Cellular solids, encompassing both naturally occurring and synthetically engineered foams, exhibit remarkable mechanical properties such as high strength-to-weight ratios, energy absorption capabilities, and tunable stiffness. These characteristics make them indispensable in a wide range of engineering and biomedical applications, including lightweight structural components, impact protection systems, and bone tissue scaffolds. To fully leverage the potential of cellular solids, accurate modeling of their mechanical behavior is essential for both predictive analysis and performance optimization. This study presents a comprehensive comparison of four primary modeling approaches commonly employed to simulate cellular solids: the Unit Cell Method, Tessellation-Based Foam Model, Phenomenological Foam Model, and CT Scan-Based Approach. Each method offers distinct advantages and trade-offs in terms of accuracy, computational efficiency, and applicability. The Unit Cell Method represents the cellular structure using idealized, repeating geometric units such as cubes, tetrakaidecahedra, or other polyhedral shapes. While this approach significantly reduces computational cost and is effective for periodic, regular structures, it falls short in capturing the variability and irregularities found in real-world foams. To address these limitations, the Tessellation-Based Foam Model introduces more realistic representations by using random or quasi-random geometries generated through techniques like Voronoi tessellation. This approach offers improved fidelity in simulating the mechanical response of disordered foams, making it particularly suitable for mimicking natural cellular structures. The Phenomenological Foam Model abstracts the microstructure entirely, instead relying on empirically derived constitutive laws to describe the macroscopic behavior of foams. Although this method is well-suited for large-scale simulations and is computationally efficient, it lacks the capacity to capture microstructural effects and localized phenomena. Finally, the CT Scan-Based Approach leverages high-resolution imaging techniques to reconstruct the actual internal architecture of cellular solids. This method enables the creation of highly detailed finite element models that can faithfully reproduce the material’s response under various loading conditions. While offering the highest accuracy, this approach is computationally intensive and dependent on the quality of scan data. By evaluating the strengths and limitations of each modeling strategy, this study aims to guide the selection of appropriate methods for different application scenarios, balancing realism, efficiency, and scalability in the modeling of cellular solids.

Acknowledgement
This study was made thanks to grant funds from the NAWA- STER program, within the framework of the NIH4DS-new international horizons for doctoral school.