## 5 Conclusions  
This paper first demonstrates how the cohesive element can simulate ice fracture and characterize ice debonding with the matrix material using ice beam three-point bending experiments, SCB, and push-out experiments. The effects of different element sizes on the computational results were compared in the numerical calculations. The cohesive element dramatically affects the computational results when simulating ice beam fracture. In contrast, the cohesive element has a negligible effect on the computational results when characterizing the debonding of the ice from the substrate material and has almost no effect in the push-out experiments. Then, the finite element model of wing electric-impulse de-icing was established, and its reasonableness was verified by comparing the skin deflection curves and de-icing rate after the doubler was loaded through experiments and simulations, as well as the feasibility of using uniform pressure to simulate the impulse force.  
Finally, the effects of various ice-skin interface shear adhesion strengths, doubler loading positions, and impulse sequences on de-icing were studied. It has been discovered that (1) varied ice-skin interface shear adhesion strengths significantly impact the de-icing effect, and the de-icing rate steadily declines from 66% to 56% as shear adhesion strength increases. To achieve the goal of reducing energy consumption and improving de-icing rates, it is recommended that the anti-de-icing system and the actual de-icing process be designed to accurately obtain the real-time ice-skin interfacial shear adhesion strength and reduce the interfacial shear adhesion strength of the ice layer using surface treatment technology or superhydrophobic material preparation. (2) When two, four, and seven  
Figure 20: Rates of de-icing with varying impulse sequences.  
impulses were delivered to doubler two, the de-icing rates were 59%, 71%, and 71%, respectively, showing a significant increase in de-icing efficiency over when the impulses were delivered to doubler one. It is recommended to place more coils on the wing's lower surface or use more lower surface coils for de-icing during the de-icing process. (3) Depending on the impulse sequence \(\alpha\), doublers one and two impulse responses are overlaid differently, resulting in varying de-icing rates when \(\alpha=20\) ms, the superposition effect is the best, and the de-icing rate reaches 100%. If multiple coils must function simultaneously during the de-icing process, the impulse sequence should be shortened suitably to increase the de-icing rate and efficiency.  
This paper uses the cohesive zone model in material fracture and delamination damage, establishing a finite element model of wing electric-impulse de-icing that considers ice-skin interface debonding and ice fracture and the factors that influence the de-icing rate. In the future, more emphasis should be placed on developing electromagnetic-force-thermal multi-field coupling models in simulation research and developing hybrid anti-icing technology in de-icing system design, in which active and passive anti-icing technologies work together.  
Conceptualization, F.M. and D.W.; methodology, F.M.; software, F.M., Z.Z. and X.J.; validation, F.M., Z.Z. and D.W.; formal analysis, F.M.; investigation, F.M.; resources, F.M.; data curation, F.M.; writing--original draft preparation, F.M.; writing--review and editing, D.W.; visualization, F.M., Z.Z. and X.J.; supervision, D.W.; project administration, D.W.; funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of the Xinjiang Uygur Autonomous Region (No. 2021D01C115).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.