Haversian cortical bone model with many radial microcracks: An elastic analytic solution

Abstract 

In this study, the fracture micromechanics of Haversian cortical bone has been considered. To this effect, a two-dimensional micromechanical fibre–ceramic matrix composite tissue materials model has been presented. The interstitial tissue was modeled as a matrix and the osteon was modeled as a fibre, followed by the application of linear elastic fracture mechanics theory. The solution for edge dislocations, in terms of Green's functions, was adopted to formulate a system of singular integral equations for the radial microcracks in the matrix in vicinity of the osteon. The problem was solved for various configurations and the corresponding stress intensity factors were computed. The results of this study indicated that the interaction between microcracks and an osteon was limited to vicinity of the osteon. Furthermore, the effect of microstructure morphology and heterogeneity on the fracture behavior has been established. The interactions between microcracks were also analyzed for various configurations. These selected configurations exhibited the effects of stress amplification and stress shielding.

Keywords: Haversian cortical bone, Microcrack interaction, Linear elastic fracture mechanics, Microstructure, Edge dislocation