Mathematical modeling of Poisson’s ratio and time-frequency interconversion of viscoelastic models based on the fractional Zener formulation

The proposed formulation, based on the four-parameter fractional Zener model, provides a versatile constitutive framework for describing the mechanical behavior of viscoelastic materials (VEMs). The central objective of this work is to theoretically and practically demonstrate that viscoelastic models identified in the time domain can be consistently transformed into their frequency-domain counterparts, and vice versa. The principal contribution lies in the development of a new mathematical model for the time-dependent Poisson’s ratio, formulated in the time domain and derived directly from the constitutive relations of the fractional Zener model. Artificial experimental datasets are employed to validate the effectiveness and internal consistency of the proposed interconversion methodology. Once the fractional parameters are identified through an optimization approach, the corresponding complex viscoelastic functions — namely, the complex Young’s modulus, complex shear modulus, and complex Poisson’s ratio — are obtained through analytical interconversion into the frequency domain. Overall, the proposed framework reinforces the theoretical foundation connecting time- and frequency-domain representations of viscoelastic behavior and advances the modeling and characterization of viscoelastic materials.