Abstract
The design of efficient and safe biocompatible artificial implants for bone replacement and reconstructions requires a thorough understanding of natural bone material. A new homogenization approach is therefore used to predict effective material properties of the human femur bone. The bone structure is idealized as a functionally graded (FG) composite made of different quantities of a collagen protein matrix reinforced by hydroxyapatite mineral acting as the filler. Two distinct composite models were investigated, one where the mineral reinforcements were assumed to be randomly dispersed inclusions in a matrix of collagen, and a second model wherein the minerals were assumed to be unidirectional fibers. Predicted results for longitudinal and transverse elastic modulus from the models compare very well with range of values from published experimental data. It is also compared to those predicted using classical homogenization models. These material properties are then used to obtain the structural response of a bone plate section under transverse load.
Issue Section:
Research Papers
References
1.
Moghadasi
, K.
, Isa
, M. S. M.
, Ariffin
, M. A.
, Jamil
, M. Z. M.
, Raja
, S.
, Wu
, B.
, Yamani
, M.
, et al., 2022
, “A Review on Biomedical Implant Materials and the Effect of Friction Stir Based Techniques on Their Mechanical and Tribological Properties
,” J. Mater. Res. Technol.
, 17
(2
), pp. 1054
–1121
.10.1016/j.jmrt.2022.01.0502.
Cheung
, C.-L.
, Ang
, S. B.
, Chadha
, M.
, Chow
, E. S.-L.
, Chung
, Y.-S.
, Hew
, F. L.
, Jaisamrarn
, U.
, et al., 2018
, “An Updated Hip Fracture Projection in Asia: The Asian Federation of Osteoporosis Societies Study
,” Osteoporosis Sarcopenia
, 4
(1
), pp. 16
–21
.10.1016/j.afos.2018.03.0033.
Elmasry
, A.
, Azoti
, W.
, El-Safty
, S. A.
, and Elmarakbi
, A.
, 2023
, “A Comparative Review of Multiscale Models for Effective Properties of Nano- and Micro-Composites
,” Prog. Mater. Sci.
, 132
(2
), p. 101022
.10.1016/j.pmatsci.2022.1010224.
Boggarapu
, V.
, Gujjala
, R.
, Ojha
, S.
, Acharya
, S.
, Venkateswara Babu
, P.
, Chowdary
, S.
, and Kumar Gara
, D.
, 2021
, “State of the Art in Functionally Graded Materials
,” Compos. Struct.
, 262
(8
), p. 113596
.10.1016/j.compstruct.2021.1135965.
Thai
, H. T.
, and Kim
, S. E.
, 2015
, “A Review of Theories for the Modeling and Analysis of Functionally Graded Plates and Shells
,” Compos. Struct.
, 128
(10
), pp. 70
–86
.10.1016/j.compstruct.2015.03.0106.
Hamed
, E.
, 2013
, Multiscale Modeling of Elastic Moduli and Strength of Bone
, University of Illinois at Urbana-Champaign
, Champaign, IL.7.
Satapathy
, P. K.
, Sahoo
, B.
, Panda
, L. N.
, and Das
, S.
, 2018
, “Finite Element Analysis of Functionally Graded Bone Plate at Femur Bone Fracture Site
,” IOP Conference Series: Materials Science and Engineering
, IOP Publishing
, Hyderabad, India
, June 1–2, p. 012027
.10.1088/1757-899X/330/1/0120278.
Eshelby
, J. D.
, 1957
, “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
,” Proc. R. Soc. London, Ser. A
, 241
(1226
), pp. 376
–396
.10.1098/rspa.1957.01339.
Reisinger
, A.
, 2011
, Modeling and Validation of Multiscale Lamellar Bone Elasticity
, Vienna University of Technology
, Vienna, Austria.10.
Alijani
, H.
, and Vaughan
, T. J.
, 2022
, “A Multiscale Finite Element Investigation on the Role of Intra- and Extra-Fibrillar Mineralisation on the Elastic Properties of Bone Tissue
,” J. Mech. Behav. Biomed. Mater.
, 129
(1
), p. 105139
.10.1016/j.jmbbm.2022.10513911.
Chao
, X.
, Hu
, H.
, Qi
, L.
, Yang
, C.
, Tian
, W.
, and Shou
, D.
, 2023
, “An Asymptotic Homogenization Model for Evaluating the Mechanical Properties of Random Fiber Reinforced Composites With High Volume Fraction
,” Compos. Commun.
, 40
(1
), p. 101633
.10.1016/j.coco.2023.10163312.
Swaroop
, D.
, Dhar
, D.
