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

Abstract

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.

A Unified Theoretical Modeling Framework for Soft and Hard Magnetorheological Elastomers

“…A quantitative comparison of the performance of different modeling approaches for the surrounding air is drawn in a recent paper (Rambausek et al, 2022). Two additional promising approaches, not discussed here, have been proposed only recently in Rambausek and Schöberl (2023), where a proper treatment of the Maxwell stress at the interface between the magnetoelastic solid and the air allows to eliminate the spurious modes present in such problems and allow for very good convergence. Another potential solution to the problem could be the use of meshfree methods (see for instance Kumar et al (2019)).…”