An arbitrary Lagrangian Eulerian approach to the three-dimensional simulation of electromagnetic forming

Electromagnetic metal forming is a contact-free high-speed forming process in which strain rates of more than 103 s−1 are achieved. The deformation of the workpiece is driven by the Lorentz force, a material body force, that results from the interaction of a pulsed magnetic field with eddy currents induced in the workpiece by the magnetic field itself. In this work, a coupled 3D simulation of this process is presented. For the mechanical structure a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The evolution of the electromagnetic fields is governed by Maxwell’s equations under quasi-static conditions. Their numerical solution in 3D requires particular arrangements due to problems connected with an adequate gauging of the fields. Hence, Nédélec elements are employed. Coupling between the thermomechanical and electromagnetic subsystems takes the form of the Lorentz force, the electromotive intensity, and the current geometry of the workpiece. A staggered scheme based on a Lagrangian mesh for the workpiece and an ALE formulation for the electromagnetic field is utilized to solve the coupled system, guaranteeing the efficiency and accuracy of the data transfer between the two meshes.