Automatic modeling together with numerical simulation of the different-scale microstructures of human tooth enamels

The present paper aims to develop an automatical strategy for generating accurate different-scale microstructures of human tooth enamels （HTEs）, and to elaborate a numerical scheme for simulating their elastic responses. At first, the strong governing formulation of these microstructures is briefly constructed, and the relevant weak formulation is then deduced based on the virtual work theorem. Afterwards, a subdividing approach, which cuts the elements intercepted by the interfaces between distinct phases automatically, is established with the aid of the level set method （LSM）, and the discrete counterpart of the governing formula is obtained by combining the weak formulation derived and a discretized model. To be noted, two silent merits are found when the elaborated strategy is applied： （1） the continents constituting the microstructures of different scales can be arbitrarily-shaped and conveniently reproduced; （2） the periodic boundary condition commonly employed can be enforced on the external surfaces of representative unit cells （RUCs） with no difficulty. Besides, a boundary value problem （BVP） involving a simplified HTE nanostructure is designed, analytically solved, and hereafter applied to verify the correctness of the proposed strategy. It is observed that both the displacement and stress predictions by the computational approach are in good agreement with the relevant analytical results irrespective of the material combinations applied. Eventually, discussions are made on the influence of material organizations of both the 2D and 3D HTE microstructures at the ultrastructural and repeated rod levels, and some concluding remarks are drawn.