One of the causes of cracks in human teeth is stress resulting from rapid temperature changes. For a better understanding of the phenomenon, this master thesis presents a numerical analysis with finite elements of a CT model of a human tooth and a comparison of the results with an analytical model with a simplified geometry. Both models follow the layering of the tooth by including all three tissues: enamel, dentine and pulp. For the model in the simulation, we start from a CT image of a human tooth, from which a 3D model is created through the segmentation of various tissues using open source software packages. After additional processing, the model is inserted into the numerical simulation in the ANSYS software package. The load represents the stationary and non-stationary temperature profile that occurs as a result of sudden temperature changes. In the analytical model, the complex geometry of the human tooth is simplified with a three-layered cylinder. In the Wolfram Mathematica software environment, the time- and space-dependent temperature profile is calculated by solving the Fourier differential equation of heat transfer. Using Hooke's law, the equilibrium equations of mechanics and assuming a generalized plane strain state, the associated stresses and strains are calculated. Both models are then compared according to the obtained temperature function and stress-strain state.
|
