[Zurück]

Ch. Hellmich:
"Nano-to-Macro Elasticity of Bone - Review of Experiments and Micromechanical Modeling";
Vienna University of Technology, Faculty of Civil Engineering, 2004.

After a short presentation of the well-known hierarchical organization of bone, the question of organization of collagen and hydroxyapatite in the ultrastructure of mineralized tissues (1 to 10 microns observation scale) is raised. By means of two independent sets of observations (mass density and distance measurements, transmission electron micrographs) it is illustrated that the average hydroxyapatite concentration is uniform in the extra-collagenous ultrastructure of mineralized tissues. The extracollagenous space is shown thereafter to be essential for the understanding of the elasticity of bones. From a study of weighing experiments and ultrasonic tests on demineralized and dried specimens in terms of stiffness-volume fraction relationships, it is inferred that - at the ultrastructural scale - mineralized tissues are isotropic crystal foams reinforced unilaterally by collagen molecules.

Finally, this reinforced foam-type morphology is represented in a micromechanical model, comprising a two-step homogenization procedure: 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 fluid phase filling the inter-crystalline 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. Going up to the milimeter scale, the second step can be extended by a third phase, the marrow-filled microporous space (Haversian canals, inter-trabecular space) with a cylindrical morphology. The input for the micromechanical model are the mineral volume fraction, the collagen volume fraction, and the micropore volume fraction, which are species and tissue-type specific. Then, on the basis of tissue-independent ('universal') micromechanical stiffness constants for hydroxyapatite, collagen, and marrow, the model is able to predict the full ultrastructural and microstructural (=macroscopic) stiffness tensors of mineralized tissues, both for trabecular and cortical bone, and all over the animal kingdom.