[Modélisation mathématique du coefficient de Poisson et de l’interconversion temps-fréquence des modèles viscoélastiques basée sur la formulation fractionnaire de Zener]
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.
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La formulation proposée, fondée sur le modèle de Zener fractionnaire à quatre paramètres, offre un cadre constitutif polyvalent pour décrire le comportement mécanique des matériaux viscoélastiques (VEM). L’objectif principal de ce travail est de démontrer, tant sur le plan théorique que pratique, que les modèles viscoélastiques identifiés dans le domaine temporel peuvent être transformés de manière cohérente en leurs équivalents dans le domaine fréquentiel, et inversement. La principale contribution réside dans le développement d’un nouveau modèle mathématique pour le coefficient de Poisson dépendant du temps, formulé dans le domaine temporel et dérivé directement des relations constitutives du modèle fractionnaire de Zener. Des jeux de données expérimentales artificielles sont utilisés pour valider l’efficacité et la cohérence interne de la méthodologie d’interconversion proposée. Une fois les paramètres fractionnaires identifiés par une approche d’optimisation, les fonctions viscoélastiques complexes correspondantes — à savoir le module de Young complexe, le module de cisaillement complexe et le coefficient de Poisson complexe — sont obtenues par interconversion analytique dans le domaine fréquentiel. Dans l’ensemble, le cadre proposé renforce les fondements théoriques reliant les représentations du comportement viscoélastique dans les domaines temporel et fréquentiel et fait progresser la modélisation et la caractérisation des matériaux viscoélastiques
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Mots-clés : Viscoélasticité, coefficient de Poisson, modélisation dans le domaine temporel, principe de correspondance
Tiago Lima de Sousa 1 ; Jucélio Tomás Pereira 2 ; Jéderson da Silva 3
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Tiago Lima de Sousa; Jucélio Tomás Pereira; Jéderson da Silva. Mathematical modeling of Poisson’s ratio and time-frequency interconversion of viscoelastic models based on the fractional Zener formulation. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 397-416. doi: 10.5802/crmeca.360
@article{CRMECA_2026__354_G1_397_0,
author = {Tiago Lima de Sousa and Juc\'elio Tom\'as Pereira and J\'ederson da Silva},
title = {Mathematical modeling of {Poisson{\textquoteright}s} ratio and time-frequency interconversion of viscoelastic models based on the fractional {Zener} formulation},
journal = {Comptes Rendus. M\'ecanique},
pages = {397--416},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {354},
doi = {10.5802/crmeca.360},
language = {en},
}
TY - JOUR AU - Tiago Lima de Sousa AU - Jucélio Tomás Pereira AU - Jéderson da Silva TI - Mathematical modeling of Poisson’s ratio and time-frequency interconversion of viscoelastic models based on the fractional Zener formulation JO - Comptes Rendus. Mécanique PY - 2026 SP - 397 EP - 416 VL - 354 PB - Académie des sciences, Paris DO - 10.5802/crmeca.360 LA - en ID - CRMECA_2026__354_G1_397_0 ER -
%0 Journal Article %A Tiago Lima de Sousa %A Jucélio Tomás Pereira %A Jéderson da Silva %T Mathematical modeling of Poisson’s ratio and time-frequency interconversion of viscoelastic models based on the fractional Zener formulation %J Comptes Rendus. Mécanique %D 2026 %P 397-416 %V 354 %I Académie des sciences, Paris %R 10.5802/crmeca.360 %G en %F CRMECA_2026__354_G1_397_0
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