In this work, by constructing the equivalent viscoelasticity between a fractional Zener model and a time-varying viscosity Zener model, we obtain the time-varying viscosity of creep and relaxation response. The derived time-varying viscosity can well interpret the physical meaning of the evolution of material from Hooke body to Newtonian fluid body. With the relaxation time gradually becoming larger, the viscosity of creep is closer to the viscosity of relaxation. The relaxation modulus and creep compliance of a time-varying viscosity Zener model obtained by inserted viscosity of creep and relaxation approximate that of a fractional Zener model. And the variation of fractional order is accompanied by the transformation of viscoelasticity. Based on the importance of relaxation time, a variable-order function related to relaxation time is proposed, and it can well interpret the physical meaning of evolution of viscoelasticity. Then, it also can reveal a process where the viscosity is consumed to resist deformation in rheology. The viscosity increases with an increase in time and a decrease in the fractional order. Finally, based on the variable-order function, a variable-order fractional viscoelastic Zener model is proposed, and it is in well agreement with experimental data.

中文翻译：

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变阶分数齐纳模型与粘弹性材料的非牛顿时变粘度之间的联系：松弛时间

在这项工作中，通过构建分数 Zener 模型和时变粘度 Zener 模型之间的等效粘弹性，我们获得了蠕变和松弛响应的时变粘度。推导出的时变粘度可以很好地解释材料从胡克体到牛顿流体体演化的物理意义。随着松弛时间逐渐变大，蠕变粘度更接近松弛粘度。通过插入蠕变和松弛粘度获得的时变粘度齐纳模型的松弛模量和蠕变柔量近似于分数齐纳模型的松弛模量和蠕变柔量。分数阶的变化伴随着粘弹性的转变。基于弛豫时间的重要性，提出了与弛豫时间相关的变阶函数，并且可以很好地解释粘弹性演化的物理意义。然后，它还可以揭示在流变学中消耗粘度以抵抗变形的过程。粘度随着时间的增加和分数阶数的减少而增加。最后，基于变阶函数，提出了变阶分数粘弹性Zener模型，与实验数据吻合较好。