# Influence of Cavity Geometry on the Fracture Strength of Dental Restorations: Finite Element Study
## 3 Results
### Resin Cement Adhesive  
The von Mises stress distributions in the resin cement adhesives are shown in Figure 5a. The adhesive of the inlay model presented the highest values of effective stress, and the area where the highest values were encountered was placed on the buccal side. The mean von Mises stress was 9.93 \(\pm\) 6.86 MPa, ranging from 0.59 to 33.28 MPa. The descriptive statistical results of this stress and the maximum shear stress are presented in Table 5 for both restorations. Figure 5b shows the histogram of the adhesive level loading distribution for both restorations. Once more, the geometry that had a greater percentage of material loaded within the range of 5-10 MPa was the onlay, whereas for loading levels higher than 27.5 MPa, the inlay had a greater percentage of material. Figure 5: Smoothed stress distributions for the adhesives of both models. (**a**) Inlay (left) and onlay (right). (**b**) Histograms of the distributions for both models. The total percentage of adhesive material that was loaded behind 27.5 MPa was 0.42% in the only geometry and 2.5% in the inlay restoration, which meant that at this level of loading, the variation of material between the two restorations was about 83.4%. Analysis of the solicitation level over the two \"bed\" geometries was also assured by comparing the von Mises and maximum shear stresses through the two restorations. Table 6 shows the descriptive values and the percentage of variation of the results between the two \"bed\" geometries. Interestingly, because the bed geometries had the same node numbers in both geometries, resulting in 31,386 samples for each, it was possible to perform a paired samples \(t\)-test for all values, and the results are presented in Table 7.  
In the inlay restoration, the magnitude of displacements was, on average, 26.05 \(\pm\) 2.96 \(\upmu\)m, and in the onlay model it was 26.18 \(\pm\) 2.98 \(\upmu\)m. The mean difference between the two models was statistically different, with statistical significance t(2, 31385) = \(-\)1036.407, \(p\) < 0.001. The variation of the different mean stresses between the two models showed similar behavior (i.e., the onlay model had the highest values, except for the second principal stress). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Aver.** & **SD** & **Min.** & **1 st Quart.** & **Median** & **3 rd Quart.** & **Max.** \\ \hline \multirow{2}{*}{Von Mises (MPa)} & _Inlay_ & 8.73 & 5.25 & 0.98 & 3.99 & 7.76 & 13.23 & 28.73 \\  & _Onlay_ & 8.78 & 5.17 & 1.03 & 4.04 & 7.73 & 13.17 & 27.72 \\ \hline \multirow{2}{*}{\((Inlay-Onlay)/Onlay\) (\%)} & \(-\)0.49 & 1.57 & \(-\)4.71 & \(-\)1.03 & 0.30 & 0.46 & 3.64 \\ \hline \multirow{2}{*}{Maximum Shear (MPa)} & _Inlay_ & 4.84 & 2.83 & 0.54 & 2.27 & 4.36 & 7.26 & 14.84 \\  & _Onlay_ & 4.86 & 2.79 & 0.58 & 2.30 & 4.35 & 7.24 & 14.38 \\ \hline \multirow{2}{*}{\((Inlay-Onlay)/Onlay\) (\%)} & \(-\)0.51 & 1.75 & \(-\)5.80 & \(-\)1.08 & 0.17 & 0.28 & 3.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical description of the stress distributions for the “bed” resin cement adhesives. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Inlay–Onlay** & **Mean** & **SD** & **SDE Mean** & **95\% CI** & _p-Value_ \\ \hline Displacement Magnitude (\(\upmu\)m) & \(-\)0.129 & 0.022 & 0.000124 & [\(-\)0.12925; \(-\)0.12876] & \textless{}0.001 \\ _Stresses (MPa)_ & & & & & \\ Von [PERSON] & \(-\)0.0428 & 0.3299 & 0.0019 & [\(-\)0.04640; \(-\)0.03911] & \textless{}0.001 \\ First principal stress & \(-\)0.0429 & 0.2292 & 0.0013 & [\(-\)0.04553; \(-\)0.04046] & \textless{}0.001 \\ Second principal stress & \(-\)0.0036 & 0.1749 & 0.0009 & [\(-\)0.00553; \(-\)0.00166] & \textless{}0.001 \\ Third principal stress & 0.0067 & 0.4103 & 0.0023 & [0.002150; \(-\)0.01123] & 0.004 \\ Maximum shear & \(-\)0.0248 & 0.1770 & 0.0009 & [\(-\)0.02680; \(-\)0.02288] & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table}