Nano and Macro Structure of Cortical Bone: Numerical Investigations

International audienceWe propose a multi-scale approach: cortical bone is structured in a hierarchy of five levels. The cortical part of a given bone is made of various areas having different physical properties adapted to locally existing solicitations. A Bony Elementary Volume (BEV) denotes the elementary part of such a zone which constitutes our first level. The other levels are in conformity with our previous studies: osteon, lamella, fiber and fibril. The latter is composed of collagen and hydroxyapatite (Hap) occurring in a viscous liquid containing mineral ions. Mathematical homogenization theory is used to determine equivalent macroscopic properties of a BEV, knowing physical properties of collagen and Hap and architectural description of this bony structure. A new behavior's law has been introduced with no continuity between the various levels. The effect of the fluid at the nanoscopic scale is modeled by a constant pressure. The computational methods have been packed into software called SiNuPrOs. For a given organization of EVMC, mechanical properties are found at each level of the bony architecture and of course at the macroscopic level. The influence of EVMC's properties on the macroscopic properties of cortical bone has been studied and the influence of the different parameters variations is also presented