# Structural Assessment of Endodontic Files via Finite Element Analysis
## 4 Discussion  
* ISO 3630-1 Simulations  
The high-definition model described for the bending test demonstrates results that exhibit a reasonable correlation with the physical test outcomes reported by [PERSON] et al. [12], particularly concerning the bending moment estimates for the F1 endodontic file. This agreement extends to the torsion tests, where the simulation outcomes closely align with the test results, reported by [PERSON] et al. [12]. Furthermore, the simulation results confirm that the outcomes obtained from the idealized models show a high level of accuracy when compared to the results from the high-definition models. While the horizontal displacement of the handle due to the geometric stiffness of the file is underestimated by the idealized models, it does not impact the calculated bending moment results. In summary, this validation confirms that the proposed methodology using high-definition models is suitable for assessing the structural stiffness of the endodontic files, and the suggested idealizations are indeed appropriate.  
Another noteworthy result is that the F1 endodontic file has approximately 57% less torsional stiffness and 68% less bending stiffness compared to the F2 file. Again, these findings align with the test data presented by [PERSON] et al. [2].
* Cyclic Fatigue Simulations  
The simulation results for the [PERSON]'s test system indicate that, during the insertion step, the mid-section of the file touches the cylinder while the tip of the file contacts the jig's cylindrical and horizontal surfaces at their junction. This pattern is consistent with the observations made by [PERSON] et al. in [6]. In the same study, focusing on the F2 endodontic file, [PERSON] has reported an average failure location of 3.5 mm from the file's tip. The present simulation predicts the highest dissipated energy density location of 3.48 mm from the tip, which corresponds to this study. For the F1 endodontic file, [PERSON] reported a failure location between 4.0-5.8 mm, a range that matches the simulation's prediction of 4.1 mm from the tip.  
For fatigue life estimation, [PERSON] has recorded an average of 367 rotations for the F1 endodontic file and 320 rotations for the F2 endodontic file before failure. Simulation results indicate 8% higher dissipated energy for the F1 file compared to the F2 file in the most critical area, pointing to a longer fatigue life for endodontic file F1. The validation further demonstrates that hysteresis energy serves as a reliable parameter for quantifying the fatigue behavior of Ni-Ti endodontic files.  
Similar to ISO 3630-1 test models, in principle, the idealized models are observed to have better numerical convergence behavior with increased computational efficiency.  
Figure 20: Maximum dissipated energy density in F2 file.  
It should be noted that the proposed methodology has certain limitations due to the utilization of the Abaqus SMA software (Abaqus 2021) module in this study [17]. While the module is well-suited for the methodology proposed in this work, particularly due to its ability to represent the inner loop effect, and its suitability and accuracy which are validated and verified with the test data, it employs a symmetric material properties implementation that treats tension and compression equally. However, an asymmetric implementation would likely result in more accurate overall results. Such an implementation could be achieved through the use of a UMAT (User Material) subroutine and would necessitate detailed material property data.