On the mechanical characterization of compact bone structure using the homogenization theory

In a previous paper (Crolet et al., 1993, J. Biomechanics26, 677–687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has a non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization. The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.