3D finite element analysis of a percolating cluster inside the mineralized collagen fibril

Bone is characterized at the nanoscale by the mineralized collagen fibril (MCF), mainly composed of apatite minerals and collagen. Among several factors, the 3D architecture of the nanostructure affects the tissue mechanical performance. In the present study, we developed a structural analysis of a model of apatite embedded in the collagen matrix, characterized by a percolating cluster, i.e. a spanning network of connected apatite minerals within the MCF. The geometric model is obtained after applying 6·106 translational and rotational perturbations to an ordered arrangement of mineral. The mechanical behaviour of the percolating cluster is compared with a model characterized by an ordered arrangement of mineral. The 3D Finite Element models are analysed under tensile and compressive simulation conditions. Normal and shear stresses are compared among the models. The outcomes suggest that the presence of a percolating cluster causes a general stiffening of the model, representing a condition of high susceptibility to fracture.