title: Study on bending behaviour of nickel-titanium rotary endodontic instruments by analytical and numerical analyses.
abstract: OBJECTIVE
  To develop analytical models and analyse the stress distribution and flexibility of nickel-titanium (NiTi) instruments subject to bending forces.
  
  
  METHODS
  The 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.
  
  
  RESULTS
  According 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.
  
  
  CONCLUSIONS
  The 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.
authors.affiliation: Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan.
authors.forename: C C
authors.initials: CC
authors.lastname: Tsao
authors.forename: J U
authors.initials: JU
authors.lastname: Liou
authors.forename: P H
authors.initials: PH
authors.lastname: Wen
authors.forename: C C
authors.initials: CC
authors.lastname: Peng
authors.forename: T S
authors.initials: TS
authors.lastname: Liu
mesh_terms: D003722:Dental Alloys; D003762:Dental Instruments; D003799:Dental Stress Analysis / Q000379:methods*; D004548:Elasticity; D004867:Equipment Design; D004868:Equipment Failure; D020342:Finite Element Analysis; D006801:Humans; D008422:Materials Testing; D009532:Nickel; D017711:Nonlinear Dynamics; D018583:Pliability; D018915:Root Canal Preparation / Q000295:instrumentation*; D013314:Stress, Mechanical; D014025:Titanium
chemical_list: D003722:Dental Alloys; C040654:titanium nickelide; D009532:Nickel; D014025:Titanium