EHD equations and transport coefficients in a strong electric field

The methods of the kinetics theory are used to obtain a closed system of equations describing the behavior of a multicomponent, partially ionized gaseous mixture in an electromagnetic field in which the space charge is significant. A criterion is presented that makes it possible to separate the problem of finding the magnetic field from that of finding the other defining parameters. Expressions are obtained for the viscosity stress tensors and the thermal and diffusive fluxes; the transport coefficients are calculated in the strong electric field. The relations for the friction force and the energy exchange between components during particle collisions are analyzed. The equations for a mixture consisting of neutral particles and charged particles of a single sign are discussed in detail. The dimensionless EHD criteria are written and analyzed. Possible simplifications of the system of equations are examined, and various forms of Ohm's law are discussed. Weak discontinuities in EHD are analyzed. The equations of EHD under various assumptions have also been considered in several studies^* and in [1–3].     

The thermostressed state of electrically conductive bodies subjected to an external electromagnetic field

A technique is proposed for mathematical and numerical modeling of thermomechanical processes in electrically conductive bodies subjected to an external electromagnetic field. The initial relations for the determination of the electromagnetic field are the Maxwell equations. The stress and strain states of the body are described using the equations of nonisothermal elastoplasticity. The model takes into account the coupling of the electromagnetic and thermal fields. All physical and mechanical parameters of the material depend on temperature. The process of high-temperature induction treatment of a ferromagnetic cylinder is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 13–25, December 2005.     

Crack movement in layered composites under electric field affect

The variation principle is applied for defining a crack in the solid body. The methods proposed in [G. Sih, C. Chen, Non-self-similar crack growth in elastic–plastic finite thickness plate, Theoretical and Applied Fracture Mechanics 3 (1985) 125–139] extend to presence of electromagnetic fields in material. Crack propagation in non-homogeneous media has been considered. It is shown that electromagnetic fields in the material are essentially affecting the trajectory. The crack trajectory stability has been studied as function of fracture energy, phase portraits of the trajectory in different media have been built, and various attractor types have been revealed. Different crack morphologies from single straight and oscillating crack propagation to straight double crack propagation were theoretically founded. In compliance with the experimental data of [R. Niefanger, V.-B. Pham, G. Schneider, H.-A. Bahr, H. Balke, U. Bahr, Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory, Acta Materialia 52 (1) (2004) 117–127], it has been demonstrated that periodic electromagnetic field results in trajectory stochastization. This can be used for switching the crack over from the mode of mainline propagation into the mode of development of the field of diffused microcracks.     

Near field diffracted at a dielectric wedge

The integral equations of macroscopic dynamics [2] are used in [1] as the basis of a solution to the problem of the diffraction of a plane electromagnetic wave with a known polarization at a rectangular dielectric wedge. Expressions are given in this paper for the total electromagnetic field both inside a dielectric wedge of arbitrary flare angle and outside the wedge. The method used is the same as in [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 174–181, July–August, 1976.     

Constitutive Equations of an Isotropic Hyperelastic Body

Stress—strain equations for an isotropic hyperelastic body are formulated. It is shown that the strain energy density whose gradient determines stresses can be defined as a function of two rather than three arguments, namely, strain–tensor invariants. In the case of small strains, the equations become relations of Hooke's law with two material constants, namely, shear modulus and bulk modulus.     

Axisymmetric analogy for three-dimensional viscous flow problems

A method of solving three-dimensional flow problems with the aid of two-dimensional solutions, which can be used for any Reynolds numbers, is proposed. The method is based on the use of similarity relations obtained in the theoretical analysis of the approximate analytic solution of the equations of a three-dimensional viscous shock layer. These relations express the heat flux and the friction stress on the lateral surface of a three-dimensional body in terms of the values on the surface of an axisymmetric body. The accuracy is estimated by comparing the results with those of a numerical finite-difference calculation of the flow past bodies of various shapes. Similar similarity relations were previously obtained in [1] for the plane of symmetry of a blunt body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–118, November–December, 1991.The authors are grateful to G. A. Tirskii for his interest in their work.     

