Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach

Bone ultrastructure at sub-lamellar length scale is a key structural unit in bone that bridges nano- and microscale hierarchies of the tissue. Despite its influence on bulk response of bone, the mechanical behavior of bone at ultrastructural level remains poorly understood. To fill this gap, in this study, a two-dimensional cohesive finite element model of bone at sub-lamellar level was proposed and analyzed under tensile and compressive loading conditions. In the model, ultrastructural bone was considered as a composite of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM) that is comprised of hydroxyapatite (HA) polycrystals bounded via thin organic interfaces of non-collagenous proteins (NCPs). The simulation results indicated that in compression, EFM dictated the pre-yield deformation of the model, then damage was initiated via relative sliding of HA polycrystals along the organic interfaces, and finally shear bands were formed followed by delamination between MCF and EFM and local buckling of MCF. In tension, EFM carried the most of load in pre-yield deformation, and then an array of opening-mode nano-cracks began to form within EFM after yielding, thus gradually transferring the load to MCF until failure, which acted as crack bridging filament. The failure modes, stress-strain curves, and in situ mineral strain of ultrastructural bone predicted by the model were in good agreement with the experimental observations reported in the literature, thus suggesting that this model can provide new insights into sub-microscale mechanical behavior of bone.