A finite element model for coupled 3D transient electromagnetic and structural dynamics problems

This paper develops a framework for coupling transient electromagnetic (EM) and dynamic mechanical (ME) fields to predict the evolution of electrical and magnetic fields and their fluxes in a vibrating substrate undergoing finite deformation. To achieve coupling between fields the governing equations are solved in the time domain. A Lagrangian description is invoked, in which the coupling scheme maps Maxwell’s equations from spatial to material coordinates in the reference configuration. Physical variables in the Maxwell’s equations are written in terms of a scalar potential and vector potentials. Non-uniqueness in the reduced set of equations is overcome through the introduction of a gauge condition. Selected features of the code are validated using existing solutions in the literature, as well as comparison with results of simulations with commercial software. Subsequently, two coupled simulations featuring EM fields excited by steady-state and transient electric current source in dynamically vibrating conducting media are studied.