## 2 Characterization of Cellular Medium Mechanical Properties
### Quasi-Static Mechanical Properties
\begin{table}
\begin{tabular}{p{108.4 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt}} \hline \hline
**Cellular Medium** & \begin{tabular}{c} **Relative** \\ **Density** \\ \end{tabular} & **Cell Size** & **Strain Rate** & **Modulus** & **Strength** & **Topiness** & **Performance** & **Ref.** \\ \hline \begin{tabular}{c} Brittle carbon \\ foam \\ \end{tabular} & 0.029-0.04 & 0.49-49 mm & - & 45-62 MPa & - & 0.04-0.05 MPa\(\sqrt{\text{m}}\) & [35] \\ \hline \begin{tabular}{c} Polycarbonate \\ (PC) foam \\ \end{tabular} & 0.56 & 2.8-37.1 mm & - & 836-978 MPa & 25.6-29.8 MPa & 7.02-10.22 J/cm\({}^{3}\) & Mechanical properties are not significantly affected by cell size. & [36] \\ \hline \begin{tabular}{c} Polyberthimide \\ (PE) foam \\ \end{tabular} & 0.75-0.9 & \begin{tabular}{c} 2-4 μm \\ 30-120 nm \\ \end{tabular} & - & 1929-2628 MPa & 641.8-67.7 MPa & 17.6-103.1 J/cm\({}^{3}\) & [37] \\ \hline \
\begin{tabular}{c} Polyurethane (PU) \\ foam \\ \end{tabular} & 0.98 & 0-800 μm & - & - & 0.06-0.11 MPa & - &
\begin{tabular}{c} Compressive strength \\ increased as the cell size \\ (20-800 nm) increased, or as the cell size \\ decreased. \\ \end{tabular} & [38] \\ \hline
3D hierarchical foam & - & 0-55 nm & - & 0.5-1 GPa & 0.8-13 MPa & - & \begin{tabular}{c} Mechanical properties \\ increased as the cell size \\ decreased. \\ \end{tabular} & [39] \\ \hline \begin{tabular}{c} Polymethyl \\ methacrylate \\ (PMMA) foam \\ \end{tabular} & 0.5 & 0.2-11 um & - & 577–791 MPa & - & 0.13-0.44 J/cm\({}^{3}\) & [40] \\ \hline \begin{tabular}{c} Aluminium (Al) \\ foam \\ \end{tabular} & 0.02-0.2 & 3-25 mm & \(10^{-4}\)–\(10^{3}\) s\({}^{-1}\) & 1–700 MPa & 1.5 MPa & - & \begin{tabular}{c} Mechanical properties \\ depend on relative density. \\ Mechanical properties hardly \\ changed by strain rate. \\ \end{tabular} & [41, 42] \\ \hline \begin{tabular}{c} Expanded \\ polybrynene \\ (ETP) foam \\ \end{tabular} & 0.04–0.11 & 130-320 μm & - & 6.5-32.3 MPa & 0.19-0.7 MPa & - & \begin{tabular}{c} Mechanical properties \\ depend on relative density \\ and are strain rate sensitive. \\ Higher relative densities are more sensitive to strain rate. \\ \end{tabular} & [43] \\ \hline \begin{tabular}{c} Polyurethane \\ (PVC) foam \\ \end{tabular} & 0.04–0.18 & 300-450 μm & \begin{tabular}{c} 0.0-4.0 mm \\ \end{tabular} & \begin{tabular}{c} 10^{-2}-1500 s\({}^{-1}\) \\ \(10^{-4}\)-2000 s\({}^{-1}\) \\ \(10^{-4}\)-2000 s\({}^{-1}\) \\ \end{tabular} & 74–400 MPa & 1.08–8.65 MPa & - & \begin{tabular}{c} Mechanical properties \\ depend on relative density \\ and are strain rate sensitive. \\ Higher relative densities are more sensitive to strain rate. \\ Strain rate hardening \\ phenomenon. \\ \end{tabular} & [47] \\ \hline \
\begin{tabular}{c} EPS foam \\ \end{tabular} & 0.021–0.044 & - & 2.68–280 s\({}^{-1}\) & 2.7–4.8 MPa & 0.171–0.478 MPa & - &
\begin{tabular}{c} Higher relative densities are more sensitive to strain rate. \\ Strain rate hardening \\ phenomenon. \\ \end{tabular} & [31] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of matrix material, relative density, cell size and strain rate. Some researchers found that under the same porosity, the mechanical properties did not change with the cell size [35; 36; 37; 49; 50]. Some researchers hold different views. [PERSON] [38] found that when the cell size was large, the compressive strength of PU foam decreased as the cell diameter decreased. However, when the cell diameter decreased to a certain extent, the compressive strength increased as the cell diameter decreased. The increase in compressive strength came from the increase in the polymer fraction in the cell walls [51; 52; 53]. [PERSON] [39] investigated the mechanical behavior of 3D layered nanofoam, and believed that the solid surface had fewer atoms than the inside (so it had excess surface energy). They found as the cell cross-sectional diameter decreased, the influence of surface effects on modulus and strength increased.