Accurate Numerical Modeling And Effective Modulus Caculation Of Enamel Micro/Nano Structure

Enamels,one kind of the hardest tissues of human beings,directly suffer external loadings during the chewing process.They have various excellent mechanical properties macroscopically and can serve in one’s mouth for the whole life because of their typical hierarchical microstructures of different scales.At the nanoscale,they are constituted by hydroxyapatite(HAP)crystal bundles consisting of hydroxyapatite crystals surrounded by thin protein layers.A number of HAP bundles are organized in a specific and compact manner and form the keyhole-like enamel rod at the micro-scale.Further,a thin region between adjacent rods,namely enamel sheath,is formed as well with a limited number of randomly distributed HAP crystals together with protein.These keyhole-shaped rods combined with the surrounding sheathes are arranged periodically and comprise the macroscopic structure of human enamel.Concerning the topic on evaluating the mechanical properties of enamels,some practical features(e.g.random distribution of defects,irregular shape of reinforcement)are commonly neglected so as to establish an effective theoretical model.Meanwhile,such simplifications also lead to discrepancy to a certain extent between the predictions and the true results.Experimental data also presents a large dispersity ascribed to the limited number of healthy enamel samples,the randomness of different-scale microstructures and the individual difference of hosts.Up to now,quite a few studies adopting the numerical strategies evaluated the overall elastic moduli of enamels simultaneously considering the influence of the sheath zones,the enamel rods as well as the accurate distribution of HAP bundles.At the same time,seldom have research on the effects of HAP bundles composition on its effective modulus.To obtain the quantitative relation between the micro/nano structures together with material proportion of enamels and the relevant overall anisotropic moduli,this thesis mainly focuses on the followings.(1)Improvement of the automatic modeling approach developed by our group: The sequence and managing approach for handling the elements at the intersection of different level set functions are modified,and a new approach is developed to categorize elements of the reinforcement and matrix phases effectively,which makes the modeling strategy more concise and versatile.Besides,the finite element models of enamel representative unit cells(RUCs)consisting of either the simplified periodic microstructures or actual complex microstructures are reproduced with the aid of our approach.(2)Establishment of a computational approach to predict the elastic response of enamel microstructures and the elastic moduli of enamels: Taking account of the practical distribution of HAP bundles in enamel rods and the micromechanics theory,we derived the expressions of the overall anisotropic moduli of enamels and then developed a computational approach to evaluate these moduli based on the periodical displacement-controlled boundary conditions.Further,the stress distributions inside a RUC model is investigated in detail by applying the loadings along different directions,and the influence of defects embedded is also studied.Hereafter,the overall elastic moduli of enamels consisting of the true and the simplified microstructures are calculated and compared to the evaluations in the open literature,which highlights the correctness and validity of our approach and the RUC model.Several factors affecting the overall moduli of enamels are then discussed with the model verified.(3)Discussions on the factors affecting the effective elastic properties of HAP bundles: the finite element model of HAP bundles is constructed.The relationship between the effective transversely isotropic properties of the nanoscale HAP bundles and its composition is analyzed.Meanwhile,the influences of crystal distribution,volume fraction,and defects on the transverse isotropy parameters of HAP crystal bundles were studied.