A. A. Bedulina, A. V. Kobelev
Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues. Processes of mechanical deformation of such continuous media have peculiarities connected, first, with accounting for internal friction and dissipation of energy, and secondly, with nonlinearity of their elastic and viscous properties, that is with violation of Hook and Newtons laws. Problem of modeling of these systems reduce to the analysis of the corresponding equivalent mechanical or electric circuit (see examples in the classical monograph by Frenkel). Rheological properties of described medium are governed by the differential equations of the first order on time (the evolution equations), as well as a huge variety of other physical processes. The physical phenomena in nonlinear systems with dissipation have a big community, including such it would seem far areas, as dynamics of magnetization in ferrite. Therefore the problem of studying new effects of viscous friction in the conditions of nonlinearity and heterogeneity, is very actual as in respect of fundamental research nonlinear and non-uniform environments, and in many areas of materials science, design of new materials, engineering of biological substitutes of living tissues and development of the micromagnetic devices using essentially new opportunities. Traditional approaches to mechanics of viscoelastic bodies sometimes are excessively difficult, and more evident and available representations are necessary. The invaluable role in studying of the operating processes mechanisms of elastic deformation and motility of biological materials, is played by the mathematical modeling.
View original:
http://arxiv.org/abs/1306.5845
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