Formulation and Numerical Verification of a New Rheological Model for Creep Behavior of Tropical Wood Species Based on Modified Variable-Order Fractional Element

This paper aims to develop a rheological model with fewer parameters that accurately describes the primary and secondary creep behavior of wood materials. The models studied are grounded in Riemann–Liouville fractional calculus theory. A comparison was conducted between the constant-order fractional Zener model and the variable-order fractional Maxwell model, with four parameters each. Using experimental creep data from four-point bending tests on two tropical wood species, along with an optimization algorithm, the variable-order fractional model demonstrated greater effectiveness. The selected fractional derivative order, modeled as a linearly increasing function of time, helped to elucidate the internal mechanisms in the wood structure during creep tests. Analyzing the parameters of this order function enabled an interpretation of their physical meanings, showing a direct link to the material’s mechanical properties. The Sobol indices have demonstrated that the slope of this function is the most influential factor in determining the model’s behavior. Furthermore, to enhance descriptive performance, this model was adjusted by incorporating stress non-linearity to account for the effects of the variation in constant loading level in wood. Consequently, this new formulation of rheological models, based on variable-order fractional derivatives, not only allows for a satisfactory simulation of the primary and secondary creep of wood but also provides deeper insights into the mechanisms driving the viscoelastic behavior of this material.