## 5 Discussion  
At present, researchers have performed much work characterizing mechanical properties, establishing the constitutive relationship and microstructure model, and optimizing current cellular media designs. This paper reviewed the mechanical properties characterization of cellular media, and provided the latest comments of key mechanical models, including classifying these models based on modeling scale and methodology, tracking the historical progress of these models, and discussing their scope of application, advantages and disadvantages. * The effects of cell size, matrix, relative density, strain rate and testing methods on the mechanical properties of cellular media were systematically investigated through quasi-static mechanical testing and dynamic mechanical testing. The investigation on mechanical properties of cellular media under explosive loading and ultra-high strain rates involves complex stress waves, and systematic analysis methods and influence laws have not yet been obtained. * The constitutive model can quickly and accurately describe the stress-strain relationship of a cellular medium, and obtain mechanical parameters (elastic modulus, plateau stress, densification strain, etc.). However, it cannot explain the microstructure deformation mechanism during stretching or compressing. The constitutive model with cell parameters (cell size and cell shape), high strain rate (greater than \(10^{4}\) s\({}^{-1}\)) and explosive loading needs further study. * The microstructure model can not only obtain the stress-strain curve, but also explain the microstructure deformation mechanism of cellular media, such as cell deformation, weak parts of the material, stress concentration and local deformation. However, most of the models are based on various algorithms and describe the local microstructure (RVE) of cellular media, which is greatly affected by random factors and is not stable. It is a great challenge to establish a stable, low-cost, real and effective microstructure model of cellular media. * Molecular dynamics, phase field method and peridynamics can be used to establish nanoscopic models to investigate the structural evolution and properties of molecules and atoms in cellular media. Due to these methods involve nanoscale, simulation results and experimental characterization results are not comparable, and the scale range is small and the calculation amount is large, so they are not introduced in this paper. The research of cellular media is growing rapidly and has been widely used in fields of packaging boxes, transportation, daily necessities, industrial manufacturing, and aerospace. There will be more applications in the future:  
* The deformation mode and failure mechanism of cellular media under explosive loading and ultrahigh strain rates, gradient cellular material (gradient mode) structural design and performance optimization [18; 57; 154; 155; 156; 157; 158; 159], and functional foam composite materials (e.g., doped metal particles, carbon nanotubes, and graphene) [160; 161; 162; 163] are the keys to future research on cellular media. * Expand the mechanical constitutive models of cellular media to suitable for various complex loads, and propose more constitutive models to understand the multifunctional performance of cellular media. * Novel design of cellular metamaterials with unprecedented properties and advanced manufacturing technology [164; 165; 166; 167]. * Molecular dynamics [168; 169; 170], phase field method [171; 172; 173], peridynamics [174] combined with multi-physics coupling calculations can obtain the nanoscale structural evolution and multifunctional performance of cellular media.