Mathematical models of thermomechanics of magnetizable and polarizable electrically conducting bodies subject to quasisteady electromagnetic radiation

Abstract

We give a brief survey of recent research on the problems of mathematical modeling of the thermomechanical behavior of deformable bodies with different electrical conductivity, magnetizability, and polarizability subject to a quasisteady electromagnetic field in the radio and infrared frequency ranges.The joint study of mechanical, thermal, and electromagnetic processes in electrically conducting bodies has attracted the attention of researchers because of the wide practical application of electromagnetic fields over the past few decades in the manufacture and processing of structural elements and devices made of traditional and new electromagnetic materials [54,55]. To construct rational regimes for such processes or use of equipment that functions subject to electromagnetic loads, it is necessary to create a method of mathematical modeling and effective methods of determining the thermostressed state of bodies of arbitrarily electrical conductivity that are magnetizable and polarizable and subject to external electromagnetic fields, in particular the quasistatic fields [36,40] that are widely applied in engineering practice.The system of initial equations of the physico-mathematical model for determining the thermostressed state of electrically conducting bodies subject to an electromagnetic field taking account of the interaction of mechanical, thermal, and electromagnetic processes includes the equations of electrodynamics and thermomechanics with heat sources and bulk force factors (ponderomotor forces and moments) caused by the electromagnetic field. Such a system is coupled and nonlinear, when account is taken of the generalized Ohm's law, the relations between the inductions and intensities of the electric and magnetic fields for arbitrarily moving conducting media that can be magnetized and polarized [36,42], the expressions for the force factors and heat emission [34,42], the coupling of the strain and temperature fields [33], and the temperature dependence of the characteristics of the material [10,33].Since rigid bodies may differ significantly in electrophysical properties and the general theory of interaction of an electromagnetic field with a material continuum mentioned above is rather complicated, it is vital to construct specially designed variants of the theory of interaction for smaller classes of materials by taking account of the specifics of their characteristic properties in processes involving electrical conduction, magnetization and polarization as functions of the amplitude-frequency characteristics of the electromagnetic field [ 10,34].In a number of studies in determining the thermostressed state of electrically conducting nonferromagnetic unpolarized bodies in a quasistatic and nonstationary (in particular, pulsing) electromagnetic field, the effect of this field on the processes of heat conduction and strain is taken into account through the Joule heat emission and the ponderomotor forces, while the effect of motion of the medium on the current is assumed unimportant [40,55].In this...

Mathematical modeling and optimization of the physicomechanical processes in electrically conducting bodies due to a quasisteady electromagnetic field

“…For a quasisteady electromagnetic field (1), (2), applying a corresponding Fourier series expansion with respect to time and taking account of the relations (7), (8), we obtain the following presentations of the functions j.., H.., E.., B.., D.. in the body [4,8]: where the complex amplitudes ~ 2k+~ (r, t) are slowly time-varying functions, which we assume constant within the limits of each individual periodf.. They are interconnected by the well-known Maxwell equations for the harmonic approximation [4,17].…”

“…As a consequence of the structure of the expressions just obtained for the paramet ........... ,~,~,.~,,~ ,.~ electromagnetic field, the thermal emission (5) and ponderomotor forces (6) have the form of a sum of terms that are slowly varying in time QO), F o) (corresponding to averaging over a period) and quasisteady terms Q(2), F(Z) [4,17].…”

“…We determine the slowly time-varying components of the temperature and stresses T ~ G o) in the quasisteady formulation, neglecting the coupling of the strain and temperature fields [4], and we determine T (2), (~ (2) in the quasisteady presentation…”

“…To control the heating in the required direction, effective application can be made of a current amplitude JA (r, t) that varies only slightly over a period f. of the electromagnetic wave (or the intensity of the electric or magnetic field) or the intensity of external radiation I~ ~ (r, t, s) incident on the body. The mode of time-variation of such an amplitude, which under the prescribed heating conditions provides an optimally low level of stresses in the body, can be set up by applying the method discussed in [4,17]. Here the restriction of quasisteadiness (2) is realized by conditions of moment type.…”

Some problems of mathematical modeling in thermomechanics of bodies of various transparencies subjected to thermal irradiation

“…Ya. Burak [11,16,19]. In these models, it is assumed that, with respect to a body, an EMF is an external action, whose influence on heat conduction and deformation processes are taken into account in thermoelasticity equations through the factors of action, namely volume heat sources (heat release, specifically the Joule heat and heat released as a result of depolarization and demagnetization) and volume (ponderomotive) forces of the action of an EMF on charges and currents, including polarization ones.…”