Effects of shape and direction of osteocyte lacunae on stress distribution of osteon

Scanning electron microscope (SEM) observations show that lacunae are non-uniform distribution and mainly located in the interface of thick lamellae and thin lamellae. These lacunae are elliptical and are along the circumferential direction of the osteon, which can be called as circumferential elliptical lacunae (CE). The observations also show that there are many circumferential microcracks in the osteons and these microcracks are initiated from two endpoints of the major axis of the CE. Nanoindentation technique is used to test the elastic modulus of the different circumferential lamella of the osteons. The test results shown that the average elastic modulus of the osteon wavily changes along its radial direction and that the average elastic modulus of the thick lamella is larger than that of the thin lamella. To learn the influence of the shape and direction of osteocyte lacunae on the stress distribution and understand the advantage of CE, three different osteon models, respectively with CE, radially elliptical lacunae (RE) and circular lacunae (CL), are created. The results show that the stress concentration factor of osteon with RE is maximal, that of CE is middle and CL is minimal. The crack-propagated route is along the circumferential direction of the osteon in CE model, which makes that the osteon possesses high facture toughness.