The family of mathematical models to describe the metal conductors motion in an electromagnetic field

The modeling of metal conductors acceleration in an electromagnetic field in a two-dimensional approximation is executed. A family of mathematical models for describing the motion of a body is presented: a model of a thermoelastoplastic body (for the case of large deformations), a model of a viscous compressible liquid and a mixed model that includes two previous models for different phase states of matter. A mathematical model of electromagnetic processes is presented, which allows to ensure the flow of total currents along the cross-sections of conductors. Numerical algorithms based on the finite element method are presented. The described models are used to solve the problem of accelerating the aluminum cylindrical shell to a speed of about 8 km/s. The results obtained for different models were compared with each other, as well as with known calculated and experimental results published in the literature.