An Analytical Model for Stress Analysis of a Tooth under the Orthodontic Force

Closed-form analytical formulas for a tooth of paraboloidal shape under the orthodontic force are presented. These formulas are based on both the approximation of strains according to the displacement of the tooth and the tooth equilibrium of the thin surrounding periodontal membrane. The proposed formulas are capable of determining the most important quantities involved the distribution of strain and stress tensors in the membrane, as well as the location of the center of resistance. It was found that the proposed formulas involve not only the root diameter but also the root length. The theory is consistence with three-dimensional finite element results for an upper central incisor.