Variational homogenization for modeling fibrillar structures in bone

Exceptional mechanical properties of bones are not only the result of the amount and type of the micro-constituents, but also of their morphological organization at the different lower scales. At the scale of several micrometers, bone tissue is formed by mineralized collagen fibrils embedded in an extrafibrillar mineral-rich matrix. Basic components of bone fibrils are collagen, mineral and water. We present in this paper a mechanical model for the mineralized collagen fibril. This model is set up in the framework of a multiscale description, based on the characterization of the basic components and of their interaction. Overall properties are obtained through a variational homogenization technique. Numerical simulations, performed by a specifically designed computer code, show the dependency of the axial elastic modulus of the fibril versus the mineral volume fraction.