关于黏弹性材料的广义Maxwell模型

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.

A method of establishing generalizedmaxwell model for viscoelastic materia

The generalized 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 Kohhrausch-William-Watts (KWW) function, which is in an exponent-spread form. In the paper, the fitting of KWW function to the generalized Maxwell model is turned into the equality 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 generalized Maxwell modulus by means of MATLAB software is proposed.