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The micro- and sub-microstructures of human cortical bone are analytically investigated in this study. Modified equations are derived as a function of sub-microstructural architectures and volumetric bone mineral density (BMD) in order to estimate the nine orthotropic elastic constants of cortical bone at sub-microlevel. In general, the analytical models contain fanning or oscillating plywood layup at the lamella level are in good agreement with the results of nanoindentation tests, and the osteon models contain combinations of twisting/oscillating or unidirectional/fanning lamellar patterns are in agreement with the experimental results of direct tensile and punching shear tests on a single osteon.

Effective elastic constants of cortical bone at lamellae and osteon levels considering mineral composition and lamellar arrangement