## 1 Introduction  
Composite materials, predominantly composed of resins and fibers, exhibit a significantly lower electrical conductivity compared to metallic counterparts such as aluminum alloys [1]. This inherent characteristic renders composite aircraft more susceptible to the adverse effects of lightning strikes. When subjected to a lightning event, the surface structure of composite aircraft can suffer from severe damage, including ablation, perforation, delamination, and fiber breakage [2, 3]. These types of damage are not only detrimental to the aerodynamic profile of the aircraft but also have the potential to compromise its structural integrity, posing a latent threat to flight performance and safety [4]. In the context of addressing minor lightning-induced ablation damage, a prevalent repair methodology involves the application of patches fabricated from the same composite material as the original [5]. This approach aims to restore the integrity and functionality of the affected area without necessitating the replacement of broader structural components. Although the patch repair method utilizing materials identical to the original structure in the aviation field can partially restore structural damage caused by lightning strikes, the effectiveness of such repairs is constrained by various factors. Current research has elucidated certain limitations within the field, providing a foundation for further investigation. Firstly, even when employing identical materials for repair, the structural integrity and mechanical properties of the repaired area are often difficult to restore to their original levels [6; 7; 8]. More critically, the material utilized for damage repair may introduce interphase discrepancies when bonded with the original material, leading to a decline in electrical and thermal conductivity [9]. This not only potentially compromises the repaired structure's resistance to lightning strikes but also may result in more severe damage upon subsequent lightning encounters [10]. Consequently, current repair techniques exhibit significant deficiencies in restoring the electro-thermal properties of composite materials. This poses further challenges for maintaining the long-term safety and functional integrity of aircraft. It necessitates an in-depth investigation that integrates a greater array of simulation and experimental methodologies. Electro-thermal coupling simulation technology plays a pivotal role in mimicking the response of composite materials to lightning strike damage. This approach affords precise simulation of material damage under various operational conditions by concurrently modeling the flow of lightning currents in composite materials and the attendant thermal effects. The electro-thermal coupled finite element analysis model proposed by [PERSON] et al. [11] has been extensively utilized to simulate the ablation damage of composites due to lightning strikes. This model employs the computed temperature fields to estimate the extent of lightning-induced damage and to characterize the electro-thermal response of the composite material to the electrical current. [PERSON] et al. [12] constructed a finite element model of curved laminates using the electro-thermal coupling analysis capabilities of the Abaqus software to investigate the impact of various factors on their lightning-induced damage performance. Furthermore, [PERSON] et al. [13] introduced alternative thermo-physical property parameters, such as the temperature-dependent dielectric constant, to simulate lightning damage and to further explore the damage mechanisms of laminates. Building upon the foundation of electro-thermal coupling, [PERSON] et al. [14] developed an electro-thermal-pyrolysis model that predicts the degree of resin pyrolysis through numerical analysis based on electro-thermal principles, thereby assessing the damage caused by lightning strikes.