Numerical simulation of the force generated by a superelastic NiTi orthodontic archwire during tooth alignment phase: comparison between different constitutive models

Nickel Titanium (NiTi) Superelastic (SE) Shape Memory Alloys (SMAs) are widely considered for applications that need high reversible strain or high recovery forces. In particular, the SE SMAs present a high interest for biomedical applications such as endodontic and orthodontic apparatus. They are available in a large variety of archwires exerting continuum forces to ensure the dental displacement. The purpose of this study is to report the clinical implications of NiTi SE wires for dental treatment in a given configuration. Three main constitutive models of the literature (Lagoudas and Boyd 1996 Int. J. Plast. 12 805–842, Auricchio and Petrini 2004 Int. J. Numer. Meth. Engng . 61 807–836 and Chemisky et al 2011 Mech. Mater . 68 361–376) are considered for the finite element (FE) numerical simulations of the SMA archwires response. Tensile tests had been carried out in order to identify the material parameters of these constitutive models. The FE numerical study allowed to predict the dental displacement and its corresponding orthodontic force level exerted by the wire in similar conditions to those in the oral environment. This work allows to predict the orthodontic generated load by a NiTi SE archwire with a 0.64 × 0.46 mm 2 rectangular cross section under prescribed thermomechanical conditions. The effect of the temperature and the alveolar bone stiffness on the orthodontic load level and the tooth displacement degree has been investigated. The performed numerical simulations demonstrate that the orthodontic load is sensitive to the displacement magnitude, to the tooth stiffness and to the temperature variations. The obtained forces applied continuously and at a constant level are within the acceptable orthodontic force level range. Some directives are therefore provided to help orthodontists to select the optimal archwire.