关于黏弹性材料的广义Maxwell模型  

A METHOD OF ESTABLISHING GENERALIZED MAXWELL MODEL FOR VISCOELASTIC MATERIAL

作　　者：帅词俊[1] 段吉安[1] 王炯[1] 

机构地区：[1]中南大学机电工程学院,长沙410083

出　　处：《力学学报》2006年第4期565-569,共5页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金重点项目(50235040)教育部新世纪优秀人才支持计划(NCET-040753)资助.~~

摘　　要：采用流变力学分析黏弹性材料的流变特性时,常要用到广义Maxwell模型表达的应力松弛模量．而从试验中获得的应力松弛模量,其表达式常为Kohlrausch—William—Watts function(KWW函数)形式．通过把 KWW函数和广义Maxwell模型的拟合问题转化为两矩阵相等的求解问题后,又把两矩阵的相等等价于两矩阵差值向量的一阶范数为无穷小的问题,并通过引入广义逆矩阵,求得两矩阵差值向量的一阶范数的最小值,最后以一阶范数的最小值为目标函数,松弛时间为约束条件,利用单纯形法对两矩阵差值向量的一阶范数的最小值优化,从而提出了一种针对黏弹材料的KWW函数与广义Maxwell模型转换的计算方法．借助于 MATLAB软件,实现了对黏弹材料的广义Maxwell模型的拟合．The generahzed Maxwell model, which describes stress relaxation modulus, is usually used for analyzing the rheological characteristics of viscoelastic materials. While data of relaxation modulus obtained from experiments are usually expressed as Kohlrausch-William-Watts （KWW） function, which is in an exponentspread form. In the paper, the fitting of KWW function to the generalized Maxwell model is turned into the equahty of two matrixes, which is equivalent to make the 1-norm of the matrix difference infinitely small. Minimum value of the 1-norm is achieved by introducing the generalized inverse of matrix. At last, taking the minimum value of the 1-norm as the objective function, and relaxation time as the constraint condition, a simplex method is used to optimize the minimum value of the 1-norm. A new computational method for fitting of KWW function to the generahzed Maxwell modulus by means of MATLAB software is proposed.

关 键 词：黏弹材料 松弛模量 Maxwell模型 参数拟合 KWW函数 

分 类 号：TN253[电子电信—物理电子学]