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Multi-Scale Modeling of Human Cortical Bone: Aging and Failure Studies

Published online by Cambridge University Press:  26 February 2011

Elisa Budyn  and
Thierry Hoc
Elisa Budyn
Affiliation:
ebudyn@uic.edu, University of Illinois at Chicago, Department of Mechanical Engineering, 842 West Taylor Street, Chicago, IL, 60607, United States, 312 996 96 31, 312 413 0447
Thierry Hoc
Affiliation:
hoc@mssmat.ecp.fr, Ecole Centrale Paris, Department of Material Science - LMSSMat, Grande Voie des Vignes, Chatenay Malabry, 92295, France
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Abstract

A multi-scale analysis for unit cells of human cortical bone is presented. Two studies are conducted: the first study concerns the effect of aging over the structural and mechanical properties of human cortical bone; the second study is devoted to the failure mechanism and the development of cracks in cortical bone under various loading conditions. Experiments are conducted on human specimen of different ages in order to measure relevant geometrical and mechanical parameters and obtain microscopic data that will be injected into finite element models. First a continuum FEM model will compute macroscopic information that will be validated through comparison with the experimental measurements. For the failure mechanism study, an XFEM model will be developed in order to allow the growth of multiple cracks until complete failure of the cell. An elastic-damage criterion will be used in order to place the initial cracks in maximum strain locations. To follow the global response of the cell, the stress intensity factors are computed at each crack tip and a load parameter is adjusted so that the stress intensity factors remain at the critical value. In the case of competitive crack tips, a stability analysis is performed by computing the second derivative of the potential energy for each crack. Fatigue loading will be also investigated. The discretization utilizes the eXtended Finite Element Method and requires no remeshing as the cracks grow. The crack geometries are arbitrary with respect to the mesh, and are described by a vector level set. Special boundary conditions and the algorithm for detecting crack bridging and crack entering Haversian canals which allows the cracks to grow until maximum failure and/or percolation is presented.

Keywords

bonefracturemicrostructure
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 975: Symposium DD – Mechanics of Biological and Bio-Inspired Materials , 2006 , 0975-DD02-06
Copyright
Copyright © Materials Research Society 2007

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References

REFERENCES

1. Hoc, T., Henry, L., Verdier, M., Aubry, D., Sedel, L. and Meunier, A., “Effect of microstructure on the mechanical properties of Haversian cortical bone”, Bone, 38, 466–474 (2006).Google Scholar
2. Belytschko, T. and Black, T., “Elastic Crack Growth in Finite Elements with Minimal Remeshing”, Int.J. Numerical Methods in Engineering, 45(5), 610–620 (1999).Google Scholar
3. Moës, N., Dolbow, J. and Belytschko, T., “A Finite Element Method for Crack Growth without Remeshing”, Int. J. Numerical Methods in Engineering, 46(1), 131–150 (1999).Google Scholar
4. Budyn, E., Hoc, T., “Multiple scale modeling for crack growth in cortical bone under tension using the eXtended Finite Element Method”, Revue Européenne de Mécanique Numérique, Special Issue, to appear, (2006).Google Scholar
5. Reilly, D.T. and Burstein, A.H., “The elastic and ultimate properties of compact bone tissue”, J. Biomechanics, 8(6), 393–405 (1975).Google Scholar
6. ABAQUS, User's Manual, Hibbit, Version 6.3, Karlsson & Sorensen, Providence, (2004).Google Scholar
7. Pattin, C.A., Calet, W.E., and Carter, D.R., Cyclic mechanical property degradation during fatigue loading of cortical bone”, J. Biomechanics, 29, 69–79 (1996).Google Scholar
8. Bayraktar, H., Morgan, E.F., Niebur, G.L., Morris, G.E., Wong, E.K. and Keaveny, T.M., “Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue “, J. Biomechanics, 37, 27–35 (2004).Google Scholar
9. Budyn, E., Zi, G., Moës, N. and Belytschko, T., “A method for multiple crack growth in brittle materials without remeshing”, Int. J. Numerical Methods in Engineering, 61(10), 1741–1770 (2004).Google Scholar
10. Moran, B. and Shih, C.F., “A general treatment of crack tip coutour integrals”, Int. J. Fracture, 35, 295–310 (1987).Google Scholar
11. Shelton, D.R., Martin, R.B., Stover, S.M. and Gibeling, J.C., “Transverse fatigue crack propagation behavior in equine cortical bone”, J. Materials Science, 38, 3501–3508 (2003).Google Scholar
12. Advani, S.H., Lee, T.S. and Martin, R.B., “Analysis of crack arrest by cement lines in osteonal bone”, Proc. ASME Annual Winter Meeting, 3, 577–581 (1987).Google Scholar
13. Guo, X.E., He, M.Y. and Goldstein, S.A., “Analysis of viscoelastic behaviour of bones on the basis of microstructure”, Bioengineering Conference – ASME, BED-29, 112–117 (1995).Google Scholar
14. Akkus, O. and Rimnac, C.M., “Cortical bone tissue resists fatigue fracture by deceleration and arrest of microcrack growth”, J. Biomechanics, 34, 757–764 (2001).Google Scholar
15. Mohsin, S., O'Brien, F.J., Lee, T.C., “Osteonal crack barriers in ovine compact bone”, J. Anatomy, 208, 8189 (2006).Google Scholar