## 4 Conclusions  
In this paper, a theoretical analysis and numerical simulation methods were used to study the hypervelocity impact of a projectile on a wave-impedance gradient material, establish an analysis model of shock-wave propagation, and quantitatively study the impact law of the wave-impedance gradient change and continuous change in impact pressure, internal-energy conversion, and projectile-breaking characteristics. The main conclusions are as follows:  
1. By analyzing the propagation characteristics of shock waves in wave-impedance gradient materials, the total-transmission-coefficient model of the incident shock waves passing through the wave-impedance-gradient-attenuation region was established. According to the model, when the surface material of the wave-impedance gradient material is titanium alloy and the back material is nylon, the total transmission coefficient increases from 0.206 to the maximum value of 0.339 with the continuous change in the gradient. It was directly proven that the continuous change in the wave impedance is better than the step change at reducing the attenuation of the amplitude of the shock wave in the projectile, keeping the stress amplitude of the shock wave at a higher level, improving the impact-breaking, melting, and gasification degree of the projectile, and, thus, enhancing the protective performance of the wave-impedance gradient material.
2. Titanium alloy, aluminum alloy, magnesium alloy, and nylon were selected to establish the numerical-simulation model. The numerical-simulation analysis showed that the decreasing amplitude of the shock wave with time was Ti-Ny > Ti-Al-Ny > Ti-Al-Mg-Ny, the transformed internal energy was Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny, and the projectile-breaking area was Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny.
3. Through the numerical simulation, it was proven that the continuous change in the wave-impedance gradient can effectively reduce the attenuation of the shock-wave amplitude, reduce the kinetic energy of the debris cloud, and increase the fragmentation degree of the projectile, so as to improve the conversion and spatial-diffusion ability of the projectile's kinetic energy and effectively improve the protective ability of the material.  
Through this study, the design principles of wave-impedance gradient materials were clarified. In the future, more hypervelocity-impact experiments are needed to further verify the hypervelocity-impact characteristics and protective performances of these materials. In addition, the shield design of different surface-density wave-impedance gradient materials could be carried out to meet the protection requirements of different types of spacecraft.  
Conceptualization, Z.Y. and Z.G.; methodology, W.L.; formal analysis, Z.Y.; investigation, Q.W.; resources, Z.Y.; writing--original draft preparation, Z.Y.; writing--review and editing, L.Y.; project administration, Y.M. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the State Key Basic Research Program of China (Grant No. 61 xxx02), and National Space Technology Pre research Project (No. D02 xx08).  
Not applicable.  
The authors declare no conflict of interest.