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在非牛顿流体黏滞阻尼元件的基础上提出了分数阶非线性黏壶元件。基于分数阶导数的定义,得到了该元件的理论表达式,其表达式与Abel黏壶的表达式相一致,进一步比较发现该元件能反映蠕变曲线的非线性加速特征。通过引入该元件建立了新的非线性蠕变本构模型。基于蠕变试验数据,对该模型进行了拟合分析。结果表明,非线性蠕变本构模型与试验数据吻合的较好,并且能很好地反映全过程蠕变曲线的特征,尤其是非线性加速蠕变阶段。
On the basis of non-Newtonian fluid viscous damping element, a fractional-order nonlinear viscous-pot element is proposed. Based on the definition of fractional derivative, the theoretical expression of the element is obtained. The expression of the element is consistent with the expression of Abel sticky pot. Further comparison shows that the element can reflect the nonlinear acceleration characteristic of creep curve. By introducing this element, a new nonlinear creep constitutive model is established. Based on the creep test data, the model was fitted and analyzed. The results show that the nonlinear creep constitutive model is in good agreement with the experimental data, and can well reflect the characteristics of the whole process creep curve, especially in the nonlinear acceleration creep stage.