## 4 Discussion  
This finite element study analyzed the effect of the number of implants on the distribution of stress transmitted to the implants and to the supporting bone tissue and the stress obtained in different types of rehabilitation. Three-dimensional finite element analysis has proven to be the ideal technique for stress, deformation, and structural displacement analyses, enabling more accurate simulations without being an invasive technique [12]. We initially tried to generate a tridimensional geometric model of the object to be studied as faithful as possible, in order to obtain the most reliable results. However, there are limitations in this kind of studies. First of all, bone is a complex structure without definite patterns and has distinctive characteristics in each person; therefore, its geometry does not have defined properties. Also, the model corresponded to only one half of the mandible which did not compromise the study. Finally, all materials were modelled as linear, elastic, isotropic, and homogeneous. These assumptions have been accepted and verified in several studies [13; 14]. [PERSON] and [PERSON] concluded that it is not necessary to construct a model of the entire mandible in order to compare the distribution of stress around implants [15; 16]. This simplification has the advantage of reducing the modeling time of the structure and the computational cost. Although some authors [17; 18; 19] report that the stress values found in their work are smaller than the fracture limits of materials such as bone and titanium, these statements must be made with some warnings so that they can be translated to the clinical field, since the simplifications assumed in the models can generate values that do not correspond to real clinical situations. In this study, in both \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Distal Section of the** & **Screw (MPa)** & **Abutment (MPa)** & **Implant/Abutment Contact (MPa)** \\ \hline M1 group & 148.92 & 22.0 & 22.2 & 51.1 \\ M2 group & 139.51 & 19.9 & 23.9 & 46 \\ Difference between models & 6.74\% & 10.55\% & 7.65\% & 11.08\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: von Mises stress measured in each group. Figure 8: Maximum principal stress [MPa] in the M2 group: (**a**) three-dimensional view; (**b**) transversal cut of the bone. models, the highest values of the stress for both compression (4.7 MPa in M1 and 3.05 MPa in M2) and traction (9.09 MPa in M1 and 10.7 MPa in M2) on the cortical bone did not exceed the maximum limits of physiological stress which the bone can support, corroborating other scientific studies [20], according to which when the maximum main compression stress exceeds 170-190 MPa and the main tensile stress exceeds 100-130 MPa bone fracture and/or the onset of bone resorption occur. Regardless of the number of implants, it was observed that the maximum stress occurred on the surface of the cortical bone near the cervical area of the most distal implant, corroborating several results found by other studies [16; 21]. The maximum stress values at the border between the cortical bone and the trabecular bone were evident during the study, demonstrating the difference in mechanical resistance between the two bones, agreeing with Reference [22]. There was compression stress across the surface of the implant, but it virtually disappeared when compared to the compression effect on the outermost surface of the cortical bone and traction on the border between the cortical and the trabecular bone. The stress was shown to be much more evident in the cortical bone because it had greater mechanical resistance and greater modulus of elasticity, and thus was able to accumulate greater stress, a conclusion similar to that of another study [23]. We measured a great difference between the compression stresses on the surface of the cortical bone in the distal region of the distal implants in the two models studied. The difference indicated a 54.69% higher compression stresses in model 1, a result similar to that of another study [24].