Automatic Modelling And Effective Modulus Prediction In The Differen T-Scale Microstructures Of Tooth E Namel Based On FEM And LSM

As one of the key members of oral cavity, human teeth play an important role for the digestive system, and can also fulfill the responsibilities, such as chewing, swallowing and expressing complicated feelings, in this very complex oral environment for decades. These merits mainly attribute to the amazing mechanical properties of the outermost tooth enamel. Generally, natural enamels have quite complex microstructure at differently length scales, an automatic modeling thus necessitates being developed to make up for the deficiencies of experimental and theoretical studies and to explore the influence of micro-organizations as well as chemical compositions in more detail. Further, the automatic strategy may save plenty of time for repeat duplication of complex microstructures as well. In brief, this study possesses much significance in deepening the scientific understanding of heterogeneous biomaterials, enriching the theory of the bionic discipline and designing new restorative materials for dentals.The main tasks accomplished in this thesis are summarized as follows:The first chapter of this thesis briefly introduces the function and structure of human teeth, and analyses the current research status and exsiting problems concerning the mechanical properties of the teeth. On the basis of these investigations, the research content and significance of this paper are elaborated.In Chapter 2, an automatic modeling method for constructing the different-scale microstructures of human enamels is established with the help of the level set method. To be noted, reinforcement phases of quite complex shapes can be accurately constructed with the eastabulished method. A numerical scheme to generate the symmetric nodes on specific boundaries is also developed based on the vector method to facilitate the enforcement of the periodic boundary conditions.In Chapter 3, a simplified model of enamel nanostructure is designed, and its analytical solution is obtained by theoretical deduction. By comparing the analytical solution and numerical results, the correctness and accuracy of the automatic modeling method are verified. Afterwards, some discussions are made on the effects induced by the microstructures and chemical composition of human enamel.In Chapter 4, we developed a numerical method to predict the effective modulus of enamel at the ultrastructural length-scale, and the validity of the proposed method is tested with the analytic solution in the open literature. Finally, the influences of the microstructure, material parameters and volume fraction of enamel on the effective modulus are examined in detail. Some key conclusions of this thesis are listed in what follows:(1) The organic phase of the nanostructure and the sheath of the microstructure of human enamel are softer than the relavant reinforcement phases, hence, more strain energy is absorbed by these regions during the process of stress transfer. When the basic constitutent phases are evenly distributed, stress concentration hardly appears in enamel nanostructures. When two HAP crystals directly contact with each other, local stress concentrations may show up due to the damage of the channel to transfer stress.(2) The shapes and distribution of HAP crystals together with the distribution of the organic phase can directly affect the displacement, stress and related physical fields, which are closely related to the material properties of enamel microstructure.(3) Concerning the material moduli at the ultrastructural level, the axial shear modulus G* and elastic modulus E3* gradually increase with the increment of the elastic modulus of HAP crystals, while negligible effect is observed for the transverse parameters μ12* and k12*. The bulk modulus k12* and shear modulus μ12* in the isotropic plane increase gradually with the increasing elastic modulus of organic phase, but there is a little effect on the axial parameters G* and E3*.(4) All effective moduli μ12*、k12*、G*、E3* increases gradually as the volume fraction of HAP crystals increases. Precisely, the values of the shear modulus μ12* as well as the bulk modulus k12* increase in a manner of gradually enlarging. While the rest moduli G* and E3* turn out to be the increasing speed of their changes decreases with an increasing volume fraction.