## 3 Results
### Stress-Relaxation Behavior  
Figure 6 shows the experimental stress-relaxation nanoindentation data gathered during the holding phase of the test for the tested materials. The average response of the tested samples is reported as a red line, and it was obtained using the global parameters (i.e., the mean values of the material and time parameters listed in Table 1) as input values for Equation (6b). Interestingly, for all the tested samples, two relaxation phases could be observed, i.e., an early non-linear decrease in the load, followed by linear decay until equilibrium was reached. This could be ascribed to the stress decrease related to the deformation and motion of the material polymer chains [59]. The comparison of the average relaxation responses of the tested samples is shown in Figure 7. The behaviors of the pig lung and GelMA samples were characterized by similar decreases in the load, while for the human lung samples, the load decay appeared to be lesser than the other two samples. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Pig Lung** & **Human Lung** & **GelMA** \\ \hline \(p_{1}\) & 0.22 \(\pm\) 0.09 & 0.16 \(\pm\) 0.09 & 0.22 \(\pm\) 0.09 \\ \hline \(p_{2}\) & 0.23 \(\pm\) 0.12 & 0.16 \(\pm\) 0.11 & 0.25 \(\pm\) 0.10 \\ \hline \(\tau_{1}\) (\(\varepsilon\)) & 1.22 \(\pm\) 0.77 & 1.37 \(\pm\) 0.78 & 1.04 \(\pm\) 0.42 \\ \hline \(\tau_{2}\) (\(\varepsilon\)) & 0.84 \(\pm\) 0.76 & 1.76 \(\pm\) 0.90 & 1.07 \(\pm\) 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Global parameters: the average values with the standard deviations of the material (\(p\)) and time (\(\tau\)) parameters for all the tested samples. Figure 5: Representative experimental and superimposed fitted curves for the tested samples, showing the goodness of the fitting method. Figure 6: Representation of the samples’ experimental curves overlapped with the fitted curves obtained with the global parameters of each sample. Figure 8 shows the contribution of the relaxation time (\(\tau\)) of the Prony series for the low and high values found in this study, as reported in Figure 9. The higher the values for \(\tau\), the longer the periods necessary for relaxing the stresses. Violin plots were selected to represent the distributions of the material and time parameters obtained through the fitting procedure, including all 15 of the solution sets for each of the analyzed experimental curves (Figure 9). The distributions of the material parameters \(p_{1}\) and \(p_{2}\) were normal for all the tested samples (Figure 9a). Differently, for the time parameters, evident bimodal distributions could be appreciated for the pig lung and human lung samples, whereas for the GelMA samples, although a bimodal distribution was present, it was considerably less pronounced (Figure 9b). Figure 8: Explanatory curves of the exponential behaviors with the low and high values for \(\tau\) found in this study. Figure 7: Comparison of the samples’ behaviors modelled with the average values of the material and time parameters. The bimodal distributions of the relaxation times are a direct consequence of the dispersion of the experimental data shown in Figure 6. It is worth noting that the two peaks characterizing the distribution of the time parameters were not the result of the implemented optimization algorithm since the normality of the parameters obtained for each curve had been verified. Furthermore, the statistical analysis, as reported in Figure 9, highlighted that there were no statistical differences (\(p>0.01\)) between the material parameters of the samples (no intravariability), but there was significant intervariability (\(p<0.01\)). On the other hand, the time parameters showed intravariability only for the biological samples (\(p<0.01\)), with no statistical differences were found between the time parameters characterizing the GelMA samples. Moreover, only the time parameter results for \(\tau_{2}\) were statistically different among all the samples.