A mathematical model of description and a method for determining the thermostressed state of non-ferromagnetic electroconductive bodies under the influence of external unsteady electromagnetic fields of pulsed type are proposed. Such fields have the character of a regime with amplitude modulation under the action of pulse modulated signal and are widely used in technologies of magnetic pulsed processing electroconductive materials. This model is the development of well-known models for quasi-steady and pulsed electromagnetic fields. As an example, the results of investigation of the thermomechanical behavior of solid and hollow cylinders under the influence of electromagnetic pulse are given.

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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...

This paper presents a mathematical and numerical model developed for coupled time-dependent electromagnetic, temperature and mechanical processes, which occur in polarizable and magnetizable electroconductive solids subjected to an electromagnetic field generated by external currents. The electromagnetic field in the solid and in its surroundings is described by Maxwell's equations. The temperature variation in the solid is governed by the classical heat-transfer equation. To predict the stress-strain state of the solid, a nonisothermal theory for thermoplastic materials is used. The model takes into account the temperature dependence of all material coefficients and the nonlinear dependence of the induction on the strength of both the electrical and the magnetic fields. The problem is solved by a finite-element method and a unified set of single time-step algorithms. As an example, the process of high-temperature induction heating of a finite cylinder is considered.