A method of establishing generalizedmaxwell model for viscoelastic materia

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.