AimTo develop analytical models and analyse the stress distribution and flexibility of nickel–titanium (NiTi) instruments subject to bending forces.MethodologyThe analytical method was used to analyse the behaviours of NiTi instruments under bending forces. Two NiTi instruments (RaCe and Mani NRT) with different cross-sections and geometries were considered. Analytical results were derived using Euler–Bernoulli nonlinear differential equations that took into account the screw pitch variation of these NiTi instruments. In addition, the nonlinear deformation analysis based on the analytical model and the finite element nonlinear analysis was carried out. Numerical results are obtained by carrying out a finite element method.ResultsAccording to analytical results, the maximum curvature of the instrument occurs near the instrument tip. Results of the finite element analysis revealed that the position of maximum von Mises stress was near the instrument tip. Therefore, the proposed analytical model can be used to predict the position of maximum curvature in the instrument where fracture may occur. Finally, results of analytical and numerical models were compatible.ConclusionThe proposed analytical model was validated by numerical results in analysing bending deformation of NiTi instruments. The analytical model is useful in the design and analysis of instruments. The proposed theoretical model is effective in studying the flexibility of NiTi instruments. Compared with the finite element method, the analytical model can deal conveniently and effectively with the subject of bending behaviour of rotary NiTi endodontic instruments.

To assist endodontic therapy, in this paper, a force sensor is designed and fabricated for measuring the axial force and the bending moment simultaneously. By detecting the bending moment, we can know the severity of bending. Axial force detection is also desired, as excessive axial forces may result in instrument buckling or even root canal perforation. This paper installs three sensing cells in each of two planes to detect the bending direction. Each sensing cell consists of a pressure-sensitive electric conductive rubber and an electrode. The size of the force sensor is 1.4-mm wide and 6-mm high for matching the size of endodontic instruments and making it feasible in the endodontic treatment. Experimental results on accuracy, repeatability, and nonlinearity are presented to validate the proposed sensor.