## 3 Results
### Elastic-Plastic Ejection Under Double Supported Shocks  
Figure 4 illustrates the 2D computational model of the elastic-plastic ejection under double supported shocks. The length and width of the aluminum sample were 500 \(\upmu\)m and 300 \(\upmu\)m, respectively, and the depth and width of the surface grooves were 20 \(\upmu\)m and 150 \(\upmu\)m, respectively. This study generated two supported shock waves by successively impacting an aluminum sample with two flyers. A free boundary condition was applied in the impact direction in the simulations, while a periodic boundary condition was imposed in the direction perpendicular to the impact. The initial particle distance is 0.5 \(\upmu\)m, and 1,788,000 particles are used in the simulation. Figure 5 illustrates the dynamic evolution of the density during the first elastic-plastic ejection, with a surface jump velocity (surface velocity variation after the shock wave reaches the free surface) of 4.0 km/s corresponding to a shock pressure of 43.0 GPa. The disturbed surface, after the reflection of the first incident supported shock wave from the grooved surface, underwent phase inversion, forming a characteristic spike-bubble structure. The ejecta was predominantly attributed to the elastic-plastic deformation in the material near the free surface because the shock pressure was below the unloading melting pressure of aluminum (64.0 GPa). The spike was eventually detached, separating from the substrate and continuing its forward motion. The spike velocity decreased continuously after reaching a peak value of 5.285 km/s, with a maximum velocity of only 4.294 km/s at 300 ns. The total mass of the ejecta at the 300 ns was 3.889 mg/cm\({}^{2}\). A spallation region was observed at the bottom of the bubble owing to the rarefaction waves reflected from the grooved surface meeting and interacting at the crest of the initial groove. Figure 4: Schematic of the 2D computational model of the elastic–plastic ejection under double supported shocks. Figure 3: Comparison of (**a**) simulation results with (**b**) experimental results at 6 \(\upmu\)s and 19 \(\upmu\)s [58]. We analyzed the evolution of the bubble region because the second ejection was closely associated with the bubble region formed during the first ejection, as shown in Figure 6. Rarefaction waves were generated after the first supported shock wave reached the surfaces on both sides of the groove and meted at the crest of the grooved surface, resulting in tensile stress. Spallation occurred as the tensile stress increased and reached the spall strength. Initially, the spallation region extended into the interior of the sample in a fan-shaped configuration and eventually reached saturation. At the same time, the substrate material on both sides of the spallation region moved under the influence of jet convergence, leading to the widening of the opening of the spallation region. The material within the spallation region underwent continuous compression at a later stage, eventually reaching a steady state. The detachment of material from the substrate after forming the spallation region caused a reduction in the velocity of the bubble, making it progressively more difficult to track the bubble over time. The formation of the spallation region at the base of the bubble led to a significant increase in defect areas within the bubble region. The morphology of the bubble gradually stabilized over time, reaching a steady configuration. Figure 7 depicts the dynamic evolution of the density during the second ejection, where the shock pressure remained consistent with that of the first ejection at 43.0 GPa. At 200 ns, the second incident supported shock wave reached the spallation region at the bottom of the bubble, followed by the recompression of the material in the spallation region. Phase inversion of the disturbed surface occurred again after reflecting the second  
Figure 5: Dynamic evolution of the density during the first elastic–plastic ejection: (**a**) 60 ns, (**b**) 70 ns, (**c**) 100 ns, and (**d**) 300 ns.