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Benchmark for the coupled magneto-mechanical boundary value problem in magneto-active elastomers

P. Metsch, R. Schiedung, I. Steinbach, M. Kästner.

Materials, MDPI AG,, 14, 2380, (2021)

Setup for the proposed benchmark problem: top-view on the center plane of the sample and a magnification of the two magnetizable particles embedded into its center—the global coordinate system is indicated within the magnified area. The problem is symmetric with respect to the depicted x1-x2-plane and the sample is loaded with an external magnetic field Bext of varying angle α—for the mechanical boundary conditions.

Abstract
Within this contribution, a novel benchmark problem for the coupled magneto-mechanical boundary value problem in magneto-active elastomers is presented. Being derived from experimental analysis of magnetically induced interactions in these materials, the problem under investigation allows us to validate different modeling strategies by means of a simple setup with only a few influencing factors. Here, results of a sharp-interface Lagrangian finite element framework and a diffuse-interface Eulerian approach based on the application of a spectral solver on a fixed grid are compared for the simplified two-dimensional as well as the general three-dimensional case. After influences of different boundary conditions and the sample size are analyzed, the results of both strategies are examined: for the material models under consideration, a good agreement of them is found, while all discrepancies can be ascribed to well-known effects described in the literature. Thus, the benchmark problem can be seen as a basis for future comparisons with both other modeling strategies and more elaborate material models.

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