## 3 Experimental Investigation
### Material Testing  
All SS-TTD specimens were built with stainless steel, grade 1.4301 (304-L AISI). The material mechanical properties were obtained following the indications of ISO 6892-1:2016 [14] from standard coupon tension tests (Figure 5).  
Since the dampers were studied under quasi-static and dynamic loads, the material was subjected to monotonic loading at two different strain rates of 0.003 and 0.115 mm/mm/s, hereafter referred to as static and dynamic loadings, respectively. The strain rate is defined here as strain increments per second at the central section of the coupon tension test specimen (i.e., between points 2 and 3 in Figure 5), between zero strain and yield strain. Two specimens were tested at each strain rate.  
Figure 6a shows the stress-strain curve obtained during the tests and a trilineal idealisation of the former. Table 1 summarizes the mean values and corresponding standard deviation of the main curve parameters obtained from direct tensile tests. In this table, \(\sigma_{0.2\%}\), is the 0.2% yielding stress (parameter commonly used to describe stainless steel), \(\sigma_{u}\) is the ultimate stress, and \(\varepsilon_{u}\) is the ultimate elongation. For convenience, the defining parameters of the trilinear approximation in Figure 6b were included, namely: \(\sigma_{y}\), \(\varepsilon_{y}\) yielding stress and strain at the limit of proportionality; and \(\sigma_{b}\), \(\varepsilon_{b}\) stress and strain at the end of the smooth transition branch from elastic to inelastic range. The stress-strain curves were idealized as follows: (i) an initial linear-elastic branch following the modulus of elasticity \(E\) until the limit of proportionality (\(\sigma_{y}\), \(\varepsilon_{y}\)); (ii) a second transition linear branch from (\(\sigma_{y}\), \(\varepsilon_{y}\)) to (\(\sigma_{b}\), \(\varepsilon_{b}\)) representing the transition curve; (iii) a final horizontal branch from (\(\sigma_{b}\), \(\varepsilon_{b}\)) to (\(\sigma_{u}\), \(\varepsilon_{u}\)) closely fitting the inelastic part. The values of \(\sigma_{b}\) and \(\varepsilon_{b}\) were determined so as the area under the real curve and the trilinear approximation was the same. As expected, the modulus of elasticity was the same in all tests, \(E=2\times 10^{5}\) MPa, irrespective of the strain rate applied. Table 1 also includes the theoretical values of \(Q_{y}\) and \(\delta_{y}\) obtained with Equations (1) and (2).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{_Strain Rate_} & \(\sigma_{0.2\%}\) & \(\sigma_{u}\) & \(\sigma_{y}\) & \(Q_{y}\) kN & \(\sigma_{b}\) & \(\sigma_{b}\)  kN & \(\varepsilon_{y}\) \% & \(\delta_{y}\) \(mm\) & \(\varepsilon_{b}\) \% & \(\varepsilon_{u}\) \% \\  & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** & **MPa** \\ \hline
0.003 & \(377\pm 15\) & \(604\pm 30\) & \(250\pm 5\) & \(15.50\) & \(405\pm 15\) & \(25.14\) & \(0.12\pm 0.05\) & \(1.08\) & \(0.40\pm 0.01\) & \(46\pm 1\) \\
0.115 & \(529\pm 6\) & \(709\pm 16\) & \(400\pm 10\) & \(24.83\) & \(560\pm 15\) & \(34.76\) & \(0.20\pm 0.01\) & \(1.73\) & \(0.57\pm 0.02\) & \(44\pm 2\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of the stainless steel at different strain rates.  
Figure 5: Coupon tension test specimen.  
Figure 6: Stress-strain curves: (**a**) tension tests; (**b**) idealisation.