Micromechanical Model for Ultrastructural Stiffness of Mineralized Tissues

Abstract

We recently found that mineralized tissues (mineralized tendons and bones), at an observation scale of some microns, are open isotropic hydroxyapatite crystal foams which are reinforced unidirectionally by (organic) collagen molecules. The collagen reinforcement is mechanically activated by crosslinks between collagen assemblies and hydroxyapatite. With this morphology in mind, we develop in this paper a continuum micromechanics model for the ultrastructural stiffness of mineralized tissues. The homogenization is achieved in two steps: At a scale of some hundred nanometers, the isotropic crystal foam is represented as a two-phase polycrystal composed of a hydroxyapatite crystal phase and a nonminerally phase filling the intercrystalline space. At a scale above of some five to ten micrometers, the polycrystal plays the role of a connected matrix, in which a collagen inclusion phase is embedded. The effective stiffness of this phase is determined by the tight links between collagen and hydroxyapatite. The input for the model are the mineral volume fraction and the collagen volume fraction, which are species and tissue-type specific. Then, on the basis of four intrinsic micromechanical stiffness constants, the model is able to predict the full ultrastructural stiffness tensor of mineralized tissues, from low-mineralized turkey leg tendon to highly anisotropic human bones, and high-mineralized isotropic ear bones of whales. This is shown on the basis of a large data set compiled in the Appendix.