## 3 Results  
The FEA showed the distribution of the reaction forces and structural stress at the fixed top end of the abutment in the dental implant system. Figure 3 shows the value and direction of the reaction force at the TMJ and the fixed end of the abutment under the four occlusion conditions in this study. As shown in the figure, under the RMOL conditions, the reaction force at the top of the abutment of the dental implant system was larger. Furthermore, in the case of ICP conditions, the TMJ has a larger reaction force. Table 3 shows the magnitude of the reaction force at the TMJ and the top of the abutment and the magnitudes of the composing forces along each axis under the four occlusion conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Material** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** \\ \hline
**Cortical bone** & - & 13,800 & 0.26 \\
**Trabecular bone** & - & 345 & 0.31 \\
**Dental implant** & Titanium & 110,000 & 0.35 \\
**Abutment** & Titanium & 110,000 & 0.35 \\
**Abutment screw** & Titanium & 110,000 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Settings of the Material properties in this study [27,30]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Clenching** & **Force** & **Central** & **Lateral** & **Canine** & **First** & **Second** & **First Molar** & **Second** & **Right TMJ** & **Left TMJ** \\
**Tasks** & **Force** & **Incisor** & **Incisor** & **Incisor** & **Incisor** & **Incisor** & **Incisor** & **Incisor** & **Incisor** & **Incisor** \\ \hline  & **Total** & **38.340 N** & **70.431 N** & & & & & & & **182.31 N** & **184.72 N** \\  & **Fx** & -5.1629 N & 14.622 N & - & - & - & - & - & -17.976 N & 20.411 N \\  & **Fy** & -31.503 N & -67.652 N & & & & & & 31.692 N & 30.499 N \\  & **Fz** & -21.235 N & -12.992 N & -12.992 N & & & & & -178.63 N & -181.04 N \\ \hline  & **Total** & & & & **28.819 N** & **40.884 N** & **61.691 N** & **80.588 N** & **356.80 N** & **357.11N** \\  & **Fx** & - & - & 25.614 N & 16.475 N & 21.270 N & 17.391 N & 15.037 N & -75.50 N & 173.586 N \\  & **Fy** & - & - & 7.8226 N & \(-13.908\) N & \(-21.296\) N & \(-35.744\) N & \(-90.697\) N & 147.24 N & 144.29 N \\  & **Fz** & & & & 10.643 N & \(-34.737\) N & \(-53.850N\) & \(-70.103\) N & \(-132.33\) N & \(-326.24\) N & \(-318.27\) N \\ \hline  & **Total** & & & & & **26.109 N** & **214.91 N** & **176.22 N** & **288.932 N** \\  & **Fx** & - & - & - & - & - & -78.038 N & 66.338 N & \(-14.648\) N & 30.628 N \\  & **Fz** & & & & & \(-58.352\) N & \(-107.97\) N & 85.602 N & 37.721 N \\  & **Fz** & & & & & \(-24.222\) N & \(-173.588\) & 153.31 N & \(-279.79\) N \\ \hline  & **Total** & & & & & **26.968 N** & **29.38** & **14.282 N** & **166.83 N** & **134.06 N** \\  & **Fx** & - & - & -45.555 N & \(-8.0485\) N & 4.8838 N & 4.8260 N & 5.5388 N & \(-26.398\) N & \(-9.2242\) N \\  & **Fy** & & & & \(-28.842\) N & \(-17.589\) N & \(-11.427\) N & \(-12.513\) N & \(-19.927\) N & 92.999 N & \(-2.301\) N \\  & **Fz** & & & & \(-28.405\) N & \(-35.174\) N & \(-23.934\) N & \(-26.267\) N & \(-37.534\) N & \(-138.16\) N & \(-133.72\) N \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The magnitude of the reaction force at the top of the abutment and TMJ. The magnitudes of the composing forces along each axis under the four occlusion conditions. Figure 4a shows the distribution of von Mises stress in the mandibular bone under the four occlusion conditions. The figure shows that under all the four occlusion conditions, high stress arises at the neck near the TMJ. Under RMOL especially, the mandible is under significantly higher stress. In addition, depending on the boundary conditions, the tops of the abutments were fixed for the different occlusion conditions. The alveolar bones surrounding the fixed top ends of the abutments received higher stress. Figure 4b shows the distribution of von Mises stress in the alveolar bone surrounding the implants at different positions under the 4 occlusion conditions.