## 2 Materials Experimental Data  
The viscoelastic material is a deformable material with a behavior which lays between a viscous liquid and an elastic solid. Their behavior deviates from [PERSON]'s elastic law, exhibiting both elastic and viscous characteristics at the same time. In this kind of materials, the stress-strain relationship is a function of time and the viscoelastic characteristics exhibit time-dependent behavior and load application speed at an established temperature value. To better understand the mechanical behavior in viscoelastic materials, two main types of experiments are usually carried out: transient and dynamic. While static characterization regards the quasi-static application of load or deformation, transient and dynamic testing procedures concern the analysis of material response to a time applied deformation or load function (elongation or shear). Two important categories regarding the transient material testing are commonly performed: the creep experiment and stress-relaxation experiment. In the creep experiment, the material is subjected to uniform load to analyze the strain time changes while during the stress-relaxation experiment, the material is subjected to a fixed deformation and the load required to maintain the deformation at a constant value is measured with time. The above transient tests allow to characterize the viscoelastic material reaction for each applied stress-strain load step. Another important testing procedure class able to describe the viscoelastic behavior consists of the dynamic experiments. These tests are commonly employed to analyze the material reaction to cyclic stress (1) or strain applied:  
\[\sigma(t)=\sigma_{0}\sin\omega t \tag{1}\]  
where \(\omega\) represents the angular frequency of an applied sinusoidal stress and depends on the time. In quasi-elastic materials, the strain generated by the stress also exhibits a sinusoidal trend with the same phase of the applied load. On the opposite side, in viscoelastic materials, the strain reaction shows a time delay towards the applied stress, characterized by a phase angle \(\delta\). Therefore, the strain response is given by (2):  
\[\varepsilon(t)=\varepsilon_{0}\sin(\omega t-\delta) \tag{2}\]  
Because of the phase displacement, the material dynamic stiffness can be considered as a complex variable \(E^{*}\) according to [PERSON]'s formulation (3):  
\[\frac{\sigma(\omega)}{\varepsilon(\omega)}=E^{*}=E^{\prime}+E^{\prime\prime} \tag{3}\]  
where \(E^{\prime}\) is the storage modulus [Pa] and \(E^{\prime}\) is the loss modulus [Pa]. These quantities are deeply linked to the way the material dissipates a part of energy provided by means of a load/stress time function. They are related to the phase angle \(\delta\), according to the following Equation (4):  
\[\frac{E^{\prime\prime}(\omega)}{E^{\prime}(\omega)}=\tan\delta \tag{4}\]  
The phase angle tangent \(\delta\) is also called loss tangent. It is important to remark that all the quantities, referring to the viscoelastic behavior, are function of the frequency at which the sinusoidal load/deformation is applied and of the material temperature. Hereafter, the output of dynamic mechanical analysis (DMA) [33] for the moduli characterization of three different polymers called A, B and C is reported. Such testing procedure prescribes an oscillatory deformation of the material sample with a constant strain or stress amplitude in order to measure the viscoelastic modulus. The oscillatory load is applied at different frequencies and then repeated at different temperatures. The master curves at a chosen reference temperature and over a wide range of frequencies is obtained exploiting the time-temperature superposition principle [34], which allows to shift the results measured at different temperatures.