Curing spurious magneto-mechanical coupling in soft non-magnetic materials

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 cures for the issue under consideration that completely 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.