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.

通过考虑部分粘弹性体中的参考应力，为瞬态材料开发了部分粘弹性-粘塑性模型。使用该模型，对冻土和 zeonex 结果的蠕变、应力松弛和应变率行为进行数值分析，同时考虑符合阶次区间限制的连续阶次函数。随后，分别建立了变阶粘弹-粘塑性蠕变模型和变阶粘弹-粘塑性应变率模型。最后，利用变阶粘弹-粘塑性蠕变模型和变阶粘弹-粘塑性应变率模型对冻土和Zeonex的流变行为进行了模拟，并对模型参数进行分析。结果表明，提出的阶函数方程是连续的，符合定义的区间效应。变阶粘弹-粘塑性流变模型考虑了材料在流变过程中的弹-粘-塑性行为，具有较高的精度。