## 5 Results
### Dynamic Impact Tests Results  
The complex modulus values back-calculated at each temperature from the FRFs measurements with the two proposed methods for specimen WF-8 are plotted, as an example, in Figure 12. For the first method of back-calculation, one value of the complex modulus is plotted for temperatures at which only one peak was considered for the optimization (\(-\)20, 0, 15 and 35 \({}^{\circ}\)C) and two values are plotted at \(-\)50 \({}^{\circ}\)C because two peaks exist for this temperature. Only one value of the complex modulus is presented for each temperature for Method 2 because the back-calculation is limited to the first resonance frequency, as explained previously. The master curve of the norm of the complex modulus at 15 \({}^{\circ}\)C was obtained considering the validity of the TTSP. The 2S2P1D model was fitted to the back-calculated modulus for both methods and the two resulting 2S2P1D model curves are also plotted in Figure 12. Good fitting of the 2S2P1D curves can be observed for both methods, which give only slightly different results. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Specimen** & **E\({}_{\text{0}}\) (MPa)** & **E\({}_{\text{0}}\) (MPa)** & **\(\delta\)** & **k** & **h** & **\(\beta\)** & **\(\tau_{\text{EIS}^{\circ}}\)C (s)** & **C\({}_{\text{1}}\)** & **C\({}_{\text{2}}\)** \\ \hline WF-4 & 28 & 33,400 & 2.28 & 0.177 & 0.57 & 154 & \(5.4\times 10^{-2}\) & 24.9 & 166.6 \\ WF-6 & 40 & 37,500 & 2.28 & 0.177 & 0.57 & 154 & \(7.0\times 10^{-2}\) & 24.9 & 166.6 \\ WF-8 & 56 & 36,900 & 2.28 & 0.177 & 0.57 & 154 & \(6.9\times 10^{-2}\) & 24.9 & 166.6 \\ GB5-3 & 65 & 39,100 & 1.80 & 0.180 & 0.60 & 350 & \(7.5\times 10^{-2}\) & 24.7 & 165.9 \\ GB5-4 & 65 & 39,500 & 1.80 & 0.180 & 0.60 & 350 & \(1.5\times 10^{-1}\) & 24.7 & 165.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibrated 2S2P1D constants to match tension–compression measurements. Figure 12: Dynamic test results and fitted 2S2P1D model curve for the two analysis methods for specimen WF-8: **(a)** Cole–Cole diagram; and **(b)** master curve for the norm of the complex modulus at 15 \({}^{\circ}\)C.  
The values of the 2S2P1D model and WLF equation constants fitting the results from the two back-analysis methods are given for all specimens in Table 5 (first method) and Table 6 (second method). Note that similarly to the results of the tension-compression tests, constants k, h, \(\delta\), \(\beta\), C\({}_{1}\) and C\({}_{2}\) have the same values for a given material. In addition, the same WLF equation constants can be used for the two methods and only constant E\({}_{0}\) differs between the first and the second method. It must be highlighted that values of constants E\({}_{00}\) and \(\beta\) are assumed because they have no influence on the complex modulus values in the frequency range involved during the dynamic tests. The constants governing the value of the Poisson's ratio \(\upnu_{00}\), \(\upnu_{0}\) and \(\uptau_{\upnu}\) do not appear in Tables 5 and 6 because the Poisson's ratio was not evaluated from the dynamic tests but assumptions on the values of these constants were necessary to back-calculate the complex modulus at each temperature in the first step of the first method. A good proximity between the results obtained with the two methods is shown in Figure 12. The same observation was made for all specimens. To validate this visual impression, the relative difference between the norm (in %) and the phase (in \({}^{\circ}\)) of the 2S2P1D simulated complex modulus obtained from the two methods are plotted in Figure 13. In this figure, the relative difference is plotted against the reduced frequency at 15 \({}^{\circ}\)C for all specimens. It is seen that the second method considering a constant complex modulus at each temperature and a constant real Poisson's ratio of 0.3 gives a norm slightly higher than the first method with a maximum relative difference of about 3.7%.