## 1 Introduction  
Expanded polystyrene (EPS) is a lightweight and closed-cell rigid plastic foam made from polystyrene (PS) beads. Its good thermal insulation properties with sufficient stiffness and strength under compression [1] make it an ideal material for transporting perishable foodstuffs, e.g., fresh fish, that are susceptible to temperature fluctuation [2] in the food industry. The subject of this study was a 3-kg capacity EPS box for transporting fresh fish fillets. A certain structural strength of the box is essential for holding the load of the shipment goods during transportation and decreases the probability of damage that occasionally happens during movement. Therefore, in industrial practice, manufacturers tend to use excessive raw materials to ensure structural strength. In order to minimize environmental impact, it is possible to maintain original strength while consuming less material by introducing lightweight designs using the finite element method (FEM). FEM is a popular modern method in structural analysis and optimization. By developing a numerical model with acceptable accuracy, the predictions made from the model iterate fast and are trustworthy. Applying optimal designs in manufacturing at the first opportunity is advantageous for companies. In the FEM analysis, crucial parameters of commonly-used materials can be pulled out directly from the engineering database. However, the parameters of a material such as EPS are usually not predefined and should be derived from mechanical properties, either from the literature or through experiments. The work conducted in this study is a prelude to the structural optimization of EPS boxes. The mechanical properties of EPS have been studied widely in the field of civil engineering regarding uni-axial and triaxial compressive properties [3; 4; 5; 6; 7] and breaking load/flexural properties [7; 8; 9] via quasi-static experiments. Compared to compressive properties, which directly link to the structural optimal design of EPS, flexural properties are more of an indicator of fusion between polystyrene beads [8]. Aside from quasi-static structural characteristics, dynamic structural behaviors have also been studied. For instance, EPS can be put inside helmets to absorb energy, thus protecting the human head; its dynamic compressive properties, shear strength, and behavior under impact have been investigated [10; 11; 12; 13]. However, studies focused on the structural strength and other mechanical properties of EPS in the field of fresh fish packaging are very few. Certain characteristics of EPS are universal, regardless of varied applications. For instance, the compressive properties of EPS are influenced by material density, strain rate, and temperature [1; 4]. The typical behavior of EPS under compression is shown in Figure 1. At the beginning stage, the material is elastic and satisfies Hooke's law; the slope of this part is referred to as the initial modulus in this paper. A toe region usually appears before elasticity, therefore, the ASTM standard specified a method named toe compensation to correct this [14], and the modified zero-strain point is shown in Figure 1. This method was also applied in the other tests whenever a toe region emerged in this study. Then, due to bending or buckling of the closed cell walls, the initial elasticity recedes and enters a plateau zone, where plasticity takes place, and the tangent modulus is herein described. At the last stage, when most of the energy dissipates through air breakout from the closed cells and the cellular structure collapses, the material becomes more dense, and this stage is called densification. In this study, elasticity and plasticity were investigated, and initial moduli and tangent moduli were obtained, but no characteristics of densification were studied. Multiple researchers have developed correlations relating the initial modulus or the tangent modulus to density and strain rate [15; 16] and through regression analysis [4; 17].