关于黏弹性材料的广义Maxwell模型
A method of establishing generalizedmaxwell model for viscoelastic materia
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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-Wattsfunction(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.Abstract: The generalized Maxwell model, which describes stressrelaxation modulus, is usually used for analyzing the rheologicalcharacteristics of viscoelastic materials. While data of relaxation modulusobtained from experiments are usually expressed as Kohlrausch-William-Watts(KWW) function, which is in an exponent-spread form. In the paper, thefitting of KWW function to the generalized Maxwell model is turnedinto the equality of two matrixes, which is equivalent to make the1-norm of the matrix difference infinitely small. Minimumvalue of the 1-norm is achieved by introducing the generalized inverse ofmatrix. At last, taking the minimum value of the 1-norm as the objectivefunction, and relaxation time as the constraint condition, a simplex methodis used to optimize the minimum value of the 1-norm. A new computationalmethod for fitting of KWW function to the generalized Maxwell modulus by means of MATLAB software is proposed.
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