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合成材料:力学,计算和应用
ESCI SJR: 0.354 SNIP: 0.655 CiteScore™: 1.2

ISSN 打印: 2152-2057
ISSN 在线: 2152-2073

合成材料:力学,计算和应用

DOI: 10.1615/CompMechComputApplIntJ.v1.i3.10
pages 191-225

ILL-POSED PROBLEMS OF THE MECHANICS (RHEOLOGY) OF VISCOELASTIC MEDIA AND THE METHODS TO REGULARIZE THEM

Yuri G. Yanovsky
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russia
Yu. A. Basistov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russia

ABSTRACT

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.


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