## 2 Characterization of Cellular Medium Mechanical Properties
### Dynamic Mechanical Properties  
As a cushioning material, cellular media are subjected to dynamic loads in many practical applications, and the loading process is usually accompanied by a high loading strain rate. The protective foam in the side door panels of automobiles has a strain rate of up to 1500 s\({}^{-1}\) when the velocity of side collision is 90 km/h. The strain rate of the foam energy-absorbing box of the automobile reaches 200 s\({}^{-1}\) at 40 km/h [47]. When the cellular medium is subjected to larger strain and higher strain rate under dynamic loading, the static test result and model cannot exactly evaluate the mechanical properties of the cellular medium. Therefore, for high strain rate loading scenarios, it is important to investigate their mechanical behavior under dynamic loads [34; 55; 56; 57]. There are different opinions on whether cellular media have strain rate effects. Some researchers found that the strain rate had little effect on cellular medium under dynamic compression [41; 42; 43; 58]. In addition, some studies have shown that cellular media have a strong strain rate effect [44; 45; 31; 46; 47; 48]. The deformation modes of cellular media under dynamic load are significantly different from that under quasi-static load. Cellular media have obvious deformation localization and stress enhancement under dynamic load [59; 60; 61; 62]. [PERSON] [45] used the pressure head test to find that the effect of energy absorption on closed-cell foams with a relative density of 8% at a velocity below 10 m/s basically did not change, but at a velocity above 10 m/s, its energy absorption effect increased significantly. [PERSON] [46] proposed that the strain rate effect of cellular media was closely related to the matrix material and cell structure. Different microstructures of cellular media experience different deformation modes and stress and strain distributions during the compression. [PERSON] [47] investigated the stress-strain behavior of PP foams in the strain rate range of 0.01-1500 s\({}^{-1}\) and found that low-porosity foams had strain rate hardening due to thicker cell walls, resulting in high yield stress. However, the high-porosity foams were not sensitive to strain rate hardening. [PERSON] [31] found that the yield strength of PVC foam material increased with the increase of strain-rate, as shown in Figure 2e. [PERSON] [48] found that when the strain-rate exceeded 113 s\({}^{-1}\), the compressive strength of EPS foam increased rapidly with the increase of strain-rate, and the densification strain decreased slightly with the increase of strain-rate. In the strain-rate range of 1-280 s\({}^{-1}\), [PERSON]'s modulus had no obvious strain rate dependence. There are also different opinions on whether cellular media can truly attenuate stress waves. Researchers used shock wave generators, explosives, and light gas guns to load metal foams to study the attenuation effect of shock waves [63]. They found that foams had better attenuation characteristics for shock waves, and the shock wave pressure decayed exponentially. [PERSON] [64] used finite element simulations to find that cellular media mainly absorbed impact loads through internal cell deformation and collapse to attenuate stress waves. [PERSON] [65; 66] found that the periodically arranged cell structure [67] can adjust the elastoplasticity of a cellular medium. Cellular media materials with simple cubic structures were prone to stress concentration, which induced emission flow and attenuated impact load energy. Cellular media materials with face-centered cubic structures were not prone to stress concentration (due to layer-to-layer symmetry) and did not induce emission flow. [PERSON] [68] used aluminum foam as a bullet to impact a dense material, and investigated the propagation of shock waves in aluminum foam. They found that the energy carried by the shock wave was severely dissipated in the deformation of the cell structure, and the shock wave stress was related to the density of the aluminum foam.