Benchmark for the Coupled Magneto-Mechanical Boundary Value Problem in Magneto-Active Elastomers

Research output: Contribution to journalResearch articleContributedpeer-review



Within this contribution, a novel benchmark problem for the coupled magneto-mechanical boundary value problem in magneto-active elastomers is presented. Being derived from an 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.


Original languageEnglish
Article number2380
Number of pages11
Volume14 (2021)
Issue number9
Publication statusPublished - 2021

External IDs

Scopus 85105681944
ORCID /0000-0003-2645-6770/work/142235673
ORCID /0000-0003-3358-1545/work/142237127



  • magneto-active elastomers, benchmark, strong magneto-mechanical coupling