänen, L. Grassid, G. Lorenzo, G. J.S. Flivike, J.S, Jurvelina., H. Isaksson, Generation of 3D shape, density, cortical thickness and finite element mesh of proximal femur froma DXA image, Medical Image Analysis,24, 125-134, (2015). https://doi.org/10.1016/j.media.2015.06.001