## 3 Results  
To evaluate the performance in terms of primary stability and the possible effect on secondary stability, different results were extracted. Because the three implants designed did not have identical bone-stem surfaces, as clearly shown in Figure 4, the effective area of the bone-implant interface and the percentage of the effective contact surface, with respect to the total stem surface, of the implants were calculated. The values are reported in Figure 8.  
The primary stability was calculated by evaluating the micromotions under a load of 1000 N representing the static load-bearing exercise carried out during the rehabilitation. Micromotions were evaluated using Abaqus 2020 built-in function CSLIP, reported in the Abaqus manual as the tangential relative motion between the nodes of the bone and the implant. The CSLIP value was evaluated at the contact surfaces along two perpendicular directions, identified as _CSLIP1_ and _CSLIP2_[24; 47]. The micromotion at the bone-implant interface was calculated as the result of the tangential relative displacements (_CSLIP1_ and _CSLIP2_) for each node-n, as defined in Equation (1):  
\[CSLIP_{n}=\sqrt{CSLIP_{1}{n}^{2}+CSLIP_{2}{n}^{2}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline Contact element & Contact formulation & Normal behaviour & Normal stiffness & Tangential behaviour \\ surface to surface & finite sliding & “Hard” penalty & 600 N/mm & penalty \\ \hline Friction coefficient & Elastic slip & Interference \(\mathcal{O}\) & Contact control & Line search control iterations \\
0.29 & 0.005 mm & 0.1 mm & 0.20\% & 5 \\ \hline \end{tabular} Sources: [15; 41; 45].  
\end{table} 
Table 2: Parameters used to define the contact. Figure 8: The effective contact area of the bone–implant interface and the percentage of contact area with respect to the entire stem surface. Figure 7: The final assembly with the constraints and the force applied. The primary stability was evaluated by assessing the micromotion values at the bone-stem interface to check if micromotions cross the value of 50 \(\upmu\)m, which represents the minimum value where fibrous tissue, instead of bone tissue, is formed, with the risk of compromising long-term stability [15; 20; 21; 22]. The maximum micromotions for the three implant designs are shown in Figure 9. The micromotion maps' distribution along the contact surface is reported in Figure 10, where it is possible to see how the amount of surface under slip conditions is different for the three implants. There is a wide zone of the SD with micromotions over 50 \(\upmu\)m.  
The implant that has shown lower values of maximum micromotions was the PSD design, with a peak value of 51.4 \(\upmu\)m. For the PPSD design, a peak of 58.6 \(\upmu\)m was recorded. The worst results were achieved with the SD implant, which shows a maximum value of 73.9 \(\upmu\)m. The von Mises stress distributions (Figure 11) and the maximum and average  
Figure 10: Micromotions distribution at the bone–implant interface from a left (**A**) and a right (**B**) view of the surfaces. Figure 9: Maximum micromotions at the bone–implant interface. contact pressure (Figure 12) of five cross-sections at five distinct levels of the contact length, from 0 to 100%, were assessed. Figure 11: Positions of the analyzed sections on the bone–implant assembly, with a detail of their positions on the implant’s stem (**A**) and the respective von Mises stress distribution for the SD, PPSD, and PSD (**B**). Figure 12: The maximum (**A**) and average (**B**) contact pressures at five sections of the bone–implant interface. From those distributions, it is possible to observe that the von Mises stress distribution for the SD implant, as shown in Figure 11, is irregular in all the analyzed sections; instead, the PPSD and PSD implants show a more regular distribution of the von Mises stress in the cortical bone.