# Mesostructural Model for the Fatigue Analysis of Open-Cell Metal Foams
## 1 Introduction  
Metallic foams are contemporary materials that have been introduced into various engineering fields in a short time due to their favorable physical and mechanical properties, making them desirable for different engineering applications [1; 2; 3]. The properties of these materials depend directly on the base metal that comprises them, and on physical properties such as density and the configuration of foam cells. Regardless of the base metal from which the foam is made, its stiffness-to-weight ratio is suitable, and it exhibits a high energy absorption capacity, high impact resistance, and significant deformation under compressive loads [4]. Metallic foams initially found applications in aerospace [5] and automotive industries [6] due to their mechanical properties. Today, their use has diversified into areas such as biomedicine [7] and civil engineering [8], where they offer significant advantages when compared with other materials and are versatile in terms of their applications. Mechanical characterization of metallic foams allows evaluating the response to monotonic or cyclic loading conditions. Previous research has mainly focused on the response to monotonic or unreversed cyclic loading conditions [9; 10; 11; 12; 13]. Nevertheless, the response to reversible cyclic loads, such as tensile-compression loading situations, has not been well understood until recently. [PERSON] et al. [14] studied the mechanical behavior of closed-cell foams under fatigue loading, proposing a failure criterion for closed-cell foams subjected to reversible loads. [PERSON] et al. [15; 16; 17; 18] studied the mechanical behavior and damage accumulation of open- and closed-cell foams under fatigue loading, proposing different models, such as failure criteria, damage accumulation, and fatigue analysis models. The mechanical characterization of metallic foams under cyclic loading conditions isnecessary to consider their use in mechanical and civil engineering applications, such as in bridges and seismic protection elements. In addition to fatigue characterization, the dynamic behavior of metallic foam sandwich structures (MFSBs) has also been investigated for their potential applications in protective equipment. Recent studies employing nonlinear finite element models have examined how these structures respond to repeated impacts, revealing that factors such as impact location and face thickness significantly influence the overall deformation, loading, and unloading stiffness of the MFSBs [19]. Furthermore, the dynamic behavior of aluminum foam sandwich beams (AFSBs) under repeated impact loadings, particularly in marine structures, has been explored, showing how cumulative damage significantly alters their deformation patterns and energy absorption capabilities [20]. These findings highlight the importance of understanding both static and dynamic responses of metallic foams for comprehensive structural design and safety applications. In [21], aluminum foams are highlighted for their unique combination of structural properties and cost-effective manufacturing processes. The study introduces a beam finite element (FE) model based on the Kelvin cell to efficiently simulate open-cell aluminum foams. The model's elastic properties are calibrated using the NSGA-II genetic algorithm, enabling it to accurately replicate the orthotropic behavior of the foams while minimizing computational demands. This method provides a precise and time-efficient alternative to traditional, more complex 3D models. Moreover, the mechanical properties and energy absorption capabilities of open-cell aluminum foams have been investigated in the context of hypervelocity impacts (HVIs), which are particularly relevant in space applications. Numerical simulations based on Voronoi tessellation models have shown that these foams exhibit high accuracy in predicting shock-wave behavior, stress-strain responses, and energy dissipation under extreme impact conditions [22].