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

  • Elisa Budyn (a1) and Thierry Hoc (a2)
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.

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References
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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, 466474 (2006).
2. Belytschko, T. and Black, T., “Elastic Crack Growth in Finite Elements with Minimal Remeshing”, Int.J. Numerical Methods in Engineering, 45(5), 610620 (1999).
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), 131150 (1999).
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).
5. Reilly, D.T. and Burstein, A.H., “The elastic and ultimate properties of compact bone tissue”, J. Biomechanics, 8(6), 393405 (1975).
6. ABAQUS, User's Manual, Hibbit, Version 6.3, Karlsson & Sorensen, Providence, (2004).
7. Pattin, C.A., Calet, W.E., and Carter, D.R., Cyclic mechanical property degradation during fatigue loading of cortical bone”, J. Biomechanics, 29, 6979 (1996).
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, 2735 (2004).
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), 17411770 (2004).
10. Moran, B. and Shih, C.F., “A general treatment of crack tip coutour integrals”, Int. J. Fracture, 35, 295310 (1987).
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, 35013508 (2003).
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, 577581 (1987).
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, 112117 (1995).
14. Akkus, O. and Rimnac, C.M., “Cortical bone tissue resists fatigue fracture by deceleration and arrest of microcrack growth”, J. Biomechanics, 34, 757764 (2001).
15. Mohsin, S., O'Brien, F.J., Lee, T.C., “Osteonal crack barriers in ovine compact bone”, J. Anatomy, 208, 8189 (2006).
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  • EISSN: 1946-4274
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