## 1 Introduction
In addition to that method, [PERSON] [18] introduced artificial neural networks to predict the initial modulus and the compressive strength values at 1%, 5% and 10% strain, and both methods yield satisfactory results with a coefficient of correlation values greater than 0.901. In terms of the compressive strength correlating to density and strain rate, [PERSON] [19] developed four coefficients for EPS foam with densities of 11, 15, 20 and 25 kg/m\({}^{3}\) under low and high strain rates. Unlike the compressive properties of EPS that have been studied extensively,  
Figure 1: Typical stress–strain behavior of EPS under compression. investigations into flexural properties are relatively scarce. It has been discovered that, with the increase in density, the flexural strength of EPS increases, the rupture happens at smaller deformation, and the stiffness of EPS also rises [7]; [PERSON] [19] validated this in recent studies. In another study, the initial modulus was found to be almost 350 times greater in compression than in flexure testing, meaning this material is more suitable for the case of compression [9], although this conclusion conformed poorly with other studies [1; 8; 20]. Aside from flexural properties, research into tensile properties is seldom conducted and the standard test method for tensile properties of EPS is not specified in ASTM D 6817: Standard Specification for Rigid Cellular Polystyrene Geofoam [21]. [PERSON] and [PERSON] [8] designed bone-shaped tensile specimens of EPS based on ASTM D 638 and found that the ultimate tensile strength of EPS rises with density. Akin to the results in the flexure test, the stiffness rises along with the increase in the density of EPS. However, ASTM D 638 was originally developed for rigid plastics with higher density and without cellular structures; for this reason, variances might be caused in the final results. ASTM has provided another standard--ASTM D1623: Standard Test Method for Tensile and Tensile Adhesion Properties of Rigid Cellular Plastics [22]--which is supposed to be more appropriate for the material. [PERSON] [23] performed lengthy experiments to characterize the tensile behavior of EPS foams of densities ranging from 60-120 kg/m\({}^{3}\) and verified that the tensile strength also rises with the increase of strain rates and density. Apart from fundamental mechanical properties investigation, [PERSON] [24] carried out a heat treatment process on EPS foams and enhanced the hardness. Nevertheless, the mechanical properties test for the treated and non-treated EPS foam followed different standards, which could impair the comparability of experimental results. Several papers related to the topic of this investigation, specifically the 3 kg capacity EPS boxes, may offer valuable insights. In an article from [PERSON] et al. [25], the staggered pattern of stacking up the 3 kg capacity EPS boxes was illustrated and further inspired the test for the stacking strength of the boxes. [PERSON] [26] tested the stacking strength of EPS boxes with a shipment capacity of between 3 and 25 kg and obtained the maximum stacking load from 11 types of boxes provided by Tempra (**Tempra**: EPS manufacturer in Hafnarfjordur, Iceland). It was found that the smallest boxes (capacity 3 kg) had relatively higher safety factors compared to larger boxes. This finding indicates that there is room for improvement on smaller boxes, which motivated this study. [PERSON] [27] tested the strength of EPS boxes with a capacity of 23 kg under three different load conditions and then used FEM to simulate lightweight design ideas, including changing the radius of rounding on edges, and thin either the bottom or the lid. However, there is uncertainty remaining in the lightweight design of [PERSON]'s study on account of the material parameters derived from the equations in the literature. In particular, [PERSON]'s modulus has considerable variance compared to obtaining it from the experiment.