## 2 Materials and Methods  
In this study, two cases of a mandibular class II Kennedy edentulous patients with PM2, M1 and M2 teeth missing were considered. For the first patient, a mandibular unilateral removable partial denture was made, in order to replace all the three missing teeth. The two anterior abutment teeth were covered using two splinted metal-ceramic surveyed crowns, with two oral milled shoulders and one interlock in between them. To retain the denture, a prefabricated unique sagittal attachment was used, with two balls (Rhein83, Bologna, Italy), one horizontal and the other sagittal. All the metallic parts of the assembly (splinted crowns with attachment, metal housing of the attachment and metal reinforcement of the saddle) were casted from Cr-Co Remanium GM 380 (Dentaurum, Ispringen, Germany). The acrylic saddles were made of thermo-polymerizable acrylic material Acry-Pole (Ruthinium Dental Manufacturing S.p.A., Badia Polesine, Rovigo, Italy) and the artificial acrylic teeth were made from Acry-Rock (Ruthinium Dental Manufacturing S.p.A., Badia Polesine, Rovigo, Italy). For the second patient, a similar mandibular unilateral removable partial denture was made, but using a posterior implant, on the position of the second molar, also with the same extra-coronal ball attachment and a metal housing positioned horizontally on top of the implant. This second denture design converted the distal extension denture base from a tooth- and tissue-supported prosthesis to a tooth- and implant-supported prosthesis. The used implant (Alpha-Bio Tec, Petach Tikwa, Israel) has the following dimensions: 3.75 mm diameter and 8 mm length. For both cases, the mandibular bone was considered to have an outer layer (1.2 mm thickness) of cancellous bone, while the rest of them were type III trabecular bone [7,8]. Finite element analysis was used in order to study the stress distribution in these two unilateral denture designs. The 3D models were created using Autodesk Inventor 2022 software (Figures 1-4); their characteristics are presented in Table 1. The geometrical form of the second premolar was cylindrical, while that of the two molars was elliptic cylindrical; their dimensions were considered equal. In addition, all the cusps were considered to be equally dimensioned and in the same occlusal plane. Figure 1: The 3D Model of the unilateral mandibular RPD. The von Mises stress levels and stress distribution that appeared in these two situations were compared using a masticatory force with an axial component of 160 N and a tangential component of 23.5 N [9]. All materials were considered isotropic with linear elasticity and they were homogeneous. The mechanical properties (obtained from the above-mentioned manufacturers and [7,8]) of all materials are presented in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristic** & **Measurement Unit** & **Value** \\ \hline Mass, without implant & grams & 6.97 \\ Area, without implant & mm\({}^{2}\) & 4629.97 \\ Volume, without implant & mm\({}^{3}\) & 5655.46 \\ Mass, with implant & grams & 7.47 \\ Area, with implant & mm\({}^{2}\) & 5117.05 \\ Volume, with implant & mm\({}^{3}\) & 5707.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The 3D models characteristics. Figure 4: The 3D Model of the metal reinforcement, artificial teeth and distal implant. Figure 3: The 3D Model of the implant and ball attachment, with matrix housing. Figure 2: The 3D Model of the unilateral mandibular RPD with distal implant. The bracket was considered to be frictionless and constrained on the support surface. The ball attachments were modeled as pin constrained. The lateral, front, back and base faces of the jawbone were considered to be fully constrained. The implant for the second patient was simulated as inserted in M2, through an HDPE cup. All contacts between parts were considered to be bonded. The mesh refinement threshold was 0.75 and the convergence of the results was set to be von Mises stress.