A creep constitutive model for salt rock based on fractional derivatives
A creep constitutive model for salt rock based on fractional derivatives
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DOI：
10.1016/j.ijrmms.2010.11.004
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发表时间：
2011-01-01
影响因子：
7.2
通讯作者：
Duan, Z. Q.
中科院分区：
文献类型：
--
作者：
Zhou, H. W.;Wang, C. P.;Duan, Z. Q.
通过用分数阶导数Abel阻尼器代替经典Nishihara模型中的牛顿阻尼器，提出了一种新的基于时间分数阶导数的蠕变本构模型。给出了分数阶导数时变本构模型的解析解。通过拟合已有的盐岩时间相关变形实验结果，确定了分数阶导数模型和西原模型的参数。分数阶导数模型的计算结果与实验数据吻合较好，而西原模型的计算结果与实验数据吻合较好。对基于时间的分数阶导数模型的解析解进行了敏感性研究，揭示了分数阶导数阶数和应力水平对盐岩蠕变应变的影响。研究表明，对于分数阶导数阶数等于1.0的特殊情况，基于时间的分数阶导数模型可以简化为Nishihara模型（C）Elsevier Ltd.版权所有。
By replacing a Newtonian dashpot in the classical Nishihara model with the fractional derivative Abel dashpot, a new creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional derivative time-dependent constitutive model is given. The parameters of the fractional derivative model and the Nishihara model are determined by fitting to existing experimental results of time-dependent deformation of salt rock. The results estimated by the fractional derivative model proposed in the paper are in better agreement with the experimental data than the results estimated by the Nishihara model. A sensitivity study for the analytic solution of the time-based fractional derivative model is carried out, showing the effects of fractional derivative order and stress level on creep strain of salt rock. It is shown that the time-based fractional derivative model can be simplified to the Nishihara model for the special case of fractional derivative order equal to 1.0 (C) Elsevier Ltd. All rights reserved.