盐岩的分数阶非线性蠕变本构模型

Fractional nonlinear creep constitutive model of salt rock

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 a non-Newton fluid viscous damping element, fractional nonlinear dashpot element has been presented.Based on the definition of fractional derivatives, a theoretical expression for the element has been obtained. Its expression is consistent with that of the Abel dashpot. Through further comparison, it is found that the element can reflect the nonlinear acceleration characteristic of the creep curve. By introducing the element, new nonlinear creep constitutive model has been established. Based on the data from the creep experiments, fitting analysis has been conducted about the model. The results show that the nonlinear creep constitutive model agrees well with the data from the experiments and can clearly reflect the characteristics of the creep curves of the whole process, especially the nonlinear acceleration creep stage.