## 4 Results and Discussion
### Simulation for Nonwoven Antistiatic Fabric  
The first ESD protective textile studied by simulation was nonwoven antistiatic fabric. The thickness of the material was assumed to be 1.8 mm, and the conductive grid was 25 mm \(\times\) 25 mm. The conductive thread was assumed to have a rectangular cross-section of 0.5 mm \(\times\) 0.25 mm. The effects of the conductivity of the base material and the conductivity of the conductive fibers on the charge decay plots were investigated. The mesh of the model is shown in Figure 8a. Simulations were carried out for base-material conductivities (\(\sigma_{1}\)) from the set of \(\{1\times 10^{-13}\), \(1\times 10^{-12}\), \(1\times 10^{-11}\), \(3\times 10^{-11}\), \(1\times 10^{-10}\)] and for conductive fiber conductivities (\(\sigma_{2}\)) from the set of \(\{17,\)500, 10,000, 100, 10, 1, 0.01, 0.0001, and 0.00001\(\}\), all in S/m. Figure 8b shows an exemplary slice plot in the \(y-z\) plane crossing the model midpoint for \(t=100\) ms, \(\sigma_{1}=3\times 10^{-11}\) S/m, and \(\sigma_{2}=1\) S/m. Figure 8c-e show slices for the same parameters in the \(x-y\) plane for three values of the \(z\) coordinate corresponding to distances (\(d\)) of 0.1 mm, 1 mm, 2 mm from the bottom surface of the specimen. Figure 9 shows the charge decay plots for all assumed conductivities of the base materials.  
Figure 8: Meshing result (**a**) and slice plots (**b–e**) for nonwoven antistiatic fabric with parameters of \(\sigma_{1}=3\times 10^{-11}\) S/m and \(\sigma_{2}=1\) S/m at \(t=100\) ms; the slice in the \(y-z\) plane (**b**); and the slices in the \(x-y\) plane for \(d=0.1\) mm (**c**), \(d=1\) mm (**d**), and \(d=2\) mm (**e**).  
The \(t_{50}\) for all \(\sigma_{2}>1\times 10^{-6}\) S/m is below 0.01 s for all base material conductivity values. For \(\sigma_{2}=1\times 10^{-6}\) S/m, \(t_{50}\) is about 530 ms for \(\sigma_{1}=1\times 10^{-13}\) S/m and \(\sigma_{1}=1\times 10^{-12}\) S/m, 500 ms for \(\sigma_{1}=1\times 10^{-11}\) S/m, 380 ms for \(\sigma_{1}=3\times 10^{-11}\) S/m, and 300 ms for \(\sigma_{1}=1\times 10^{-10}\) S/m. Thus, all the textiles meet the EN 1149-3 standard. To provide further insight into the results, plots were also created for a fixed \(\sigma_{1}\) and four values of \(\sigma_{2}\) (10,000, 100, 0.0001, and 0.000001, all in S/m) (Figure 10).  
Figure 9: Charge decay plots for a textile thickness of 1.8 mm (result of simulations).  
Most plots show a rapid decay of the electric field norm from the maximum (or near-maximum) value to \(E_{R}\). The time of this decay for large \(\sigma_{2}\) values is a fraction of nanoseconds. Therefore, it is necessary to run simulations with a tiny step near zero to illustrate this phenomenon. For \(\sigma_{1}=1\times 10^{-13}\) S/m and \(\sigma_{2}=10,000\) S/m, the analysis time should be 0 to 1 ns with a step of 1 ps. Figure 11 depicts the change in electric field norm over a time window of 0 to 200 microseconds for \(\sigma_{1}=3\times 10^{-11}\) S/m and \(\sigma_{2}=0.01\) S/m, revealing the expected exponential nature of the charge decay. Figure 12 shows slice plots in the \(y-z\) plane for 16 time points. After about 1 microsecond under the parameters of the base material and conductive grid, the first effects of the grid on the electric field can be seen. The shielding effect and a decrease in the electric field norm at the point probe can be observed with increasing time. Figure 13 shows slice plots in the \(x-y\) plane 2 mm away from the bottom surface of the specimen for the same 16 time points.  
Figure 11: Charge decay plots for a textile thickness of 1.8 mm, \(\sigma_{1}=3\times 10^{-11}\) S/m, and \(\sigma_{2}=0.01\) S/m (result of simulation).  
Figure 10: Charge decay plots for a textile thickness of 1.8 mm (result of simulations).  
Figure 13: Slice plots in the \(x-y\) plane 2 mm away from the bottom surface of the specimen for \(\sigma_{1}=3\times 10^{-11}\) S/m, \(\sigma_{2}=0.01\) S/m, and 16 time points.