# The Restored Premolars Biomechanical Behavior: FEM and Experimental Moire Analyses
## 2 Materials and Methods
### Finite Element Analysis  
Finite element analysis has been used in other studies to determine stress and strain distribution. In [18] the hypothesis that restoration of class II meso-oclusal-distal (MOD) cavities can be strengthened through judicious choice of restoration geometry and material properties was proven. Research by [PERSON] et al. 2021 [19] used computational analysis of prepared crowned teeth to differentiate the possibility of using porcelain material for typical clinical conditions. In the present work, the FEM analysis was developed using the computational code ANSYS Academic. The establishment of the physical model was performed using the mean dimensions of the premolars selected set and favorable coronary anatomy as a standard for the healthy and the repaired cases. Thereafter, with the help of a scanner, the outer tooth surface was generated, using a 0.2 mm contact tip trace calibration. The external geometry data was stored in the type ''STL'' computer files (Stereolithographic), generated by the scanner system. These files were exported to Bio-CAD modeling software (Computer Assisted Design; Rhino3D 4.0, rhinoceros USA) to produce the standard three-dimensional model of the healthy tooth. The repaired main dental regions were generated by using the software called NURBS (Non-Uniform Rational Basis Spline) suitable for modeling complex geometries. Figure 5 shows: (a) Model STL computer connected to the scanner system; (b) Software Bio-modeling CAD (Computer Assisted Design; Rhino3D 4.0, Rhinoceros, New York, NY, USA) NURBS surfaces (Non-Uniform Rational Basis Spline); (c) three-dimensional model generation that serves as a standard healthy tooth. Figure 6 shows the model generation of healthy teeth based on the main anatomical landmarks and with the help of a specific tool program (NURBS surfaces). Finally, Figure 7 shows the volumes of the internal and external structures of the reference teeth. Figure 5: (a) Model STL, (b) Bio-CAD modeling, and (c) three-dimensional model generation. Figure 6: Model generation is healthy, based on the main anatomical landmarks and with the help of a specific tool program (NURBS surfaces). The geometric models were exported to ANSYS Academic preprocessing software and, for each model, meshes were generated using tetrahedral elements of the linear type, with a total of 68,860 nodes and 40,358 elements. The generated meshes on the models with MOD cavity [20], and endodontic access plus restoration on models with cervical [21], and corresponding restoration cavity are shown, respectively, in Figures 8 and 9. As shown in Figure 10, the boundary conditions were defined for perfectly simulating contacts between the fixing structure (gray cylinder) and models with MOD cavities restored with composite resin. The tetrahedral model consists of 68,860 nodes and 40,358 elements. The analysis employed was a structural, linear, and elastic type for all such structures were isotropic, linear, and homogeneous. For this, it was necessary to obtain the elastic moduli and Poisson's ratios of the structures which characterize each model, which are described below in Table 1.  
For the teeth modeled with FEM, the periodontal tissue PDL was not considered to be maintained under the same conditions as in the moire experiments. Axial and oblique loads of 25 N, 50 N, 75 N, and 100 N were applied in the red area shown in Figure 10. The models were exported to the software processing core (Ansys Academic). For analysis of the results, criteria for normal direction deformation were used. The materials were considered homogeneous, isotropic, and with linear-elastic behavior. The FEM numerical simulation estimated the normal elastic strain (for \(X\)-, \(Y\)-, and \(Z\)-axis) for all the specified cases mentioned before. Figure 11 shows, as an example, only for loading 100 N, a typical 3D color strain representation on the \(Z\)-axis direction.