Compact bone: numerical simulation of mechanical characteristics

One of the main difficulties encountered in the numerical simulation of the anisotropic elastic characteristics of compact bone is to account for the Haversian microstructure when determining the overall macroscopic behavior. Engineering analyses of such problems are usually based on 'homogenized approximations'. Compact bone is not exactly a composite material, but rather a heterogeneous medium which exhibits a multiscale composite structure. If the homogenized approximation is precise enough (and this is true for the mathematical theory of homogenization), it is then possible to simulate the macroscopic behavior from the microscopic mechanical characteristics. The present paper is devoted to such mathematical developments. Moreover, the 'inverse simulation' allows the computation of the microscopic stress fields in the haversian structure from the macroscopic stress fields, taking into account bone microstructure.