## 3 Results and Discussion
### Validation of the EPS Material Properties for 7-Duy-Long Creep Behavior Tests  
After recreating the same specimen and compression conditions as those in the EPS compressive creep test with the FE model, two-step FEA was performed. Figure 10 shows an example of the displacement and stress distribution at the end point of steps 1 and 2 as a result of the analysis. In Figure 11, which shows an example of the process of changing the displacement step by step of the FEA, step 1 is the FEA result for instantaneous elastic displacement (time-independent); [PERSON]'s modulus (Table 3) and [PERSON]'s ratio (Figure 7), which are the EPS elastic properties, were used in the FEA. On the other hand, step 2 shows the FEA result for plastic displacement (time-dependent); 7-day-long creep test data were used in the FEA. The validation of the FEA material properties of these creep behaviors is related to the CAE prediction technology development for 7-day multi-stage (unitized) loads in the warehouses of packaged appliances of relevance to EPS-based cushioning systems; thus, 7-day-long creep test data were used for validation.  
Figure 12 shows the creep test results and FEA results calculated by the Prony series for one level of applied stress, for the different EPS density scenarios. Table 6 lists the analysis results, and it can be seen that the concordance between the experimental and FEA results is 89.5-95.2% for step 1 and 88.4-97.7% for step 2; the overall concordance is 90.3-100%. These results show that the elastic and viscoelastic properties measured in this study are captured well by FEA. Therefore, by applying the validation results for the creep behavior to the material properties in FEA, the reliability of the FEA prediction for the inclination amount of unitized loads caused by the displacement of EPS-based cushioning systems in multiple stages of the actual packaged product can be improved.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & & & \(\epsilon(t)=a+b[1-exp(-c)t]+dt\) & & & \(\epsilon(t)=c_{\sigma}/\epsilon_{e}+c_{\sigma}/\epsilon_{e}/\epsilon_{e}/ \epsilon_{e}/\epsilon_{e}/1-exp(-t/\tau_{\sigma})+(\sigma_{e}/\tau_{\sigma})+t\) & & & & & \\ \(\rho\) & \(\sigma_{a}\) & & & & \(\epsilon=\) Creep Strain, \(t=\) Elapsed Time (min) & & & \(\epsilon=\) Creep Strain, \(t=\) Elapsed Time (min) & & & & \\ (kg/m\({}^{\ddagger}\)) & (MPa) & & & & & & & & & & & & \\ \cline{3-10}  & 0.0275 & \(1.0722\times 10^{-2}\) & \(2.6926\times 10^{-3}\) & \(3.7601\times 10^{-3}\) & \(7.7037\times 10^{-8}\) & \(2.5648\) & \(10.2132\) & \(266\) & \(2716\) & \(357\) & \(0.9660\) & \(0.0003\) \\ \cline{3-10}  & 0.0396 & \(1.7717\times 10^{-2}\) & \(7.3523\times 10^{-3}\) & \(1.5326\times 10^{-3}\) & \(2.6785\times 10^{-7}\) & \(2.2351\) & \(5.3861\) & \(652\) & \(3514\) & \(148\) & \(0.9741\) & \(0.0009\) \\ \cline{3-10}
16 & 0.0506 & \(3.6583\times 10^{-2}\) & \(3.8350\times 10^{-2}\) & \(2.8778\times 10^{-4}\) & \(1.0335\times 10^{-6}\) & \(1.3832\) & \(1.3194\) & \(3475\) & \(4585\) & \(49\) & \(0.9933\) & \(0.0020\) \\ \cline{3-10}  & 0.0594 & \(5.9483\times 10^{-2}\) & \(1.0872\times 10^{-1}\) & \(3.1283\times 10^{-4}\) & \(2.5180\times 10^{-6}\) & \(0.0001\) & \(0.5464\) & \(3197\) & \(1747\) & \(23\) & \(0.9902\) & \(0.0073\) \\ \cline{3-10}  & 0.0683 & \(8.2382\times 10^{-2}\) & \(1.8915\times 10^{-1}\) & \(3.1658\times 10^{-4}\) & \(4.0009\times 10^{-6}\) & \(0.8291\) & \(0.3611\) & \(3159\) & \(1141\) & \(17\  
Figure 11: Example of a displacement change process by step in the FEA: \(\rho\) = 30 kg/m\({}^{3}\), \(\sigma_{\rm o}\) = 0.1020 MPa.  
Figure 10: Example of the stress and displacement distribution by step in the FEA: \(\rho\) = 18 kg/m\({}^{3}\), \(\sigma_{\rm o}\) = 0.0520 MPa. (**a**) the end point of step 1: (**left**) displacement, (**right**) stress. (**b**) the end point of step 2: (**left**) displacement, (**right**) stress.