# Structural Assessment of Endodontic Files via Finite Element Analysis
## 1 Introduction  
Endodontic instruments that are utilized for root canal treatment might undergo large bending deformations during the procedure due to root canal curvature. Due to their super-elastic properties, Nickel-Titanium alloys (NiTi) can withstand large strains without any permanent deformation and are therefore suitable materials for endodontic instruments. Structural failure of the NiTi endodontic instruments during root canal treatment is not uncommon. Moreover, the understanding of the mechanical response of these files during canal treatment is crucial for selecting the appropriate endodontic file for a specific root canal curvature and operational technique. Consequently, in order to understand the mechanical response and limits of these instruments, several structural assessment test methodologies have been developed, and significant effort has been devoted to measuring and comprehending the structural stiffness and failure behavior of various endodontic file sets. In addition, there has been a significant effort to decrease testing and reduce costs through the development of simulation methods replicating physical tests. In the context of physical tests, the bending and torsional stiffness of these instruments is evaluated using standardized tests defined by ISO 3630-1 [1]. The ISO standard provides a detailed description of the test apparatus and testing procedure. Several studies have been performed to evaluate the mechanical strength of the ProTaper Universal (PTU) endodontic files, which are the files evaluated in the current study. For instance, [PERSON] et al. compared the flexibility and mechanical response of ProTaper and ProTaper Universal files [2]. Meanwhile, [PERSON] et al. delved into the effects of clinical use on the torsional behavior ofthe ProTaper Universal files [3]. When it comes to measuring the cyclic fatigue durability of endodontic files, although a variety of approaches exist, a specific standard remains elusive [4]. [PERSON] et al. developed a cyclic fatigue test apparatus and methodology wherein the endodontic instrument is introduced into a simulated root canal and subjected to rotation until failure [5]. Subsequent studies have adopted [PERSON]'s methodology to evaluate the cyclic fatigue behavior of diverse endodontic file sets across a spectrum of operational conditions. [PERSON] et al. examined the influence of clinical use of ProTaper endodontic files on their fatigue behavior [6], whereas [PERSON] et al. compared the fatigue resistance of ProTaper Universal and V-Taper files [7]. In their study, [PERSON] et al. also investigated the effects of different root canal treatment techniques on the fatigue behavior of the same instrument. [PERSON] et al. probed the temperature's impact on cyclic fatigue of endodontic instruments [8]. Considering the effects of electromotor torque, [PERSON] undertook an investigation employing ProFile instruments [9]. Furthermore, [PERSON] et al. employed a test setup encompassing various curving angles to quantify the fatigue life of ProTaper Universal and ProTaper Next file sets [10]. Examination of the finite element simulations of physical tests reported in the literature demonstrates that numerous studies concentrate on modeling of ISO 3630-1 bending and torsion test scenarios. [PERSON] et al. [11], [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14] generally outlined the file fixation setup and the load application procedure. They compared and assessed the bending and torsional resistance of the investigated endodontic files by comparing measurements from the test apparatus to results obtained by finite element simulations. Most of these studies provide sufficient information about loading and fixation conditions being simulated but lack comprehensive descriptions of boundary conditions and load application. Furthermore, they omit crucial details concerning the geometry and finite element mesh for both the files and the test apparatus. Additionally, exploration of alternative modeling approaches is notably absent.