A viscoelastic-viscoplastic mechanical model of time-dependent materials based on variable-order fractional derivative

A fractional viscoelastic-viscoplastic model is developed for time-dependent materials, by considering the reference stress in the fractional viscoelastic body. Using this model, the creep, stress relaxation and strain rate behavior is numerically analyzed for frozen soil and zeonex results, with the consideration of continuous order functions that conform to the order interval limits. Subsequently, a variable-order viscoelastic-viscoplastic creep model and also a variable-order viscoelastic-viscoplastic strain rate model are established by the developed variable-order viscoplastic and fractional viscoelastic models, respectively. Finally, the rheological behavior of frozen soil and Zeonex is simulated using the variable-order viscoelastic-viscoplastic creep model and variable-order viscoelastic-viscoplastic strain rate model, and the model parameters are analyzed. The results show that the proposed order function equation is continuous and conforms to the interval effect of the definition. The variable-order viscoelastic-viscoplastic rheological model takes into account the elastic-visco-plastic behavior of the material in the rheological process, and has high accuracy.