Finite element modeling of bone deformation at the submicroscopic scale

By means of the direct finite element simulation and homogenization the analysis of variation influence in the morphological characteristics (hydroxyapatite crystals disorientation, sizes and orientation of mineral bridges, mineralization) on mechanical properties of the representative volume element of bone at the nanoscale (at the collagen fibrils level) is carried out. The morphological model of bone with an account of the mineral bridges between the associations of the hydroxyapatite crystals is used in the computations. The purpose of the paper is to analyze the influence of the nanostructure parameters of bone on its elastic and strength properties. Such studies are important for the creation of artificial bone-substitute materials. The analysis of the stress-strain state of the RVE of bone tissue has been performed in order to determine the location of the most critical points and deformation mechanisms of bridges. The most loaded elements are the corners of conglomerates and corners of bridges. Taking account of the bridges leads to the decrease of the von Mises stresses in the corner of the conglomerate and to the increase of the effective elastic moduli in the vertical and horizontal directions. The effects of orientation of conglomerates and bridges on the stress state of the representative volume were analyzed. The influence of the bone mineralization on the effective elastic moduli and stress state were investigated. The comparison of obtained results with experimental data was performed and discussed.