Variational Methods of Constructing Models of Continuous Media
At present in plasma mechanics, in mechanics of plastic solids, of polymers, in the continuum theory of dislocations, when taking account of electromagnetic properties and effects in various media, when taking account of quantum laws in macroscopic phenom
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L. I. Sedov Moscow (U.S.S.R.) At present in plasma mechanics, in mechanics of plastic solids, of polymers, in the continuum theory of dislocations, when taking account of electromagnetic properties and effects in various media, when taking aCCOUllt of quantum laws in macroscopic phenomena, and in many other cases, it is necessary to construct new models of continuous media. The classical models of the perfect viscous fluid and of linear theory of elasticity are continuing to play an important role in mechanics but by their nature they obviously came to be insufficient. As important trends in the theory of new models for liquid and gaseous media let us mention the complicated models required to investigate motions and various processes in plasma, averaged motions and processes in turbulent motions of various media, in the theory of motion of multicomponent mictures, fluids, gases in which phase and chemical transformations and interactions with deformable bodies are taken into consideration, in particular, in porous media. A significant importance is attaining the theory of constructing models of non-Newtonian fluids in connection with biological problems, with problems of chemical technology, with the theory of liquid helium at very low temperatures etc. Lately, interesting theoretical models of fluids and solids (ferromagnets) have been considered, in which the small particles possess significant magnetic fields and mechanical angular momentum i. e., spins. In recent years, a great deal of papers have been published which involve complicated equations of motion and state for physical media. However, in many cases such papers have a particular character, sometimes, they are connected essentially only with simplest particular problems and with empirical formal approach. Because of diffioulties, in essence, a large number of these papers poorly or in no way coordinate H. Parkus et al. (eds.), Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids © Springer-Verlag/Wien 1968
Constructing Models of Continuous Media
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with universal or specific physical approachs. At best, only certain general restrictions imposed by the second law of thermodynamics on formally "ad hoc" introduced relations are considered. In the following I will dwell on the highly general variational method of constructing models of continuous media, on the method which is based on and uses fundamental physical ideas and the knowledge of modern theoretical constructions. I mean the rational treatments of the field theory and physical media in theoretical mechanics and in relativity theory, in thermodynamics and statistical physics. Undoubtedly, it is time to introduce in daily practice a unified treatment of mechanical and electromagnetic phenomena. The importance of this statement is also connected with the fact that all the essential internal microscopic interactions in physical media are of electromagnetic nature. Taking into consideration the universal properties of physical or geometrical invar
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