Viscous shock layer near the stagnation point on a rotating body with unsteady injection and surface cooling

Unsteady supersonic flow regimes in the neighborhood of a stagnation point are investigated on the basis of a system of viscous shock layer equations [10] containing all the terms of the Euler equations and the boundary layer equations. An analytic solution of the unsteady equations valid near the surface of the body is found in the case of strong injection. The unsteady equations of the viscous shock layer are solved numerically on the basis of a divergent implicit scheme of the second order of approximation across the shock layer, using Newtonian linearization and vector sweep methods with allowance for the boundary relations on the surface of the body and at the isolated bow shock. Certain calculation results illustrating the effect of injection, surface cooling, the swirl of the external flow and the angular velocity of the body on the structure of the steady and unsteady viscous shock layer are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 114–122, September–October, 1987.     

Onsager reciprocity relation for rarefied gas flow in a laser radiation field

The Onsager relations are established in general form on the basis of the fundamental properties of the transport equations describing the motion of a rarefied gas in a laser radiation field. Expressions are obtained for the transport coefficient corresponding to the lightinduced drift effect and for the cross coefficient. The relation between them is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–167, January–February, 1991.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.     

Elasticity-theoretic plane problem for an anisotropic body subject to an electrical effect

The elastic properties of the body are assumed inseparable from its electrical properties (piezoelectric effect). The static problem is considered for an infinitely long homogeneous rod under the action of a plane system of forces or a lengthwise uniform distribution of electric field potential. The general equations of theory of elasticity and of electrical field theory, together with the piezoelectric relationships, are used. Conditions on the material parameters are obtained, under which a plane electric field and a plane deformation state appear in the body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 2, pp. 96–103. March–April, 1970.     

Integrals of Motion of an Incompressible Fluid Occupying the Entire Space

This paper studies integral relations to which the solutions of the Navier–Stokes equations or Euler equations satisfy in the case of fluids filling the entire threedimensional space. The existence of these relations is due to a rapid decrease of the velocity field at infinity (but not too rapid in order that the required asymptotic forms are reproduced with time). Of special interest are the integrals of motion whose density depends quadratically on the velocities or their derivative with respect to the coordinates. Such integrals (conservation laws) for the Navier–Stokes equations were recently found by Dobrokhotov and Shafarevich. In the present paper, new conservation laws are obtained, which are quadratic in the derivatives of the velocity and lead to identities that link the averaged and pulsation characteristics of ree turbulent flows.     

Nonresonance parametric interactions of surface waves in isotropic solid bodies

A solution in parametric approximation is given of the nonlinear interaction problem of Rayleigh surface waves propagating in a solid body with given elastic fields. Shortened equations that govern the modulation effect of the surface waves, and also expressions for the modulation index in terms of the third-order elasticity constant, are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–172, July–August, 1973.     

Investigation of an Electromagnetic Pulse Generated by a System on a Standard Spacecraft

Results on generation of an electromagnetic pulse on a spacecraft under the action of X-ray and gamma radiation are described. The computational technology used is based on a hierarchical system of mathematical models constructed on a system of the Maxwell-Vlasov equations and spacecraft models that rather accurately describe all physical processes typical of origination of secondary electromagnetic fields and the object geometry. It is shown that polarization components of the electric field, which are directed normal to irradiated surfaces, depend weakly on geometric factors and are mainly determined by the photon radiation flux density. Formation of the magnetic field is determined by the dynamics of variation of the first derivative of the dipole moment of the electron layer formed owing to emission of particles under the action of ionization radiation and depends on the object shape, characteristic size of the irradiated surface, and spacecraft attitude.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 3–13, September–October, 2005.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

轴向运动导电薄板磁弹性耦合动力学理论模型

针对磁场环境中轴向运动导电薄板的动力学理论建模问题进行研究,得到较为完备的磁弹性耦合振动基本方程及相应的补充关系式。在考虑几何非线性效应下,给出薄板运动的动能、应变能以及外力虚功的表达式。应用哈密顿变分原理,推得磁场中轴向运动薄板的非线性磁弹性耦合振动方程,并得到力和位移满足的边界条件。基于麦克斯威尔电磁场方程,并考虑相应的电磁本构关系和电磁边界条件,推得任意磁场环境中轴向运动导电薄板满足的电动力学方程和所受电磁力表达式。分别针对纵向磁场环境、横向磁场环境、条形板等具体情形,给出了振动方程、电动力学方程和电磁力的简化形式。所得结果,可为此类问题的进一步求解和分析提供理论参考。     

Allowing for Rotations about the Normal in Nonlinear Theories of Shells

Consideration is given to three versions of nonlinear strain–displacement relations in the case of small strains and moderately small angles of rotation: (i) relations that neglect rotations about the normal in conformity with the hypotheses of the Donnel–Mushtary–Vlasov theory; (ii) relations, derived from the elasticity equations using Novozhilov's tensor, that exactly allow for rotations; and (iii) relations, proposed by Sanders, that allow for rotations but neglect shear strains. These versions are compared by comparing the solutions of the stability problem for a corrugated cylindrical shell. It is established that the critical loads are close when rotations are allowed for exactly and when Sanders' technique is used     

Degeneration of an isotropic random field of electric charge pulsations in electrodynamics

The conditions under which an isotropic field of electric pulsations can exist in an electrically charged medium are indicated, with allowance in Ohm's law for the convection and diffusion of charged particles and their drift in the electric field. Mean parameter distributions are found for isotropic random fields and equations are obtained for correlation moments containing electric pulsations. The equations are analyzed with respect to the two-point correlations between the pulsations in the electric charge densities (the limit of single-point correlations is reached, invariant relations are obtained, and particular solutions are constructed). The degeneration laws of the isotropic fields of the electric parameters as a result of diffusion and drift. processes are found. Field degeneration due only to drift particle motion is studied under arbitrary initial conditions. Such field degeneration if there is no diffusion mechanism is a fundamental feature of turbulent electro-hydrodynamic motions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–47, January–February, 1987.The authors thank V. R. Kuznetsov for his useful discussion of the paper.     

Nonstationary conducting free flow in a transverse magnetic field

In magnetohydrodynamic flow the viscous friction at the walls can be substantial. The role of viscous friction can be considerably reduced by using a free or a semirestricted flow of the conducting fluid. Nonstationary phenomena in one-dimensional motion of a free plane incompressible fluid flow in a transverse magnetic field are examined. The narrow sides of the flow come into contact with the sectional electrodes connected through external circuits with an active-inductive load. The magnetic Reynolds number and the magnetody-dynamic interaction parameter are assumed to be large. When the electric field due to electromagnetic induction in the channel is much smaller than the field due to the external circuits, the problem can be reduced to the characteristic Cauchy problem for a quasilinear hyperbolic system of first-order equations which can be solved by the method of characteristics using a computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 34–39, July–August, 1970.     

Boundary integral equations for 2D elasticity and its application in discrete dislocation dynamics simulation in finite body: 1. General theory

A unified approach, originating from Cauchy integral theorem, is presented to derive boundary integral equations for two dimensional elasticity problems. Several sets of boundary integral equations are derived and their relations are revealed. Explicit expressions for materials with different symmetry planes are listed. Special attention is given to the formulation that is based on the tractions and the tangential derivatives of displacements along solid boundary, since its integral kernels have the weakest singularities. The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary, without involving the linear superposition technique that was often used in the literature. Its application in simulating discrete dislocation motion in a finite solid body is discussed.