Original Article

Fractional model for the characterization of the linear viscoelastic behavior of thermoplastic polymer

Institut National des Sciences Appliquées Centre Val de Loire, Laboratoire de Mécanique Gabriel Lamé EA 7494, 3 Rue de la Chocolaterie, 41000 Blois, France

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Received: 25 November 2025
Accepted: 22 March 2026

Abstract

This study proposes fractional models to describe the linear viscoelastic behavior of polymethyl methacrylate over a wide range of frequencies and temperatures. The objective of this work is to investigate the efficiency of the fractional model in the identification of the viscoelasticity of the polymer. The experimental data were obtained based on the dynamic mechanical analysis over a limited frequency range at different temperatures. The time–temperature superposition principle was utilized to extend the experimental data across an expanded frequency range. The validity range of this approach was confirmed through the Cole–Cole plot. A master curve for polymethyl methacrylate at a reference temperature was constructed by shifting the dynamic mechanical analysis curves acquired at different temperatures along the frequency axis. The horizontal shift factors were efficiently fitted using the Williams–Landel–Ferry equation. The experimental data, which failed to affirm the time–temperature superposition principle, were precisely characterized using the fractional element model. The master curve was accurately characterized by employing the fractional Zener model. A good agreement between the numerical models and experimental data was achieved. The efficiency of these models was validated by error estimation. The superiority of the fractional models was substantiated through comparative analysis with the integer models. The fractional model was confirmed to be accurate for the prediction of the viscoelastic behavior of polymethyl methacrylate. The Williams–Landel–Ferry equation can be incorporated into the fractional models to address the temperature-dependent viscoelastic properties of the material.