Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.