# Computerized Generation and Finite Element Stress Analysis of Endodontic Rotary Files
## 4 Discussion  
FE models have been proposed to analyze the mechanical performance of endodontic rotary files, isolating the variables independently under controlled settings [38] to facilitate the comparison between the mechanical behavior and stress distribution of existing endodontic rotary files and even to allow the design of new endodontic rotary instruments by reducing time and costs [27]. In addition, [PERSON] and [PERSON] used FE methods to improve the geometrical design of existing endodontic rotary instruments and therefore the mechanical behavior under bending and torsional loads to reduce the prevalence of failure [2]. [PERSON] and [PERSON] also analyzed the influence of the helix angle, taper and flute length on the bending flexibility and torsional stiffness of endodontic files (V-Paper) through numerical simulations and concluded that the geometric features influence on the mechanical performance of endodontic files under bending and torsional conditions [2]. [PERSON] et al. compared numerically the mechanical behavior of Hero, HeroShaper, ProFile, Wtwo and ProTaper F1 endodontic rotary NiTi instruments under bending and torsional conditions and showed that the different designs for tapers, pitch and cutting blades influence on the bending and torsional mechanical behavior [39]. [PERSON] et al. evaluated the effect from pitch and cross-section design on torsional stiffness of NiTi endodontic rotary instruments and evidenced that torsional deformation and fracture of NiTi rotary files might be reduced by reducing the pitch and increasing the cross-sectional areas rather than the center core area [40]. Although metallurgical properties and metallurgical treatments have been shown to influence the properties of NiTi endodontic rotary instruments, geometrical design has been highlighted to be directly related to the stiffness [41], clinical efficiency and cutting performance of endodontic rotary files [29; 42]. The cross-section design of endodontic rotary files has experienced a continuous development; [PERSON] et al. reported that increasing the cross-sectional surface area lead to a decrease in the flexibility of endodontic rotary files by a stress accumulation at the upper and lower edges of the cross section during bending tests, compared with smaller cross-sectional surface areas [17]. In addition, cross-sectional morphology has been also widely analyzed, and [PERSON] and [PERSON] reported that a convex triangular cross-section design showed maximum von Misses stresses upon bending tests (1962 MPa), followed by a triangular cross-section design (1535 MPa), parallelogram cross-section design (870 MPa) and rectangular cross-section design (814 MPa); however, a convex triangular cross-section design showed maximum von Misses stresses upon torsional tests (4321 MPa), followed by a triangular  
Figure 13: Results of the parametric study of the diameter of the tip of the active part: (**a**) bending analysis and (**b**) torsional analysis. cross-section design (4285 MPa), rectangular cross-section design (2659 MPa) and parallelogram cross-section design (2307 MPa). Additionally, the stress distribution pattern was localized at the cutting edges under bending tests and more concentrated in the base of the flutes in the first 2 mm of the triangular cross-section design under torsional tests [43]. These results agree with the findings reported by [PERSON] et al., who showed a maximum von Misses stress of 1170 MPa at the cutting edges of a triangular cross-section design endodontic rotary file after applying a transverse load of 1 N at the tip of the endodontic rotary file during bending tests [44]: additionally, [PERSON] et al. showed a maximum von Misses stress of 1146.6 MPa at the convex triangular cross-section design of a Wave One endodontic reciprocating file, followed by the S-shaped cross-section design of Reciproc (942.48 MPa), the parallelogram cross-section design of WaveOne Gold (847.35 MPa) and the S-shaped cross-section design of Reciproc Blue (614.21 MPa) under bending conditions.