## 1 Introduction  
Aluminum foam is a porous material produced by the foaming process of aluminum or aluminum alloys [1, 2, 3]. Its unique microstructure endows it with extensive application potential in numerous fields [4, 5, 6]. Composed of a continuous metal matrix and dispersed air phase, aluminum foam features closed-cell or open-cell structures, and combines excellent properties such as low density, sound absorption, energy absorption, vibration damping, thermal insulation, and electromagnetic shielding [7, 8, 9]. These characteristics have led to its widespread use in industries like automotive manufacturing [10, 11], aerospace [12, 13, 14, 15, 16, 17], defense, electronics [11], architectural acoustics [18], and petrochemicals. Compared with traditional metal materials, although aluminum foam has a lower yield strength, its longer plateau stage and stronger energy absorption capacity provide unique advantages for its application in protective structures.  
In recent years, many scholars have conducted in-depth research on the mechanical properties of aluminum foam [19, 20, 21, 22, 23]. [PERSON] et al. [24] analyzed in detail the load-displacement response characteristics of aluminum foam under compressive loads through uniaxial and biaxial compression tests. [PERSON] et al. [25] quasi-static compression tests showed that aluminum foam has a wide yield plateau during compression, and can absorb a large amount of energy at an approximately constant stress on this plateau. [PERSON] et al. [26] further revealed the strain rate sensitivity of closed-cell aluminum foam, finding that its energy absorption capacity increases with the increase of strain rate. [PERSON] et al. [27] observed significant changes in the internal pore structure of cylindrical foam samples during deformation using micro-computed tomography and CT image analysis.  
Samples with smaller spatial variations in porosity can withstand greater strain until failure under compressive loads. [PERSON] et al. [28] research indicated that the crushing stress and plateau stress of foam metals both increase with the increase of initial density, and the relationship between them is basically a power function. [PERSON] et al. [29] explored the temperature effects on the compressive mechanical behavior of closed-cell aluminum foam, providing theoretical basis for its application in high-temperature environments. [PERSON] et al. [30] investigated the strain rate sensitivity of aluminum foams by numerical simulation and found that their mechanical properties changed significantly with increasing strain rate.  
Despite the wide application of aluminum foam in many fields, its application in the packaging engineering field, especially in the packaging protection of valuable goods under special conditions (such as energy absorption protection under free fall and collision conditions), is still relatively limited. In addition, the mechanical properties and energy absorption efficiency of aluminum foam-polyurethane composite materials under quasi-static compression are affected by relative density and pore size, which provides new ideas for the application of aluminum foam in packaging protection. Given this, the present study aims to systematically investigate the lightweight and high-toughness properties of closed-cell aluminum foam under static and dynamic loads. By conducting quasi-static and dynamic compression experiments at room temperature, and combining the establishment of constitutive models and damage research, the strain rate dependence of its mechanical properties will be revealed. Moreover, this study will also observe the deformation and fracture behavior under high-speed loading, in order to provide scientific guidance for the structural design of packaging protection engineering, and promote the application development of aluminum foam in the field of packaging protection.