Micro- and meso-scale modeling of dental composite materials

In spite of the vast application of dental composite materials in dentistry rather than traditional tooth fillings, durability of these composites is still of great concern. This dissertation provides a micromechanical modeling of dental composites to investigate the failure mechanisms and proposes some ideas to improve and optimize the mechanical properties of such materials. Lumpy appearance of the fracture surfaces of dental composite fillings indicates the microscopic matrix cracking along the material interfaces. Zero-thickness cohesive interface elements governed by the traction-separation law are utilized in this work to model the interface debonding as well as the breakdown of the matrix zone. The constitutive equations of the cohesive zone model contains suitable criteria for the initiation and evolution of damage under mixed mode loading conditions. A viscous regularization approach is employed to suppress the convergence difficulties of the implicit finite element analysis, while the time dependent explicit solution scheme is utilized for three dimensional problems. Direct numerical homogenization together with the necessarily statistical computations are applied to investigate the influences of morphology and distribution of fillers on the effective elastic properties of the composites. The numerical results are in a good agreement with the experimental data available at the medical school of Hannover and institute of inorganic chemistry. A parametric study on the effects of various properties of the filler and interface zones on the stress-strain responses of the damaged microstructure is carried out as well. Furthermore, a nested two-scale FE2 method is presented in this work to predict the macroscopic behavior of dental composites during interface degradation. In order to model the microcrack propagation within the matrix phase along the interfaces of different filler shapes, a suitable strategy for automatically generation of interface elements is developed. The main challenge is how to deal with the alteration of elemental connectivities. The simulation results of nucleation and progression of cracks are validated by the benchmark tests. It is hypothesized that the application of high aspect ratio fibers at the microstructure of dental composites can improve the fracture resistance of them. Hence, complex fracture mechanisms of crack deflection and crack bridging induced by the incorporation of such fillers are simulated and also analyzed. The crack growth results are illustrated in both two and three dimensional spaces.