Advanced Creep Modeling of Acetal Using Variable-Order Fractional Mechanics

Resumo

Polymer-based plastics such as acetal exhibit time-dependent deformation under constant stress, known as creep, which can eventually lead to rupture or static fatigue. A common misconception is that materials under tolerable static loads remain unaffected over time. However, accurate long-term deformation predictions require experimental data and advanced modeling techniques. Traditional rheological models, composed of basic elements like springs and dampers, often fall short in capturing the intrinsic power-law behavior of creep. While the springpot—based on fractional calculus—provides a power-law relationship, its fixed-order nature limits its effectiveness when the deformation rate evolves over time. This study presents a nonlinear creep model based on a variable-order springpot, specifically developed to characterize the viscoelastic behavior of acetal. The model dynamically adapts to the evolving properties of the material, accurately capturing transitions among the glassy, transition, and rubbery phases. Model parameters are calibrated using a robust identification procedure based on the cross-entropy method, resulting in physically consistent and highly accurate predictions. This advanced modeling framework not only overcomes the limitations of fixed-order formulations but also establishes a foundation for the application of variable-order mechanics to viscoelastic materials—offering a powerful and tailored tool for predicting the long-term structural performance of acetal.