Micromechanical Model for Ultrastructural Stiffness of Mineralized Tissues
Publication: Journal of Engineering Mechanics
Volume 128, Issue 8
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.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 128 • Issue 8 • August 2002
Pages: 898 - 908
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Mar 25, 2002
Accepted: Apr 1, 2002
Published online: Jul 15, 2002
Published in print: Aug 2002
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