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For an accurate description of electromagneto-thermomechanical systems,electromagnetic fields need to be described in a Eulerian frame, whereby thethermomechanics is solved in a Lagrangean frame. It is possible to map theEulerian frame to the current placement of the matter and the Lagrangean frameto a reference placement. We present a rigorous and thermodynamicallyconsistent derivation of governing equations for fully coupledelectromagneto-thermomechanical systems properly handling finite deformations.A clear separation of the different frames is necessary. There are variousattempts to formulate electromagnetism in the Lagrangean frame, or even tocompute all fields in the current placement. Both formulations are challengingand heavily discussed in the literature. In this work, we propose anothersolution scheme that exploits the capabilities of advanced computational tools.Instead of amending the formulation, we can solve thermomechanics in theLagrangean frame and electromagnetism in the Eulerian frame and manage theinteraction between the fields. The approach is similar to its analog in fluidstructure interaction, but more challenging because the field equations inelectromagnetism must also be solved within the solid body while followingtheir own different set of transformation rules. We additionally present amesh-morphing algorithm necessary to accommodate finite deformations to solvethe electromagnetic fields outside of the material body. We illustrate the useof the new formulation by developing an open-source implementation using theFEniCS package and applying this implementation to several engineering problemsin electromagnetic structure interaction undergoing large deformations.

Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations