Investigating the post-yield behavior of mineralized bone fibril arrays using a 3D non-linear finite element unit-cell model.

In this study, we propose a 3D non-linear finite element (FE) unit-cell model to investigate the post-yield behavior of mineralized collagen fibril arrays (FAY). We then compare the predictions of the model with recent micro-tensile and micropillar compression tests in both axial and transverse directions. The unit cell consists of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM), and the FE mesh is equipped with cohesive interactions and a custom plasticity model. The simulation results confirm that MCF plays a dominant role in load bearing prior to yielding under axial tensile loading. Damage was initiated via debonding in shear and progressive sliding at the MCF/EFM interface, and resulted in MCF pull-out until brittle failure. In transverse tensile loading, EFM carried most of the load in pre-yield deformation, and then mixed normal/shear debonding between MCF and EFM began to form, which eventually produced brittle delamination of the two phases. The loading/unloading FE analysis in compression along both axial and transverse directions demonstrated perfect plasticity without any reduction in elastic modulus, i.e., damage due to the interfaces as seen in micropillar compression. Beyond the brittle and ductile nature of the stress-strain curves, in tensile and compressive loading, the simulated post-yield behavior and failure mechanism are in good quantitative agreement with the experimental observations. Our rather simple but efficient unit-cell FE model can reproduce qualitatively and quantitatively the mechanical behavior of bone ECM under tensile and compressive loading along the two main orientations. The model's integration into higher length scales may be useful in describing the macroscopic post-yield and failure behavior of trabecular and cortical bone in greater detail.