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. 2016 Feb 6;6(1):20150070. doi: 10.1098/rsfs.2015.0070

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© 2015 The Author(s)

Published by the Royal Society. All rights reserved.

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Figure 8. — Interpretation of data through homogenization bounds and multiscale models. The SBF + Fet specimens (filled markers) initially stiffened within mineralization at a rate close to the upper bound expected for stiffening by diffuse spheres of mineral, as captured by the estimate of Saadat et al. [33]. However, additional mineral had markedly less stiffening effect, with higher volume fractions producing stiffening that fell outside of the three-point bounds for randomly distributed spheres (cf. [30]), then below the Hashin–Shtrikman bounds and Mori–Tanaka estimate (cf. [29–31]) that represent the range possible for randomly distributed mineral. At the highest levels of mineralization, the stiffening was at the lower end of the Voigt–Reuss range, indicating that mineral was not well connected to the collagen. The SBF specimens (open markers) led to a reduction of stiffness, consistent with equation (2.5) with (no bonding between the mineral and collagen). The rapid drop in stiffness and the asymptote at high levels of mineralization indicate that mineral coating the fibril must have contributed negligibly to stiffening of the collagen ( in equation (2.6)). (Online version in colour.)

Inline graphic — Interpretation of data through homogenization bounds and multiscale models. The SBF + Fet specimens (filled markers) initially stiffened within mineralization at a rate close to the upper bound expected for stiffening by diffuse spheres of mineral, as captured by the estimate of Saadat et al. [33]. However, additional mineral had markedly less stiffening effect, with higher volume fractions producing stiffening that fell outside of the three-point bounds for randomly distributed spheres (cf. [30]), then below the Hashin–Shtrikman bounds and Mori–Tanaka estimate (cf. [29–31]) that represent the range possible for randomly distributed mineral. At the highest levels of mineralization, the stiffening was at the lower end of the Voigt–Reuss range, indicating that mineral was not well connected to the collagen. The SBF specimens (open markers) led to a reduction of stiffness, consistent with equation (2.5) with (no bonding between the mineral and collagen). The rapid drop in stiffness and the asymptote at high levels of mineralization indicate that mineral coating the fibril must have contributed negligibly to stiffening of the collagen ( in equation (2.6)). (Online version in colour.)