Hierarchical modelling of elastic behaviour of human enamel based on synchrotron diffraction characterisation.

Human enamel is a hierarchical mineralized tissue with a two-level composite structure. Few studies have focused on the structure-mechanical property relationship and its link to the multi-scale architecture of human enamel, whereby the response to mechanical loading is affected not only by the rod distribution at micro-scale, but also strongly influenced by the mineral crystallite shape, and spatial arrangement and orientation. In this study, two complementary synchrotron X-ray diffraction techniques, wide and small angle X-ray scattering (WAXS/SAXS) were used to obtain multi-scale quantitative information about the structure and deformation response of human enamel to in situ uniaxial compressive loading. The apparent modulus was determined linking the external load and the internal strain in hydroxyapatite (HAp) crystallites. An improved multi-scale Eshelby model is proposed taking into account the two-level hierarchical structure of enamel. This framework has been used to analyse the experimental data for the elastic lattice strain evolution within the HAp crystals. The achieved agreement between the model prediction and experiment along the loading direction validates the model and suggests that the new multi-scale approach reasonably captures the structure-property relationship for the human enamel. The ability of the model to predict multi-directional strain components is also evaluated by comparison with the measurements. The results are useful for understanding the intricate relationship between the hierarchical structure and the mechanical properties of enamel, and for making predictions of the effect of structural alterations that may occur due to the disease or treatment on the performance of dental tissues and their artificial replacements.