An analytical model for stress analysis of a tooth in translation

Closed-form analytical formulas for a tooth of paraboloidal shape in pure translation are presented. These formulas are based on both the approximation of normal and tangential strains in terms of the translational displacement of the tooth and the tooth equilibrium of the thin surrounding periodontal membrane (or on the strain energy conservation equivalently). The tooth is considered to be a rigid body while the surrounding membrane is assumed to be an elastic foundation of uniform thickness. The proposed formulas are capable of determining the most important quantities involved in the case of tooth translation; these are the stiffness of the tooth-support in translation, the distribution of strain and stress tensors in the membrane, the maximum value of hydrostatic stress, as well as the location of the center of resistance. It was found that the proposed formulas involve not only the root length h, as the previous literature reports, but also the root diameter D. The theory is successfully compared to three-dimensional finite element results for an upper central incisor. (C) 2001 Elsevier Science Ltd. All rights reserved.