Effects of geometry and loading on the elastic behavior of a single osteon via analytical structural mechanics approaches

Abstract

In this study, two analytical approaches for lamella texture at micro-scale including disordered mineralized and organized collagen fibers are employed to provide analytical models of an osteon. A two-step homogenization procedure is also applied to characterize the elastic properties of the osteon. Numerical evaluations are accomplished to explore the effects of loading and geometrical parameters on the behavior of the osteon. Results show the diameter of the Haversian canal is the dominant geometrical parameter influencing the elastic stresses in the osteon. The radial and hoop stresses as well as radial displacement are insensitive to the changes in the number of lamellae. The ordered motif osteon model can also be used to explain circumferential micro-cracks along lamellae leading to irregular profiles of fracture in osteon direct tensile tests. The theoretical model of osteon based on the lamination theory generally indicated better agreement with existing experimental results.