Mathematical and computational modeling of electromagnetic field propagation and magnetic-elastic-plastic deformation of technological systems. A review

The article considers the state of the problem in relation to mathematical and computational modeling of the processes of electromagnetic field propagation and the deformation of technological systems caused by it. The electromagnetic field is an integral factor in the functioning of various technical and technological systems. The effect of the electromagnetic field on bodies and continuum differs depending on their properties. In the case of action on electrically conductive bodies and continuum, the main role is played by the force effect (due to the emerging electromagnetic forces) and the effect on temperature changes (due to the emerging common sources of heat dissipation according to the Joule-Lenz law). The force effect of the electromagnetic field is used in a huge number of technological processes. It is possible to note the processes of geological exploration (due to the pulses of the electromagnetic field), metallurgical processes (here the electromagnetic field is used, for example, for mixing melts), processing processes. A large class of machining technological operations, which has the general name electromagnetic forming, uses electromagnetic forces for irreversible shape change of workpieces due to the occurrence of zones of plastic deformation. In this case, both the workpiece and the source of the electromagnetic field - the inductor (solenoid) - are subjected to force action. When developing technological operations for electromagnetic forming, it is very necessary to ensure both the required degree of deformation of the workpiece and the performance of the inductor, which is determined by its strength. These needs necessitate mathematical and computational modeling, which allows you to determine rational quantitative values of design and operational parameters. Such modeling should be based on the relevant theoretical models regarding the propagation of the electromagnetic field and the elastic-plastic deformation caused by it. In the case of considering technological systems of electromagnetic forming, it is permissible to use a macroscopic approach to describe the propagation of the electromagnetic field, and the description of deformation processes can be based on the principles of the theory of electro-magneto-elasticity. The modern approach to mathematical modeling and computational analysis in electromagnetic forming systems requires the use of numerical methods, the most widely used of which is the finite element method due to its versatility. The finite element method in this case allows you to simulate the almost real geometry of the system and take into account most of the design and operational features associated with the properties of materials, contact interaction conditions, etc.