Algorithmic formulation and numerical implementation of coupled electromagnetic-inelastic continuum models for electromagnetic metal forming

Abstract

Electromagnetic metal forming is a contact-free high-speed forming process. The deformation of the workpiece is driven by a material body force, the Lorentz force, that results from the interaction of a pulsed magnetic field with eddy currents induced in the workpiece by the magnetic field itself. The purpose of this work is to present a fully-coupled 3D simulation of the process. 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 equations under quasistatic conditions. Their numerical solution in 3D requires particular arrangements due to a reduced regularity at material interfaces. Hence, Nedelec 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.