Iterative finite element analysis of molar uprighting using superelastic Nickel Titanium spring: introducing an Element-Iteration-Specific (EIS) material model

BACKGROUND: Superelastic Nickel Titanium (NiTi) exhibits nonlinear and path-dependent behavior that complicates accurate simulation of orthodontic appliances. Standard iterative finite element (FE) formulations often fail to maintain realistic stress evolution during simulations, leading to non-physiologic force predictions. This study introduced an Element-Iteration-Specific (EIS) material model implemented within the FE framework to incorporate the behavior of superelastic NiTi alloy into an iterative simulation, aiming to investigate the biomechanics of a molar uprighting spring and estimate the clinical treatment duration. METHODS: A two-dimensional (2D) model was constructed representing a 30° mesially tilted mandibular second molar uprighted using a prefabricated superelastic NiTi spring. At each iteration, the EIS algorithm redefines the element specific material parameters of the spring according to the stress-strain state inherited from the preceding iteration, thereby preserving the continuity of its behavior and enabling realistic stress evolution and load transfer between the wire, brackets, and teeth. RESULTS: The simulation achieved 23.3° of molar uprighting with 3.0 mm of tangential distal and 2.4 mm of normal extrusive displacements, over an equivalent of 14-week clinical duration. The NiTi spring generated an initial 12.4 N·mm (~ 1265 g·mm) counter-clockwise moment and 0.9 N normal extrusive force. The mean PDL stress remained physiologic, decreasing from 20.3 KPa at wire activation to 13.3 KPa at the end of the simulation. The model successfully tracked the spatial and temporal evolution of the superelastic NiTi's stress-induced martensitic transformation during activation and uprighting. CONCLUSIONS: The EIS framework effectively reproduced the nonlinear and history-dependent response of superelastic NiTi, offering clinically representative predictions and establishing a validated computational foundation for optimizing NiTi-based orthodontic appliances and improving treatment outcomes.