Electromagnetic forming by distributed forces in magnetic and nonmagnetic materials

In this paper, we discuss the electromechanical force densities associated with pulsed electromagnetic fields in inhomogeneous, linear media with conductive losses, in the context of a process of shaping metal objects. We show that the conductivity and the gradients in permittivity and in permeability lead to volume forces, while jump discontinuities in permittivity and permeability lead to surface forces. These electromagnetic forces are assumed to act as volume (body) source densities in the elastodynamic equations and as surface source densities in the corresponding boundary conditions that govern the elastic motion of deformable matter. As an example, we apply the theory to the calculation of the elastic field in a hollow cylindrical object made of a conducting magnetic or nonmagnetic material. We compare the numerical results with those for the classical theory of elasticity with concentrated forces on the boundaries of the material as the source of the elastodynamic field.