# Recovered Foam Impact Absorption Systems
## 3 Results  
### Characterization of Compressive Behavior in Foam: Analysis and Curve Fitting  
Understanding the compressive behavior of foam materials is crucial for assessing their performance in various applications. This assessment involves analyzing the stress-strain relationships that characterize how the foam responds under load. Figure 4 presents the stress-strain curves of the foam specimens, highlighting three distinct regions: the linear region, the plateau region, and the densification region. Across the five specimens with eight tests, the foam demonstrates good reproducibility, with curves for each specimen closely overlapping. This consistency is crucial for ensuring reliable performance in applications. However, slight deviations are observed in some tests, such as Test 8, particularly within the densification region. These minor variations might be attributed to small differences in foam structure or test conditions. Overall, the foam's compressive behavior remains consistent across different iterations, reinforcing its reliability. When comparing specimens, the stress-strain behavior is notably similar across all five samples, indicating uniform material properties. This consistency is essential for practical applications, ensuring reliable performance. Although the point where densification begins varies slightly between specimens, this variation is likely due to differences in foam density or minor manufacturing inconsistencies. The tested specimens, being significantly larger than the standard size specified in DIN 53577 (200 mm \(\times\) 200 mm \(\times\) 200 mm), might exhibit different stress distributions. Nonetheless, the overall similarity in behavior suggests that the increased size did not introduce significant variability in the results, as seen in Figure 4.  
The graphs offer a thorough understanding of the compressive behavior of the foam specimens. The foam exhibits consistent performance across various specimens and test iterations, with clear linear, plateau, and densification regions evident in the stress-strain curves. This high level of reproducibility underscores the foam's reliable and predictable mechanical properties under compression. Consequently, the foam appears well suited for applications requiring uniform compressive strength and deformation characteristics. Further analysis could involve calculating precise values for the modulus of elasticity in the linear region, the plateau stress, and the strain at which densification commences, providing more quantitative insights into the material's properties. Ultimately, the goal is to develop an equation for the characteristic curve based on these extensive tests to better describe the foam's behavior. The curves illustrate consistent performance across different specimens and test iterations, despite some observed hysteresis in the initial iteration of each specimen, where higher stress-strain values were recorded. This observation indicates that, while the tests are reproducible, the first iteration may slightly deviate, suggesting a need to account for hysteresis when developing the characteristic curve equation. To cluster these signals and calculate the most representative signal of the largest group--assuming the initial signals are discarded--K-means and K-medoids are used, and  
Figure 4: Stress–strain curves of foam specimens demonstrating the linear, plateau, and densification regions. the results are compared without prior knowledge of the number of clusters. The steps in Python are as follows: (i) Data Preparation: the signals are organized in a matrix, with each row representing one signal, (ii) Calculation of Statistics: statistical measures such as mean, variance, etc., can be used, or the entire signals can be directly employed, (iii) Application of Clustering Algorithms: K-means and K-medoids are applied for clustering.