高等学校化学学报

高等学校化学学报

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Mittag-Leffler函数及其在粘弹性应力松弛中的应用

陈宏善, 李明明, 康永刚, 张素玲   

  1. 西北师范大学物理与电子工程学院, 高分子材料重点实验室, 兰州 730070

  • 收稿日期:2007-10-24 修回日期:1900-01-01 出版日期:2008-06-10 发布日期:2008-06-10
  • 通讯作者: 陈宏善

Mittag-Leffler Function and Its Application to Viscoelastic Stress Relaxation

CHEN Hong-Shan*, LI Ming-Ming, KANG Yong-Gang, ZHANG Su-Ling   

  1. Key Laboratory of Polymer Materials, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070
  • Received:2007-10-24 Revised:1900-01-01 Online:2008-06-10 Published:2008-06-10
  • Contact: CHEN Hong-Shan

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被引次数

56

摘要： Mittag-Leffler函数在分数阶粘弹理论中起着重要作用. 我们对该函数的计算及收敛性进行了分析; 利用遗传算法结合共轭梯度法, 提出了对广义函数进行非线性参数拟合的方法. 用分数Maxwell模型对强弱、硬柔具有显著差别的塑料、玻璃态合金及聚合物近熔体的应力松弛过程进行了研究.

关键词: 分数Maxwell模型, Mittag-Leffler函数, 粘弹性, 应力松弛

Abstract: Functions of Mittag-Leffler(M-L) type play a special role in the fractional order viscoelastic theory. However, this function converges very slowly and it will likely result in divergence in numerical evaluation. The convergence criterion and the evaluation of M-L functions is discussed. When applying fractional Maxwell model to the stress relaxation, the parameters determined by using the asymptotic solutions of M-L functions are not correct to describe the relaxation process. A method combining genetic algorithm and conjugated gradient was proposed to optimize the model parameters. And the fractional Maxwell model based on the optimized parameters can be used to simulate viscoelastic relaxation process very well.

Key words: Fractional Maxwell model, Mittag-Leffler function, Viscoelasticity, Stress relaxation

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