## 1 Introduction
Furthermore, in terms of frequency domain, both models are efficient only within a small frequency range, but they become insufficient within low and high frequency ranges, representing an important limit in case the specific application could require different boundary conditions in terms of excitation frequency to be applied on the same material model. When the deformations of a viscoelastic material are neither small nor very slow, its behavior is no longer linear, and there is no universal rheological constitutive equation that can predict the response of the material to such a deformation. Hence, for modelling their behavior in these cases, finite strain-based viscoelastic models are required. Some notable studies can be found in literature regarding finite viscoelastic modelling of polymers. The finite strain thermo-viscoelastic constitutive model, proposed by [PERSON] et al. [11] employs a non-linear evolution law based on the classical concept of the multiplicative decomposition of the deformation gradient using specific hyper-elastic parameters identified at reference temperature values. Following the Bergstrom-Boyce model for nonlinear finite rubber viscoelasticity [12], [PERSON] et al. proposed a modified version of the micro-mechanically motivated Bergstrom-Boyce viscoelastic model used along with a finite linear evolution law [13], while a model for rate-dependent phenomena in elastomers founded on finite strain theories in consistence with the natural laws of thermodynamics is proposed in [14]. In order to get around the specific characterization procedures, generalized models are often employed allowing to describe the viscoelastic behavior of the materials in a wide range of frequencies and time scales. The above models, consisting of a combination of a number of elementary springs and dashpots, generally known as the Generalized Maxwell model (GM) and generalized Kelvin-Voigt model (GKV), offer a good description of the real viscoelastic material but they consist of a considerable amount of appropriately connected spring and dashpot elements. This means that a set of differential equations must be solved to evaluate the dynamic behavior of the components under investigation [15], which could considerably complicate the mathematical formulation describing the dynamic state of the system and might significantly increase the computational load due to a larger set of motion equations to be solved. To overcome these issues, fractional models are becoming more and more popular because of their ability to describe the behavior of viscoelastic materials using a limited number of parameters with an acceptable accuracy over a vast range of excitation frequencies. Several authors have put the focus on the modelling approach based on fractional calculus allowing the characterization of rheological behavior of linear viscoelastic systems [16; 17; 18; 19; 20], pointing out several significant problems connected with the robust identification of model parameters. The parameters' identification procedure can be classified according to the data domain employed (time-based or frequency-based) and according to the methods employed. Time-domain-based identification procedures can exploit creep and relaxation experimental tests [21], hysteresis loops of steady-state harmonic experimental tests [22] and impact tests [23]. Frequency-domain-based procedures can exploit magnitude and phase of the frequency response function [24] or the definition of storage modulus and loss factor [25; 26]. Recently, [PERSON] et al. [27] have proposed a new frequency-domain-based identification procedure defining an ad-hoc testing setup. As concerns the classification by the identification method, an accurate literature review points out that the authors generally adopt a multitude of different procedures, i.e., [PERSON] [26] and [PERSON] et al. [28] have proposed a genetic algorithm method, while procedure based on a curve fitting has been used by [PERSON] et al. [25] and [PERSON] et al. [19].