Multi-scale modeling and diffraction-based characterization of elastic behaviour of human enamel

The relationship between the ultrastructure of human enamel and its mechanical behaviour is studied in this paper. Two synchrotron X-ray diffraction techniques, wide and small angle X-ray scattering (WAXS/SAXS) were used in combination to obtain multi-scale quantitative information about the response of human enamel to in situ uniaxial compressive loading. The interpretation of WAXS data gives elastic lattice strains within the hydroxyapatite (HAp) crystals, the stiff reinforcing phase in human enamel. The apparent modulus was determined linking the external load and the internal HAp strain. SAXS interpretation, allows the quantification of the nano-scale HAp crystallite distribution within human enamel. A multi-scale Eshelby equivalent inclusion model of the enamel was proposed that represents the hierarchical mineralized tissue as a two-level composite: micro-level model with rod embedded in the homogenised enamel material, and nano-level model with HAp crystallites embedded in the rod. Satisfactory agreement was achieved between model and experiment, suggesting that the new multi-scale approach accurately reflects the structure and mechanics of human enamel, and may help guide new biomimetic designs.