PSI - Issue 1

R. Baptista et al. / Procedia Structural Integrity 1 (2016) 018–025 Author name / Structural Integrity Procedia 00 (2016) 000 – 000

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4. Discussion and Conclusions

The authors fully achieved their goals on developing a new model for crack initiations and propagation in the neighborhood of one or several osteons. Although a lot of work still needs to be done to fully understand why cortical bone is so resistant to crack propagation several conclusions arise from the present work. Small and larger crack can be attracted by the osteon but the ratio between the size of the osteon and the distance to the crack is very important. The angle and the vertical distance of the crack, in relation to the osteon is also important, but if the osteon is softer than the interstitial matrix, the osteon will be able to attract the cracks. Stiffer osteons and harder cement lines will decrease the attraction tendency. Finally using a dynamic model it was possible to study the crack path around the osteons distribution and it was verified that soft osteons do in fact attract and arrest the crack propagation by deflecting their path and directing them to the Haversian channel, where the propagation stops. Abdel-Wahab, A.A., Maligno, A.R. & Silberschmidt, V. V., 2012. Micro-scale modelling of bovine cortical bone fracture: Analysis of crack propagation and microstructure using X-FEM. Computational Materials Science , 52(1), pp.128 – 135. Available at: http://www.sciencedirect.com/science/article/pii/S0927025611000450. Budyn, É. & Hoc, T., 2007. Multiple scale modeling for cortical bone fracture in tension using X-FEM. Revue européenne de mécanique numérique , 16(March 2015), pp.213 – 236. Huang, J., Rapoff, A.J. & Haftka, R.T., 2006. Attracting cracks for arrestment in bone-like composites. Materials and Design , 27(6), pp.461 – 469. I. Babuska and J. M. Melenk. The partition of unity method. International Journal of Numerical Methods in Engineering, 40:727-758, 1996. Libonati, F., 2013. Realization of a bone-inspired composite by means of a biomimetic approach. Convegno Igf Xxii Roma 2013 , pp.1 – 3. Available at: http://www.gruppofrattura.it/ocs/index.php/cigf/IGF22/paper/download/10899/10280. Mohs in, S., O’Brien, F.J. & Lee, T.C., 2006. Osteonal crack barriers in ovine compact bone. Journal of anatomy , 208(1), pp.81 – 9. Available at: http://www.scopus.com/inward/record.url?eid=2-s2.0-33645961577&partnerID=tZOtx3y1. Najafi, A.R. et al., 2007. Haversian cortical bone model with many radial microcracks: An elastic analytic solution. Medical Engineering & Physics , 29(6), pp.708 – 717. Available at: http://linkinghub.elsevier.com/retrieve/pii/S1350453306001573. Raeisi Najafi, A. et al., 2009. A fiber-ceramic matrix composite material model for osteonal cortical bone fracture micromechanics: Solution of arbitrary microcracks interaction. Journal of the Mechanical Behavior of Biomedical Materials , 2(3), pp.217 – 223. Available at: http://linkinghub.elsevier.com/retrieve/pii/S1751616108000532. Raeisi Najafi, A. et al., 2007. Micromechanics fracture in osteonal cortical bone: A study of the interactions between microcrack propagation, microstructure and the material properties. Journal of Biomechanics , 40(12), pp.2788 – 2795. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0021929007000619. Vashishth, D., Tanner, K.E. & Bonfield, W., 2000. Contribution, development and morphology of microcracking in cortical bone during crack propagation. Journal of Biomechanics , 33(9), pp.1169 – 1174. Vergani, L., Colombo, C. & Libonati, F., 2014. Crack Propagation in Cortical Bone: A Numerical Study. Procedia Materials Science , 3, pp.1524 – 1529. Available at: http://www.sciencedirect.com/science/article/pii/S2211812814002478. Zahan, N., Brown, J. & Elliott, D., 2009. Relationships Among Microstructural Features and Crack Propagation in Osteonal Bone Identified Using Finite Element Analysis. Critical Care , p.2009. T. Belytschko. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5):601-620, 1999. References