Fractional Viscoelastic Modeling of Creep and Stress Relaxation Behaviors in Polymer-Based Energetic Materials

This study compares low-parameter fractional viscoelastic models for the unified characterization and extrapolation of creep and stress relaxation behaviors in polymer-based energetic materials, including polymer-bonded explosives (PBXs) and solid propellants. Fourteen candidate models composed of springs and spring-pot elements were considered under controlled parameter complexity. Their creep compliance and relaxation modulus were evaluated through Laplace-domain formulations, and the parameters were identified using a combined Talbot inverse Laplace transform and Gray Wolf Optimizer. Published creep and stress relaxation datasets were used to assess both fitting performance and early-stage data extrapolation behavior. The results show that the fractional Zener model and Model 13 can each describe both creep compliance and relaxation modulus within compact six-parameter rheological forms. Both models generally achieved coefficients of determination above 0.99. When the first 10% of the time span was used for calibration, the selected fractional models showed extrapolation capability over an approximately one-order-of-magnitude longer time window, with rRMSE values below 8.5% in reported cases and below 2% under suitable conditions. Compared with Prony series and power-law models, these fractional models offer compact alternatives for broad viscoelastic response characterization. These results provide guidance for selecting compact viscoelastic models for long-term response analysis of polymer-based energetic materials.