## 2 Electro-Thermal Modeling and Analysis of Composite Materials Under Lightning Strike
### Analysis of Lightning Strike Simulation Results  
When subjected to a lightning current with an 8/20 \(\upmu\)s and a peak value of 20 kA, the temperature variation predominantly affects the initial four plies of the laminates. Among these, the ablation damage is predominantly concentrated in the top three plies, corresponding to areas where temperatures exceed 250 \({}^{\circ}\)C, as illustrated in Figure 5a-c, with no significant ablation damage observed in the fourth ply and those below.  
The in-plane damage to the laminate exhibits distinct directional characteristics. The most severe damage is observed in the first ply at the lightning entry point, manifesting as an approximately elliptical shape aligned with the 45\({}^{\circ}\) fiber direction, as shown in Figure 5a. The superior electrical and thermal conductivity along the fiber axis accounts for the preferential propagation of current and heat, resulting in a more extensive temperature rise and consequently more pronounced thermal damage within these regions. The second ply's damage pattern, which does not align with its 0\({}^{\circ}\) fiber orientation, is due to heat conducted from the upper ply, as shown in Figure 5b. This heat transfer results in damage propagation towards the angle between the two plies. The third ply exhibits damage consistent with the pattern observed in the second ply. To comprehensively analyze the damage phenomena induced by lightning, this study conducted a series of simulated lightning strike simulations with different peak values. The results of the damage are compiled and presented in Figure 6.  
The greater the peak current, the higher the intensity of the transient current through the laminate, resulting in a greater amount of energy transferred by the lightning strike, and consequently, an increased area of ablation damage.  
The most severe areas of ablation damage consistently localize near the primary strike point of the first ply, extending predominantly along the 45\({}^{\circ}\) fiber orientation. Increased  
Figure 5: Peak 20 kA lightning strike current analysis of ablation damage. (**a**) first layer; (**b**) second layer; (**c**) third layer; (**d**) fourth layer.  
peak currents correspond to enlarged damage areas. The damage pattern in the second ply mirrors that of the first ply, following the same principles of current conduction. At peak currents of 5 kA, 10 kA, and 20 kA, the damage and ablation areas of the laminate measure 4.91 cm\({}^{2}\), 10.24 cm\({}^{2}\), and 15.35 cm\({}^{2}\), respectively.  
Furthermore, an increase in peak current is associated with deeper damage, suggesting a direct correlation between electrical current intensity and ablation depth. A comparative analysis with the 20 kA peak current scenario reveals a noticeable reduction in ablation depth at lower peak currents (5-10 kA), primarily confined to regions of the first two piles exhibiting temperatures exceeding 250 \({}^{\circ}\)C. No ablation damage regions manifest in the third ply. This observation can be attributed to the dissipation of most of the lightning current's thermal effects, including resin pyrolysis and carbon fiber sublimation, by the preceding layers.  
In all, the damage patterns at varying peak currents remain nearly consistent, with changes in current intensity primarily affecting the extent and depth of damage, rather than altering the propagation pathway of the current.  
Figure 6: Ablation damage of the original laminates under different peak currents. (**a**) first layer at 5 kA; (**b**) first layer at 10 kA; (**c**) first layer at 20 kA; (**d**) second layer at 5 kA; (**e**) second layer at 10 kA; (**f**) second layer at 20 kA; (**g**) second layer at 5 kA; (**h**) second layer at 10 kA; (**i**) second layer at 20 kA.