Multiscale Modelling Of The Hierarchical Microstructures Together With Evaluation Of The Effective Moduli Of Tooth Enamels Considering The Nano Hap-crystallite Effects

Tooth enamels,which locate at the outermost layer and possess the highest degree of mineralization of the hard mineral tissue in an animal body,are a typical multi-scale biological composite.Due to the optimal hierarchical microstructures and specific proportion of basic materials formed during the natural selection process,they generally have various excellent properties simultaneously,including the high strength,perfect toughness,good anti-fatigue effect and many others.Therefore,exploring the quantitive relationship between these macroscopic properties and the multi-scale micro/nano structures can not only help us to reveal the fundamental mechanism of such hierarchical biological tissues,but also to provide a guidance for synthesizing new high-performance biomimetic materials and to optimize the performance of heterogeneous materials and structures.The main contents and results in this thesis are summarized as follows:In chapter 1,some common hierarchical structures and their characteristics are expounded with the aid of the natural biological materials.The current state of the art concerning the multi-scale modeling methods of enamel microstructures,evaluation of the enamel elastic moduli and so forth,are reviewed in this thesis.Besides,the contents and significance of this study are also introduced in detail.In chapter 2,an explicit expression is established based on the level set function method to accurately describe the irregular configurations of the micro-prism and nano-HAP crystallites,and a mathematical model to describe the HAP crystallite orientations inside the microprisms is further obtained by fitting the experimental data.Hereafter,the micro&nano representative volume element models constituted by either the regularly or the irregularly shaped components are reconstructed by applying the automatic modeling strategy established by our research group.In chapter 3,the homogenization method in micromechanics and common equivalent constitutive relations of enamel are briefly introduced.The effective modulus of enamel representative unit is evaluated by the developed simulation method,and the predicted moduli shows that with the decrease of the thickness of sheath layer the results are prone to reach the existing simulation values gradually.These results indicate that the model and simulation method are effective in this research.On the basis of these results,the effects of both crystallite shape and material composition on the macroscopic modulus of enamel are further discussed.In chapter 4,a multi-scale homogenization approach is developed by combining the static condensation technique,the representative volume element model at the micro scale and the function to identify the inclined orientation of HAP crystallites in Chapter 2.To be noted,the influence of the microscopic prism shape,the nanoscale crystallite organization and so forth factors can be examined directly with this approach.In addition,the effects induced by the HAP crystallite size,shape and volume fractions on the overall moduli of enamels are further analyzed.The main conclusions of this thesis are drawn as follows:(1)A reconstruction approach is established for complex enamel microstructures by approximating the outlines of the micro prisms with several piecewise polynomial functions.An automatic modeling strategy is further elaborated by combining the level set method and the reconstruction approach to reproduce the complex representative volume element models at both the micro and nano scales.The modeling process of complex biological structures can be greatly simplified with this strategy.(2)In view of the close correlation between the macroscopic moduli of the enamel and its unique micro/nano structure and material composition,the static condense technique is applied in this study to develop a multi-scale computational strategy for evaluating the macroscopic moduli of enamels.Specifically,the effects of the micro-prism shape and nano-crystallite organization and so forth may be examined quantitatively.(3)The material properties of the micro sheath regions significantly affect the overall moduli of enamels.Precisely,all overall moduli increase dramatically with the increment of the sheath stiffness,and D11,D22 and D33 increase faster than the others.(4)The volume fraction of nano-HAP crystallites and the moduli of protein layers have significant influence on the macroscopic moduli of enamel,while the shape and size of HAP crystallites have limited effects.