Elastic anisotropy of bone lamellae as a function of fibril orientation pattern.

In this study, the homogenized anisotropic elastic properties of single bone lamellae are computed using a finite element unit cell method. The resulting stiffness tensor is utilized to calculate indentation moduli for multiple indentation directions in the lamella plane which are then related to nanoindentation experiments. The model accounts for different fibril orientation patterns in the lamellae--the twisted and orthogonal plywood pattern, a 5-sublayer pattern and an X-ray diffraction-based pattern. Three-dimensional sectional views of each pattern facilitate the comparison to transmission electron (TEM) images of real lamella cuts. The model results indicate, that the 5-sublayer- and the X-ray diffraction-based patterns cause the lamellae to have a stiffness maximum between 0° and 45° to the osteon axis. Their in-plane stiffness characteristics are qualitatively matching the experimental findings that report a higher stiffness in the osteon axis than in the circumferential direction. In contrast, lamellae owning the orthogonal or twisted plywood fibril orientation patterns have no preferred stiffness alignment. 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 toward a deeper understanding of the structure-mechanical function relationship of bone lamellae.