Methods: Finite element calculations using ANSYS software were carried out to determine the stresses and deformations in a model of the tooth. The tooth was modelled to consist of two concentric cylinders, an inner cylinder of 7 mm diameter dentine (E=14.7 GPa and n=0.31) and an outer layer of 1 mm thick enamel (E=84.1 GPa and n=0.33). The total tooth thickness was thus 9 mm and the height was 5 mm. The two cylinders were assumed to be rigidly fixed at one end and the other end was free. Different sizes of occlusal cavities (2, 4 and 7 mm) were simulated through removal of dentine from the centre. By an additional removal of parts of the enamel, mo and mod fillings were also simulated. The fillings were subjected to an internal pressure of 10 MPa and a chewing pressure of 1 MPa.
Results: Since the cylinders were rigidly fixed at one end, the inner part of the cavity (dentine) tended to bend outwards, thus compressing the outer (enamel) layer. This behaviour leads to widely different distributions of stress in the tooth as the cavity sizes and filling types are varied. The radial deformations were in the order of microns, most of it occurring in the softer dentine. The maximum stresses occur in the stiffer enamel layer regardless of filling type and often at the interface between enamel and dentine.
Conclusions: By theoretical calculations it was possible to obtain the magnitude and distribution of stresses in a simplified model of a tooth with an expanding or shrinking filling. The calculations show that most deformation occurred in the dentine but the enamel carries most of the stress.