ON THE MECHANICAL CHARACTERIZATION OF COMPACT-BONE STRUCTURE USING THE HOMOGENIZATION THEORY

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677-587) , 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 th e lamellae and the osteons: the lamella and the osteon were divided in to cylindrical sectors, each sector being approximated as a parallelep iped having a periodic structure (fibrous composite for the lamella, s uperimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved tha t the homogenized elasticity tensor for a lamella, which has a non-per iodic structure, is obtained at each geometrical point as a homogenize d 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, whic h is the computational method associated with this model, allows one t o obtain a better understanding of the effects of many bony parameters . The obtained results are in accordance with experimental data. Copyr ight (C) 1996 Elsevier Science Ltd.