Metsch Philipp, Schiedung Raphael, Steinbach Ingo, