# Influence of Cavity Geometry on the Fracture Strength of Dental Restorations: Finite Element Study
## 3 Results
### Czm  
The results presented in this section were obtained with the assumption that the adhesive resin cement had a yield stress of 21 MPa and plastic bilinear behavior, with an isotropic strain hardening modulus of 770 MPa and rupture stress of about 37 MPa. The adhesive resin cement's yield point was about 1.24 times the tension failure strength of the interface. This value can be considered small when the interest is adhesion enhancement [39]. Nevertheless, the only information available showed a similar magnitude [40].  
Figure 8a shows the von Mises stress distribution in the \"bed\" adhesive resin of each restoration. The main difference was related to the maximum value, being 211.4 MPa in the inlay model and 204.7 MPa in the onlay model. Note that because the assumption of automatic rupture at the lowest stress-strain point was used, the deformed configurations of both \"beds\" showed damaged areas without finite elements. Figure 8b shows the von Mises boxplot and the maximum shear stresses at the \"beds\" without showing the outliers. These outliers were a consequence of the automatic rupture assumption, leading to higher concentration stresses around the zones where finite elements were removed. Therefore, their maximum values were about 100 times higher than the mean value. The descriptive statistical results of these values are presented in Table 11.  
The values presented in Table 11 show that descriptive statistics of both adhesive resin cement beds were quite similar, with the higher variations appearing in the SD, in the first quartile and the maximum values. Other statistical measures that give information about the location and variability of a data set are skewness and kurtosis. These two parameters showed variations to the order of 1.84% and 3.75% for the von Mises stress and 1.76 and 3.48 for the maximum shear stress, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Inlay–Onlay (MPa)** & **Mean** & **SD** & **SDE Mean** & **95\% CI** & \(p\) **Value** \\ \hline Von Mises & \(-0.0174\) & \(0.1891\) & \(0.0012\) & \([-0.01963;-0.01511]\) & \(<\)0.001 \\ First principal stress & \(-0.0336\) & \(0.1201\) & \(0.0007\) & \([-0.03506;-0.03220]\) & \(<\)0.001 \\ Second principal stress & \(0.0038\) & \(0.0812\) & \(0.0005\) & \([0.002808;0.004745]\) & \(<\)0.001 \\ Third principal stress & \(-0.0096\) & \(0.2076\) & \(0.0013\) & \([-0.01208;-0.00712]\) & \(<\)0.001 \\ Maximum shear & \(-0.0120\) & \(0.0987\) & \(0.0006\) & \([-0.01319;-0.01084]\) & \(<\)0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Paired differences in the results between pairs of models. Statistical analysis with a paired samples \(t\)-test, with confidence intervals for the difference for the “bed” dentin.  
\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}{*}{[PERSON] (MPa)} & \(\mathit{Inlay}\) & \(9.90\) & \(5.44\) & \(1.53\) & \(5.23\) & \(9.15\) & \(13.98\) & \(28.05\) \\  & \(\mathit{Onlay}\) & \(9.92\) & \(5.42\) & \(1.67\) & \(5.28\) & \(9.11\) & \(13.99\) & \(27.88\) \\ \hline \multirow{2}{*}{\(\left(\mathit{Inlay-Onlay}\right)/\mathit{Onlay}\) (\%)} & \(-0.18\) & \(0.35\) & \(-8.11\) & \(-0.92\) & \(0.41\) & \(0.01\) & \(0.56\) \\ \hline Maximum Shear & \(\mathit{Inlay}\) & \(5.42\) & \(2.87\) & \(0.88\) & \(2.97\) & \(5.09\) & \(7.54\) & \(15.19\) \\ (MPa) & \(\mathit{Onlay}\) & \(5.43\) & \(2.86\) & \(0.96\) & \(2.99\) & \(5.08\) & \(7.54\) & \(15.11\) \\ \hline \multirow{2}{*}{\(\left(\mathit{Inlay-Onlay}\right)/\mathit{Onlay}\) (\%)} & \(-0.22\) & \(0.42\) & \(-8.03\) & \(-0.79\) & \(0.25\) & \(-0.01\) & \(0.57\) \\ \hline \end{tabular}
\end{table}
Table 9: Statistical description of the stress distributions for the “bed” geometry at the dentin of both restorations.