Mathematical Modeling of the Motion of Metal Conductors in an Electromagnetic Field Taken Into Account of the Presence of Different Phases of the Accelerated Matter

The problem of mathematical modeling of the acceleration of metal conductors in an electromagnetic field in a two-dimensional approximation has been solved. Mathematical models are presented to describe the motion of bodies using Lagrangian and Eulerian coordinates using the constitutive relations of a thermoelastoplastic body (for the case of large deformations) and a viscous compressible fluid (gas). A mathematical model is presented that allows us to describe the movement of a body taking into account the presence of different phases of matter in it at one point in time. The model explicitly identifies the transition phase from solid to liquid; for this phase, both constitutive relations are taken into account, taken with appropriate weights. Numerical algorithms based on the finite element method have been constructed. The presented model is used to solve the problem of accelerating an aluminum cylindrical shell to a velocity of about 8 km/s. The calculation results are demonstrated, and individual characteristics are compared with known calculated and experimental results.