RÉSUMÉ

Classical linear and original nonlinear (suggested by the present authors) pheno-menological and mathematical models describing the behavior of viscoelastic media (polymers above the glassy-state temperature, composites on their basis, etc.) are analyzed. A nonlinear model of a viscoelastic medium based on the Hammerstein-type nonlinear operator is suggested. The methods of regularization of ill-posed, according to Hadamard, inverse problems suitable for identification of the models describing the behavior of viscoelastic media by using full-scale experimental data are considered. To identify the linear model on the basis of the Fredhom first-kind integral operator it is suggested to use Tikhonov's method. To identify the model with the well-known non-linearity function, a method of statistical regularization based on the Bayes criterion is suggested. To identify a model with the unknown function of nonlinearity, the method of bit-linear approximation on the basis of the succession of Fredholm first-kind operators is suggested. The adequacy of the proposed theoretical approaches has been checked by comparing with full-scale experimental rheological data obtained by the authors for homogenous and heterogeneous polymeric media and composites with the aid of modern rheoviscometers.