A method of establishing generalizedmaxwell model for viscoelastic materia
关于黏弹性材料的广义Maxwell模型

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.