## 4 Discussion  
The total mass of the second ejecta is an important aspect of the study of the ejection, but the lack of clarity of the physical mechanism prevented its further study. [PERSON] et al. [18] examined the second ejection using an explosively driven two-shockwave apparatus. The results showed that there were two mechanisms leading to second ejection: RM instability and the recompression of localized spallation, where the recompression of localized spallation led to a significant increase in the total mass of the second ejecta. [PERSON] et al. [20] developed a theoretical model for the total mass of the second ejecta based on the RM in-stability theory in the case where the material underwent melting, with hydrodynamic simulations validating their results. However, the model was unable to reproduce the phenomenon of a significant increase in total mass. Recently, [PERSON] et al. [59] investigated the ejection production from twice-shocked tin using MD simulations. They found that the second ejecta was also related to the first ejecta. In summary, the present research results attribute the source of the second ejecta to RM instability, the recompression of localized spallation, and the convergence of the first ejecta. However, the physical mechanism of the second ejection is still in the exploratory stage, and the lack of more systematic and detailed studies hinders the theoretical modeling of the total mass of the second ejecta. Revealing the physical mechanism of the second ejection and the generation mechanism of the second ejecta is an urgent requirement for the present research and the basis for theoretical modeling. In this paper, we studied the elastic-plastic ejection from grooved aluminum surfaces under double supported shocks using the SPH method. In agreement with the experimental results [18], a spallation region was formed at the bottom of the bubble in the first ejection due to the rarefaction wave interactions, and we obtained the evolution law of this spallation region and its influence on the bubble evolution. This phenomenon has not been observed in previous MD simulations since the spallation strength of solid Al is up to 8 GPa at high strain rates [60], whereas it is only 2-3 GPa in the explosion drive experiments. Further, we obtained the spatial structure of the second ejecta, including low-density high- and medium-velocity ejecta formed due to the recompression of the spallation material, and high-density low-velocity ejecta formed due to RM instability and the convergence of the first ejecta. The total mass of the second ejecta (15.259 mg/cm\({}^{2}\)) was significantly increased compared to the first ejecta (3.889 mg/cm\({}^{2}\)). The increase in bubble area due to the spallation region led to a significant increase in the mass of the low-velocity ejecta due to RM instability and ultimately led to a significant increase in the total mass of the second ejecta. This finding differed from the results of [PERSON] et al. [18], which attributed the significant increase in the total mass of the second ejecta to the recompression of localized spallation. Therefore, the simulation results in the present study were expected to provide a new idea and theoretical basis for the subsequent modeling of the total mass of the second ejecta. We analyzed the effect of the shock pressure on the second ejection. The shock pressure threshold required for the second ejection was significantly reduced compared with the first ejection. This is consistent with the experimental results [18] that a significant amount of second ejecta was formed despite the significant reduction in second shock pressure [18]. Therefore, the pressure threshold for forming the second ejecta should also be an important aspect of the modeling. This is due to the fact that in engineering applications, the peak pressure will inevitably decrease due to the reflection and transmission of shock waves. In addition, we analyzed the effect of the time interval on the second ejection.