## 5 Conclusions  
The present paper studies and highlights--using numerical methods of modeling and simulation offered by COMSOL Multiphysics software (specifically three of its simulation modules: solid state mechanics module, electric current module and heat transfer module)--the dependence between the contact voltage (the voltage drop on the contact) and the variation in its temperature, but also in the current path within the contact. The results obtained after the simulations show that, from a mechanical point of view, the maximum value of the contact force is found at the points of contact, and the von Misses stress takes higher values in the current path area where the flat part intersects with the cylindrical shape for each contact element, and also in the area of the physical touching of the two contact elements. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Electric Potential (Contact** & \multicolumn{2}{c}{**Maximum Contact Temperature**} & \multicolumn{1}{c}{**Temperature**} \\ \cline{2-4}
**Voltage) Difference [mV]** & **[K]** & **[\({}^{\circ}\)C]** & **Variation** \\ \hline \multicolumn{4}{c}{Ambient temperature \(T\) = 293.15 K/20 \({}^{\circ}\)C} \\ \hline
0 & 293.15 & 20.00 & 0.00 \\
0.50 & 294.28 & 21.13 & 1.13 \\
1.00 & 298.07 & 24.92 & 4.92 \\
2.00 & 312.93 & 39.78 & 19.78 \\
3.00 & 337.65 & 64.50 & 44.50 \\
4.00 & 372.39 & 99.25 & 79.25 \\
5.00 & 416.96 & 143.81 & 123.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Temperature increase function of the contact voltage resulting from simulations. Figure 30: Variation of the temperature as a function of the contact voltage. From electro-thermal points of view, the theoretical aspects presented in the Introduction section and shown in Figure 7 are proven by the graphical representation of temperature gradient along the contact, where the highest temperature occurs in the touching area and the gradient increases in the direction from the zero potential contact elements towards the contact point. Also, various representations (on a plane of symmetry, and using streamlines) were plotted for the dependence between the temperature variation of the contact elements and the variation of the current density. Finally, temperature variation diagrams along the edges of the contacts were traced to highlight the maximum values. The maximum contact temperature values were computed by simulation for contact voltages between 0 and 5 mV. Thus, the curve of variation of the increase in contact temperature relative to the contact temperature was plotted, finding this variation to be parabolic. The study of the obtained values during simulations indicates an undesirable increase in contact temperature for values higher than 4 mV of voltage drop, with temperatures that may affect the integrity of insulating materials in the electrical contact. This finding is important, as damage to the insulation materials may cause the phenomenon of overturning, or short-circuiting in the electrical contact devices, thus leading to fire and damage. The analysis of these aspects can constitute a future direction of research. Another future direction of research could be the extension of the study to analyze contact behavior not only for the static stresses implied by the normal closing of contact, but also considering dynamic mechanical stresses induced by shock or vibration. A third possible development of this study could be an experimental study and the comparison of its findings to the results of numerical simulation. All authors have contributed to the preparation of this manuscript. Conceptualization, A.A., F.D.P. and D.P. ; methodology, S.M.R., A.A., I.B. and M.A.R. ; software, F.D.P., A.A., and D.P. ; writing--original draft preparation, S.M.R., F.D.P. and A.A.; writing--review and editing, D.P., M.A.R., I.B. and D.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data availability Statement: Data are contained within the article. The authors declare no conflicts of interest.