# Computerized Generation and Finite Element Stress Analysis of Endodontic Rotary Files
###### Abstract  
The finite element method has been extensively used to analyze the mechanical behavior of endodontic rotary files under bending and torsional conditions. This methodology requires elevated computer-aided design skills to reproduce the geometry of the endodontic file, and also mathematical knowledge to perform the finite element analysis. In this study, an automated procedure is proposed for the computerized generation and finite element analysis of endodontic rotary files under bending and torsional conditions. **Methods:** An endodontic rotary file with a 25 mm total length, 0.25 mm at the tip, 1.20 mm at 16 mm from the tip, 2 mm pitch and squared cross section was generated using the proposed procedure and submitted for analysis under bending and torsional conditions by clamping the last 3 mm of the endodontic rotary file and applying a transverse load of 0.1 N and a torsional moment of 0.3 N - cm. **Results:** The results of the finite element analyses showed a maximum von Mises stress of 398 MPa resulting from the bending analysis and a maximum von Mises stress of 843 MPa resulting from the torsional analysis, both of which are next to the encastre point. **Conclusions:** The automated procedure allows an accurate description of the geometry of the endodontic file to be obtained based on its design parameters as well as a finite element model of the endodontic file from the previously generated geometry. endodontic file; bending; torsion; stress distribution; finite element analysis 2021 2021 8 May 2021  
In addition, root canal dentine removal during the retrieval procedures of separated files can weaken the tooth structure up to 4.25 \(\pm\) 0.68 mm\({}^{3}\)[11]. Moreover, fractures of endodontic instruments on teeth with periapical pathology significantly decrease the success rate of root canal treatment [12]. Therefore, improvements of the chemical composition of the alloy and geometrical design may increase torsional and bending resistance, preventing the fracture of the endodontic rotary instruments [13]. Furthermore, some geometrical factors have been highlighted as influencing the instrument's performance, such as taper [14], apical diameter [7; 14], cross section [15], flute length, helix angle and pitch [16]; however, most studies were conducted experimentally using custom-made cyclic fatigue devices, hardly reproducing the clinical setting and the absence of regulation prevents data comparison [17]. However, finite element (FE) analysis is an alternative that allows the mechanical behavior and stress distribution of endodontic rotary instruments subjected to different conditions to be simulated through mathematical analysis [18]. Moreover, FE analyses have been previously used in endodontics to assess both the mechanical behavior of endodontic instruments [19] and stress distribution during root canal treatments [16]. Two different approaches can be found in recent works when developing FE models for the stress analysis of endodontic files, which differ in the way in which the endodontic file geometry is obtained. In both cases, the obtained geometry must be converted to a finite element model by means of a FE analysis pre-processor, in order to proceed to its analysis. In addition, elevated solid mechanics knowledge is required in both cases, in order to define a finite element model that can accurately reproduce the physics of the problem. In the most conventional approach [1; 20; 21], the generation of the geometry of the file is conducted through computer-aided design (CAD) software. This approach requires elevated CAD knowledge to accurately reproduce the geometric characterization of the endodontic rotary file parameters. In fact, there are several cases in which the generated geometries cannot accurately reproduce the geometry of the actual endodontic file, especially at the transition between the active part and the shaft. In another approach [22], the geometry of the endodontic file is obtained from a tomography scanner.