## 2 Materials and Methods  
A flowchart of the finite element analysis is shown in Figure 1. The finite element analysis process began with the use of a dental tomography instrument to obtain a 3D image of the left permanent maxillary first molar tooth (J Morita MFG Corp., Kyoto, Japan) in DICOM format. The DICOM files were imported into the Materialize interactive medical image control system (Mimics 12.00, Leuven, Belgium) program, where different masks were created for each dental tissue (the enamel, dentin, and pulp). The density thresholdswere adjusted manually to accurately depict the anatomy of the tooth. Afterward, 3D objects of each mask were created and converted to STL files (Figure 2). The 3D image was then separated into surfaces using the Geomagic Design X 2020.0 program to generate the appropriate arrangements for the finite element analysis. Figure 1: Flowchart for performing finite element analysis. The tooth model was placed in a coordinate system, with the \(x\)-axis indicating the buccolingual direction, the \(y\)-axis indicating the mesiodistal direction, and the \(z\)-axis oriented upward. Class II DO cavity modeling was performed on the 3D model using Solidworks 2013 software (Solidworks Corp, Waltham, MA, USA), with a cavity angle of 95 degrees (Figure 3). The class II cavity had an occlusal depth of 4 mm and an occlusal-gingival depth of 6 mm, and it was fixed with the occlusal margin of the enamel and the gingival margin of the dentin. To reduce the stress concentration, the cavity's inner line angles were rounded. The relationship between the elastic modulus, stress, strain, and Poisson's ratio values was explained using [PERSON]'s law, and the values were reported by the programs used in the finite element analysis via this law [19]. \[\varepsilon_{11}=\frac{1}{E}[\sigma_{11}-\
u(\sigma_{22}+\sigma_{33})]\]  
\[\varepsilon_{22}=\frac{1}{E}[\sigma_{22}-\
u(\sigma_{11}+\sigma_{33})]\]  
\[\varepsilon_{33}=\frac{1}{E}[\sigma_{33}-\
u(\sigma_{11}+\sigma_{22})]\]  
\[\varepsilon_{12}=\frac{1}{2G}\sigma_{12};\ \varepsilon_{13}=\frac{1}{2G}\sigma_{13}; \ \varepsilon_{23}=\frac{1}{2G}\sigma_{23};\]  
\(\sigma\) = _Stress; E = Young' modulus; \(\varepsilon\) = Strain; \(\
u\) = Poisson's ratio; G = Shear modulus_  
Figure 2: CBCT-scan data as seen in MIMICS 12. The tooth is presented in three different cross-sectional views. The enamel, dentin, resin cement, and material characteristics were assumed to be isotropic and linearly elastic to simplify the complexity of the three-dimensional finite element models. The models were assigned the properties of the teeth and the materials, and the relevant data are presented in Table 1.  
Different combinations were simulated, including the same modulus of elasticity for the two cement groups (V1 and V2; Table 1) and different thicknesses (50 \(\upmu\)m (A), 100 \(\upmu\)m (B), and 150 \(\upmu\)m (C)). As a result, six study groups were created (Table 2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \begin{tabular}{c} **Young’s Modulus** \\ **(GPa)** \\ \end{tabular} & **Poisson’s Ratio** & \
\begin{tabular}{c} **Tensile Strength** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Compressive** \\ **Strength (MPa)** \\ \end{tabular} \\ \hline Dentin & 18.6 [20] & 0.31 [20] & 98.7 [21] & 297.0 [21] \\ Enamel & 84.1 [20] & 0.33 [20] & 10.3 [21] & 384.0 [21] \\ Pulp & 0.002 [22] & 0.45 [22] & - & - \\ Amalgam & 35.0 [7;23] & 0.35 [7;23] & 3–58 [24] & 45–550 [24] \\ Resin Cement (V1) Variolink II & & & & \\ (Ivoclar Vivadent, Schaan & 8.3 [25] & 0.35 [25] & - & - \\ Liechtenstein & & & & \\ Resin Cement (V2) Variolink II & & & & \\ (Ivoclar Vivadent, Schaan & 8.3 [26] & 0.24 [26] & - & - \\ Liechtenstein & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the material used in 3D FE models of maxillary molars.