Hierarchical modelling of in situ elastic deformation of human enamel based on photoelastic and diffraction analysis of stresses and strains.

Human enamel is a typical hierarchical mineralized tissue with a two-level composite structure. To date, few studies have focused on how the mechanical behaviour of this tissue is affected by both the rod orientation at the microscale and the preferred orientation of mineral crystallites at the nanoscale. In this study, wide-angle X-ray scattering was used to determine the internal lattice strain response of human enamel samples (with differing rod directions) as a function of in situ uniaxial compressive loading. Quantitative stress distribution evaluation in the birefringent mounting epoxy was performed in parallel using photoelastic techniques. The resulting experimental data was analysed using an advanced multiscale Eshelby inclusion model that takes into account the two-level hierarchical structure of human enamel, and reflects the differing rod directions and orientation distributions of hydroxyapatite crystals. The achieved satisfactory agreement between the model and the experimental data, in terms of the values of multidirectional strain components under the action of differently orientated loads, suggests that the multiscale approach captures reasonably successfully the structure-property relationship between the hierarchical architecture of human enamel and its response to the applied forces. This novel and systematic approach can be used to improve the interpretation of the mechanical properties of enamel, as well as of the textured hierarchical biomaterials in general.