The anisotropy of bone lamellae as a function of diverse fibril orientation patterns

In this study, the homogenized anisotropic elastic properties of single bone lamellae are computed. The lamella itself is modeled by a finite element unit cell method and the underlying hierarchical levels of bone are described by a multiscale mean field model. The resulting stiffness tensor is utilized to calculate indentation modules for multiple indentation directions in the lamella plane which are then related to nanoindentation experimental results. Diverse fibril orientation patterns are taken into account and are compared: The orthogonal plywood pattern, the twisted plywood pattern, a 5-sublayer pattern and an x-ray diffraction based pattern. Results show, that in the osteon's axial direction, the model results of all investigated fibril orientation patterns are inside the standard deviation range of the experimental nanoindentation results. In circumferential direction, the twisted and orthogonal plywood patterns are too stiff compared to the experiments. These two patterns have equal stiffness properties in axial and circumferential direction which was not observed in the measurements. The 5-sublayer or the x-ray diffraction based pattern have a clear privileged stiffness alignment and match the experimental findings qualitatively. This work shows that the variety of fibril orientation patterns leads to qualitative and quantitative differences in the lamella elastic mechanical behavior. The study is a step towards a deeper understanding of the structure - mechanical function relationship of bone lamellae.