Validation of finite-element-simulated orthodontic forces produced by thermoplastic aligners: Effect of aligner geometry and creep

Purpose: Finite element (FE) models for determining the orthodontic forces delivered by clear aligners often lack validation. The aim of this study was to develop and validate accurate FE models for clear aligners, considering the small but important geometrical variations from the thermoforming process and the creep behavior of the aligner material. Methods and materials: The tooth misalignment considered was a 2.4 degrees torque aberration (rotation about the mesial-distal axis at the level of the center of resistance) of the maxillary left central incisor. FE models were created from Micro-CT scans of a model dental arch and five nominally identical aligners with the aforementioned misfit. Fitting of the aligners onto the dental arch was simulated using Abaqus's Interference Fit function, followed by surface-to-surface frictional interaction. Stress relaxation of the aligner material was measured using double-cantilever beam bending and modeled with a Prony series. The assembled FE models were validated by comparing the predicted forces and moments delivered to the maxillary left central incisor with experimental data, obtained with a custom-built but fully calibrated apparatus. Results: Good agreement between prediction and measurement was obtained for both the short- and long-term forces and moments. In the short-term, i.e., after 30 s, the dominant force in the labial-lingual direction had a maximum difference of 2.9% between experiment and simulation, and the dominant moment about the mesial-distal axis had a maximum difference of 8.3%. In the long-term, i.e., after 4 h, the experimental and numerical forces had a maximum difference of 8.4%. There were statistically significant differences in the forces delivered among the nominally identical aligners, which were predicted by the geometrically accurate FE models and attributed to the variations in the points of contact between the aligners and the dental arch. The decay in force applied was affected by both the viscoelastic material behavior and friction between the aligner and arch. Conclusion: For accurate prediction of the forces and moments delivered by thermoplastic aligners, FE models that can accurately capture the point contacts between the aligners and the underlying teeth are essential. Stress relaxation of the aligners could be adequately modeled using the Prony series to represent the temporal changes of their elastic modulus.