APPLICATION OF MINIMAX METHOD FOR CALCULATION OF VISCOELASTIC MATERIAL FUNCTIONS AND RELAXATION SPECTRA OF POLYMER MELTS AND SOLUTIONS

Many publications were devoted to the problem of finding methods for c alculating the distribution function of relaxation time spectra H(tau) for viscoelastic media. Direct calculations of this function on the b asis of known relations of the linear theory of viscoelasticity connec ted with the solution of Fredholm integral equations of the first kind involve serious difficulties. At the same time, numerical approaches to determining the function H(tau) based on the use of experimentally determined material functions were proposed in a number of recent publ ications. Since the accuracy of calculating the functions depends dire ctly on the confidence of determining the primary experimental data th at generally always contain errors of a statistical nature, a number o f authors employ smoothing numerical methods of determining the materi al functions, or ones that fail to react to the appearance of rough er rors. These methods include methods of regularization and maximum of e ntropy. However, they have a number of serious shortcomings limiting t he possibilities of their successful use. In the present work, we prop ose to employ a different numerical method for these purposes, namely, the minimax technique. In our opinion, it is more accurate, rapid, an d universal. We consider a scheme of constructing an algorithm, give e xamples of solving test problems showing how the algorithm functions i n various extreme hypothetic situations. The results of the numerical calculations of the function H(tau) for a real object, viz. polybutadi ene are based on experiments run in a rotary viscometer Rheotron of th e firm Brabender.