, Suriyan
, A.
, and Jain
, A.
, 2022
, “Of Spheres and Infinite Cylinders: A Critical Relook at Multi-Step Mean-Field Homogenization Formulations
,” Mech. Mater.
, 174
(1
), p. 104447
.10.1016/j.mechmat.2022.10444713.
Yassine
, R. A.
, Elham
, M. K.
, Mustapha
, S.
, and Hamade
, R. F.
, 2018
, “Heterogeneous Versus Homogeneous Material Considerations in Determining the Modal Frequencies of Long Tibia Bones
,” ASME J. Eng. Sci. Med. Diagn. Ther.
, 1
(2
), p. 021001
.10.1115/1.403844814.
Ahirwar
, H.
, Gupta
, V. K.
, and Nanda
, H. S.
, 2021
, “Finite Element Analysis of Fixed Bone Plates Over Fractured Femur Model
,” Comput. Methods Biomech. Biomed. Eng.
, 24
(15
), pp. 1742
–1751
.10.1080/10255842.2021.191812315.
Tiwari
, A.
, Wahi
, P.
, and Sinha
, N.
, 2019
, “Finite Element Analysis of Human Tibia Modeled as a Functionally Graded Material
,” ASME J. Eng. Sci. Med. Diagn. Ther.
, 2
(3
), p. 031007
.10.1115/1.404405416.
Kabir
, M.
, Pervez
, T.
, Al-Jahwari
, F. K. S.
, and Qamar
, S. Z.
, 2024
, “Modeling of Human Femoral Bone Idealized as Functionally Graded and Laminated Composite Structure
,” ASME
Paper No. IMECE2023-112920.10.1115/IMECE2023-11292017.
Kabir
, M.
, Pervez
, T.
, Qamar
, S. Z.
, and Al-Jahwari
, F. K. S.
, 2024
, “Weighted Mori-Tanaka Approach for Homogenization of Particulate Composites at High Filler Fractions
,” ASME
Paper No. IMECE2023-112951.10.1115/IMECE2023-11295118.
Kahla
, B. R.
, and Barkaoui
, A.
, 2021
, Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling
, Academic Press
, London, UK
.19.
Schwarcz
, H. P.
, 2015
, “The Ultrastructure of Bone as Revealed in Electron Microscopy of Ion-Milled Sections
,” Semin. Cell Dev. Biol.
, 46
(1
), pp. 44
–50
.10.1016/j.semcdb.2015.06.00820.
Chen
, P.-Y.
, Toroian
, D.
, Price
, P. A.
, and McKittrick
, J.
, 2011
, “Minerals Form a Continuum Phase in Mature Cancellous Bone
,” Calcif. Tissue Int.
, 88
(5
), pp. 351
–361
.10.1007/s00223-011-9462-821.
Aboudi
, J.
, Arnold
, S. M.
, and Bednarcyk
, B. A.
, 2013
, Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach
, Butterworth-Heinemann
, Oxford, UK
.22.
Weng
, G. J.
, 1990
, “The Theoretical Connection Between Mori-Tanaka's Theory and the Hashin-Shtrikman-Walpole Bounds
,” Int. J. Eng. Sci.
, 28
(11
), pp. 1111
–1120
.10.1016/0020-7225(90)90111-U23.
Zhao
, Y. H.
, Tandon
, G. P.
, and Weng
, G. J.
, 1989
, “Elastic Moduli for a Class of Porous Materials
,” Acta Mech.
, 76
(1–2
), pp. 105
–131
.10.1007/BF0117579924.
Soden
, P. D.
, Hinton
, M. J.
, and Kaddour
, A. S.
, 1998
, “Lamina Properties, Lay-Up Configurations and Loading Conditions for a Range of Fibre-Reinforced Composite Laminates
,” Compos. Sci. Technol.
, 58
(7
), pp. 1011
–1022
.10.1016/S0266-3538(98)00078-525.
Morgan
, E. F.
, Unnikrisnan
, G. U.
, and Hussein
, A. I.
, 2018
, “Bone Mechanical Properties in Healthy and Diseased States
,” Annu. Rev. Biomed. Eng.
, 20
(1
), pp. 119
–143
.10.1146/annurev-bioeng-062117-12113926.
Pervez
, T.
, and Zabaras
, N.
, 1992
, “Transient Dynamic and Damping Analysis of Laminated Anisotropic Plates Using a Refined Plate Theory
,” Int. J. Numer. Methods Eng.
, 33
(5
), pp. 1059
–1080
.10.1002/nme.1620330511Copyright © 2025 by ASME
You do not currently have access to this content.
