Consideration is given to one of the new classes of smart materials, namely, to electrorheological fluids. The latter are suspensions of dielectric particles of different concentration in a viscous medium, which have unique properties and may change their rheological characteristics by hundreds of thousand times in superposition of electric fields. The given materials hold much promise from the practical standpoint (they have been applied in space engineering, biomechanics and biomedicine). Experiments show that the electrorheological effect is basically related to electrostatic interaction of particles and dynamics of changes in the structure of disperse particle distribution under the action of the electric field and strain rate gradients. Below, the well-known theoretical and experimental papers on rheology of such media are briefly reviewed and analyzed critically. The paper deals with the original approach based on a physical crystal model (a 3D multiparticle ordered model), which allows a well-developed mathematical body of crystal theory to be used. Consideration is given to the approximation of pair interaction between particles as equivalent dipoles and the force of electrostatic interaction of particles polarized by the external field with regard to the nearest neighbors up to and including the third order. The defining rheological relationships derived in the framework of the model are analyzed. Besides, theoretical predictions based on model media are verified experimentally over a wide range of changes in dielectric and structural-rheological properties of components. The advantages of the theory are discussed and the results obtained are compared to those obtained by foreign scientists. The direction of further development and the way of theory generalization for high (ultimate) strains are considered.

The present work focuses on an application of the new and original computational methods to analyze the interfacial stress-transfer behavior and to prognosis the macromechanical properties and behavior of polymer composites in taking into consideration the real interfacial attributes and dynamics of molecular interrelation of the constituents.

The accuracy of solving incorrectly stated problems for the Tikhonov regularization method depends markedly on the accuracy of prescribing additional a priori information with respect to starting data, and in the present case to error parameters.