## 4 Simulation Results and Discussion
### Results of the Electro-Thermal Simulation  
The effects of variations in the electrical potential on the current path of the contact are shown in Figure 18. As expected, they vary between 0 V, which corresponds to the right-hand side element of the contact that is grounded, and 3 mV, corresponding to the left-hand side element. The difference in electric potential is actually the voltage drop in the elements of the electrical contact. The variation in the electric field amplitude along the current path is shown in Figure 19a. The Multislice mode combined with the Streamline Multislice mode was used for this rep  
Figure 17: The contact forces. Figure 18: The electrical potential of the contact along the current path. sentation. Figure 19b shows a detail of the variation in the electric field amplitude in the area where the contact elements are touching. The variation in the temperature of the current path following the simulation is visible in Figure 20, where one can observe that the highest temperature developed in the touching area of the electrical contact. Figure 21a shows the simulation results related to the temperature gradient variation along a cut plane passing through the axis of the current path and parallel to plane XY. It can be seen both from the representation of the magnitude of this quantity <K/m> and from the streamline representation that the heat transfer from the element of contact with zero electrical potential is greater than that corresponding to the element of contact with an electric potential of 3 mV. Figure 19: (**a**) The variation of the electric field amplitude. (**b**) Details of variation of the electric field amplitude at the touching area. Figure 20: The variation of temperature in the current path and on the contact surface. Figure 21b shows the spatial variation in the current path's temperature gradient. Figure 22 shows the temperature variation of the two contact elements and the variation in the current density on a surface that passes through the axis of symmetry of the current path and is parallel to plane XY, using streamline representation. A cut plane was built parallel to plane XZ, passing through the origin of the cartesian coordinate system (Y = 0). Figure 23a,b show the details regarding the positioning of this cut plane. In Figure 24, the variation in current density on the cut plane defined above is presented. In Figure 25, the variation in the current density is shown using a three-dimensional representation and a Max/Min-Point diagram showing the density of electric energy. One can see that the highest density of electric energy developed at the touching area of the contact elements. Figure 23: Cut plane building and details on its positioning. Figure 24: Variation in the current density on the cut plane. A dataset element of the type Edge 3D was created (see in Figure 26) along an edge line of one contact element in order to plot the temperature variation along this edge, as presented in Figure 27.  
Figure 27: Variation of the temperature along the contact element edge. Figure 26: Edge 3D-type dataset created for the edge of a contact element. Figure 17:0 Variation in the current density at the contact (3D), and the Max/Min-Point diagram of the electric energy density. In a similar way, two Edge 3D type datasets have been created (Figure 28a,b) for the contours of both electrical contact elements, to be used for the plotting of the variation graph of the electrical potential, as shown in Figure 17:1  
In order to highlight the variation in the maximum temperature of the current path, and its dependence on the value of the contact voltage, the simulations were run for various values of the potential difference between the two elements of the electrical contact. These data, the values of the maximum temperature, and the values of the temperature increase as compared to the ambient temperature are all summarized in Figure 17:2  
Figure 17:3 The two Edge 3D datasets created for the contours of: (**a**) Top contact element. (**a**) Bottom contact element.