  The present work is concerned with the issue of spurious coupling effects
that are pervasive in fully coupled magneto-mechanical finite element
simulations involving very soft non-magnetic or air-like media. We first
address the characterization of the spurious magneto-mechanical effects and
their intuitive interpretation based on energy considerations. Then, as main
contribution, we propose two new ways to prune the undesired spurious
magneto-mechanical coupling in non-magnetic media. The proposed methods are
compared with established methods in the context of magnetic bodies embedded in
(i) air or vacuum and (ii) very soft elastic non-magnetic media. The comparison
shows that the proposed approaches are accurate and effective. They,
furthermore, allow for a consistent linearization of the coupled boundary value
problems, which is crucial for the simulation of compliant structures. For
reproducibility and accessibility of the proposed methods, we provide our
implementations with Netgen/NGSolve as well as all codes necessary for the
reproduction of our results as supplementary material.
