  For an accurate description of electromagneto-thermomechanical systems,
electromagnetic fields need to be described in a Eulerian frame, whereby the
thermomechanics is solved in a Lagrangean frame. It is possible to map the
Eulerian frame to the current placement of the matter and the Lagrangean frame
to a reference placement. We present a rigorous and thermodynamically
consistent derivation of governing equations for fully coupled
electromagneto-thermomechanical systems properly handling finite deformations.
A clear separation of the different frames is necessary. There are various
attempts to formulate electromagnetism in the Lagrangean frame, or even to
compute all fields in the current placement. Both formulations are challenging
and heavily discussed in the literature. In this work, we propose another
solution scheme that exploits the capabilities of advanced computational tools.
Instead of amending the formulation, we can solve thermomechanics in the
Lagrangean frame and electromagnetism in the Eulerian frame and manage the
interaction between the fields. The approach is similar to its analog in fluid
structure interaction, but more challenging because the field equations in
electromagnetism must also be solved within the solid body while following
their own different set of transformation rules. We additionally present a
mesh-morphing algorithm necessary to accommodate finite deformations to solve
the electromagnetic fields outside of the material body. We illustrate the use
of the new formulation by developing an open-source implementation using the
FEniCS package and applying this implementation to several engineering problems
in electromagnetic structure interaction undergoing large deformations.
