## 1 Introduction  
Carbon-fiber-reinforced plastics (CFRPs) have excellent mechanical properties and are widely used in various industries [1; 2; 3]. With the massive expansion of wind power and the rapid growth in the number of aircraft, the chances of wind turbine blades and aircraft being struck by lightning have inevitably increased substantially. Because the destructive effects of lightning strikes often lead to serious consequences, research on lightning damage in CFRPs has received unprecedented attention [4; 5; 6; 7; 8]. In structural design, depending on the excellent formability of composite materials, the number of fasteners can be reduced by optimizing the design; however, completely eliminating the need for fasteners is difficult. These fasteners have greater electrical conductivity than the other materials in CFRP laminates. Therefore, when a lightning strike occurs, the current is discharged through the fasteners first and then into each layer of the CFRP laminate, which leads to fiber breakage, resin degradation, and internal delamination [9]. In addition, the temperature and air pressure inside the fastener hole will change dramatically during the lightning strike [10], which leads to damage around the hole, loss of fastener support, and weakening of the mechanical and electrical properties of the CFRP [11]. Therefore, research on the damage in CFRPs with fasteners subjected to lightning strikes is the key point of composite lightning protection [10; 12]. The duration of a lightning strike is extremely short, during which a large amount of energy is released in an instant, resulting in extremely high temperatures. Observing the damage characteristics near the attachment point of the lightning strike in real time with instruments is difficult. Therefore, finite element analysis (FEA) has become an effective method for studying the damage evolution process of CFRP laminates with fasteners under lightning strikes and for verifying the correctness of the test results. [PERSON] et al. [13] used the finite volume method in the time domain and unstructured mesh to establish the mechanism model of CFRPs with fasteners, and simulated the spark phenomenon in fasteners. The research showed that sparking may occur when the current density is greater than 10 kA/mm\({}^{2}\). [PERSON] [10] simulated the gas conditions and related local geometric changes in the interior space around the fastener during lightning strikes, and discussed the importance of chemical change modeling in future work. Meanwhile, the electrothermal coupling model is used to investigate the damage of CFRP under lightning strike. [PERSON] et al. [14] developed a finite element model to consider the damage sources observed in a lightning strike, such as thermal damage caused by Joule heat. [PERSON] et al. [11] established a three-dimensional electrothermal coupling model of ablation damage of CFRP with fasteners based on the relationship of the energy balance in s lightning strike. The results indicated that fasteners distributed the lightning current to each layer, and a larger conduction current dispersion area led to less damage to the laminate. [PERSON] et al. [15] proposed a physical model to predict lightning strike damage for composite materials. The finite element method of non-linear material model was used to analyze composite materials with copper mesh protection. [PERSON] et al. [16] proposed a electrothermal coupling model of angle ply composite laminates, which considered the anisotropic thermoelectric behavior of layer and unidirectional composite laminates. However, their work neglected the arc heat effect in numerical simulation. [PERSON] et al. [17] considered the influence of the arc heat effect and replaced it with heat flux in the models, while the damage to CFRP with fasteners was not mentioned.