## 2 Materials and Methods
### Split-Hopkinson Pressure Bar (SHPB) System  
This study employs an improved Split Hopkinson Pressure Bar (SHPB) device to conduct dynamic impact loading experiments on closed-cell aluminum foam samples (\(\Phi\)40 mm \(\times\) 20 mm). The SHPB device is an experimental setup widely used for investigating the dynamic mechanical properties of porous materials under high strain rates and can effectively simulate the mechanical response of materials under extreme conditions such as impact or explosion. As shown in Figure 4, the experimental setup mainly consists of the following components: the striker bar, the incident bar, the transmitted bar, and the absorber bar. During the experiment, the striker bar is accelerated by a pneumatic device to impact the incident bar, generating a stress pulse that is transmitted to the specimen. The incident and transmitted bars record the incident wave, reflected wave, and transmitted wave signals, respectively. By analyzing these signals, the stress-strain relationship, energy absorption characteristics, and deformation mechanisms of the specimen under dynamic loading can be calculated. To ensure the accuracy and reliability of the experimental data, the device was strictly calibrated before the experiment, and multiple repeated experiments were conducted on each specimen to verify the consistency of the results. All bars have a diameter of 60 mm, with the striker bar being an aluminum rod of 1000 mm in length, while the incident and transmitted bars are aluminum rods of 3000 mm in length. These aluminum rods have a material density of 2.7 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) and a Young's modulus of 71 GPa, possessing excellent elasticity and wave-guiding characteristics, which ensure the efficient propagation of stress waves within the bars and precise measurement.  
Figure 4: Schematic of the pulse-shaped SHPB setup.  
Figure 3: Quasi-Static Compression Experiment System.  
By utilizing lead sheets as a pulse shaper, we can effectively extend the duration of the incident pulse and ensure that the stress waves undergo multiple reflections within the closed-cell aluminum foam samples, thereby achieving a state of stress equilibrium. The strain gauges mounted on the incident and transmitted bars are used to capture the signals of the incident wave, reflected wave, and transmitted wave, respectively. A typical signal diagram is shown in Figure 5. By accurately measuring these strain signals and combining them with the theory of one-dimensional stress waves, we can calculate the stress, strain, and strain rate of the samples under dynamic conditions using the wave velocity, the material's elastic modulus, and relevant geometric parameters. The specific derivation formulas are shown below:  
\[\dot{\epsilon}=-\frac{2c_{0}}{l_{s}}\epsilon_{r} \tag{1}\]  
\[\epsilon=\int_{0}^{t}\dot{\epsilon}dt=\int_{0}^{t}\frac{2c_{0}}{l_{s}}\epsilon _{r}dt \tag{2}\]  
\[\sigma=\frac{A_{0}}{A_{s}}\epsilon\epsilon_{t} \tag{3}\]  
where \(l_{s}\) and \(A_{s}\) denote the uncompressed length of the closed-cell aluminum foam and its cross-sectional area, respectively; \(E,c_{0}\) and \(A_{0}\) denote the Young's modulus of the aluminum bar, the wave speed of the bar and the cross-sectional area of the bar, respectively.