A multi-scale computational approach to evaluate the overall anisotropic elastic moduli of natural enamels accounting for the actual nano-HAP crystallite effect

In this study, a multi-scale computational methodology was developed to directly incorporate the HAP orientation and architecture effects into the overall elastic moduli of natural enamels. Precisely, the strong, weak and discretized governing formulations of the enamel representative unit cell were first constructed, and a numerical approach was then presented to compute the relevant moduli. Further, a top-down modeling scheme was proposed to evaluate the stiffness of each element accurately using the meshing scheme established previously. The computational methodology was validated with the predictions in the open literatures, and discussions were made on the HAP organization and material proportion effects.