## 2 Materials and Methods
### Loading and Boundary Conditions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Clenching Tasks**} & \multirow{2}{*}{**Side**} & \multirow{2}{*}{**Direction**} & \multicolumn{6}{c}{**Muscular Force (N)**} & \multirow{2}{*}{**Constraint of Abtment**} \\ \cline{3-4} \cline{6-10}  & & & **SM** & **DM** & **MP** & **AT** & **MT** & **PT** \\ \hline \multirow{6}{*}{**INC**} & **Right** & **Force** & **76.2** & **21.2** & **136.3** & **12.6** & **5.7** & **3.0** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & 15.8 & 11.6 & \(-\)66.3 & 1.9 & 1.3 & 0.6 & \\  & & \(\mathrm{Fy}\) & 31.9 & \(-\)7.6 & 50.9 & 0.6 & \(-\)2.9 & \(-\)2.6 & \\  & & \(\mathrm{Fz}\) & 67.3 & 16.1 & 107.8 & 12.5 & 4.8 & 1.4 & Constrained the \\ \cline{2-10}  & **Left** & **Force** & **76.2** & **21.2** & **136.3** & **12.6** & **5.7** & **3.0** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & \(-\)15.8 & \(-\)11.6 & 66.3 & \(-\)1.9 & \(-\)1.3 & \(-\)0.6 & \\  & & \(\mathrm{Fy}\) & 31.9 & \(-\)7.6 & 50.9 & 0.6 & \(-\)2.9 & \(-\)2.6 & \\  & & \(\mathrm{Fz}\) & 67.3 & 16.1 & 107.8 & 12.5 & 4.8 & 1.4 & \\ \hline \multirow{6}{*}{**ICP**} & **Right** & **Force** & **190.4** & **81.6** & **132.8** & **154.8** & **91.8** & **71.1** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & 39.4 & 44.6 & \(-\)64.6 & 23.1 & 20.4 & 14.8 & \\  & & \(\mathrm{Fy}\) & 79.8 & \(-\)29.2 & 49.6 & 6.8 & \(-\)45.9 & \(-\)60.8 & \\  & & \(\mathrm{Fz}\) & 168.3 & 61.9 & 105.1 & 153.0 & 76.8 & 33.7 & \\ \cline{2-10}  & **Left** & **Force** & **190.4** & **81.6** & **132.8** & **154.8** & **91.8** & **71.1** & Constrained the canine, \\ \cline{2-10}  & & \(\mathrm{Fx}\) & \(-\)39.4 & \(-\)44.6 & 64.6 & \(-\)23.1 & \(-\)20.4 & \(-\)14.8 & \\  & & \(\mathrm{Fy}\) & 79.8 & \(-\)29.2 & 49.6 & 6.8 & \(-\)45.9 & \(-\)60.8 & \\  & & \(\mathrm{Fz}\) & 168.3 & 61.9 & 105.1 & 153.0 & 76.8 & 33.7 & \\ \hline \multirow{6}{*}{**RMOL**} & **Right** & **Force** & **137.1** & **58.8** & **146.8** & **115.3** & **63.1** & **44.6** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & 28.4 & 32.1 & \(-\)71.4 & 17.2 & 14.0 & 9.3 & \\ \cline{2-10}  & & \(\mathrm{Fy}\) & 57.4 & \(-\)21.0 & 54.8 & 5.1 & \(-\)31.5 & \(-\)38.1 & \\ \cline{2-10}  & & \(\mathrm{Fz}\) & 121.2 & 44.5 & 116.1 & 114.0 & 52.8 & 21.1 & Constrained the \\ \cline{2-10}  & **Left** & **Force** & **114.2** & **49.0** & **104.9** & **91.6** & **64.1** & **29.5** & right molars \\ \cline{2-10}  & & \(\mathrm{Fx}\) & \(-\)23.6 & \(-\)26.7 & 51.0 & \(-\)13.7 & \(-\)14.2 & \(-\)6.1 & \\  & & \(\mathrm{Fy}\) & 47.9 & \(-\)17.5 & 39.1 & 4.0 & \(-\)32.0 & \(-\)25.2 & \\  & & \(\mathrm{Fz}\) & 101.0 & 37.1 & 83.0 & 90.5 & 53.6 & 14.0 & \\ \hline \multirow{6}{*}{**RGF**} & **Right** & **Force** & **34.3** & **29.4** & **12.2** & **104.3** & **61.2** & **46.9** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & 7.1 & 16.0 & \(-\)6.0 & 15.5 & 13.6 & \(-\)9.8 & \\ \cline{2-10}  & & \(\mathrm{Fy}\) & 14.4 & \(-\)10.5 & 4.6 & 4.6 & \(-\)30.6 & \(-\)40.1 & \\ \cline{2-10}  & & \(\mathrm{Fz}\) & 30.3 & 22.3 & 9.7 & 103.0 & 51.2 & 22.2 & \\ \cline{2-10}  & **Left** & **Force** & **51.4** & **21.2** & **132.8** & **11.1** & **5.7** & **4.5** & \\ \cline{2-10}  & & \(\mathrm{Fx}\) & \(-\)10.6 & \(-\)11.6 & 64.6 & \(-\)1.7 & \(-\)1.3 & \(-\)0.9 & \\ \cline{2-10}  & & \(\mathrm{Fy}\) & 21.5 & \(-\)7.6 & 49.6 & 0.5 & \(-\)2.9 & \(-\)3.9 & \\ \cline{2-10}  & & \(\mathrm{Fz}\) & 45.4 & 16.1 & 105.1 & 10.9 & 4.8 & 2.2 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The loading conditions in this study, values, and directions of the external forces applied in different occlusion conditions, and fixed-top end of the abtment in the dental implant system [21; 22; 23; 24; 25]. For the boundary conditions (Figure 2e), the temporomandibular joint (TMJ) was set as the fixed end and the displacements on the X-axis, Y-axis, and Z-axis in this region were set to 0. In addition, according to each clenching task, the top end of the abutment in the dental implant system was fixed at the incisor, canine, premolar, and molar to simulate the actual conditions of teeth occlusions.