Nanostructure and effective elastic properties of bone fibril

Mechanical properties of bone tissue result from its hierarchical structure. At the scale of several micrometers, the relevant structure is the bone fibril. Bone fibril is mainly composed of collagen, mineral, and water. Exact composition and arrangement of these constituents are hardly available through nowadays experimental techniques. In this paper, the influence of the subfibrillar organization on the effective elastic properties of the fibril using a multiscale homogenization approach was studied. The model uses energetic equivalences between the relevant scales to estimate the effective elastic properties of the fibril. The axial modulus of the fibril was computed considering different scenarios at the subfibrillar scale. Composition and arrangement of the fibrillar nanoconstituents were varied to test different modeling hypotheses. Special focus was set on the mineral content and the shape of the mineral platelets. Mineral content turned out to be the only relevant parameter in highly mineralized fibrils. Specific subfibrillar organization was shown to be much more relevant in weakly mineralized fibrils. In particular, the effect of the shape of the mineral platelets was highlighted.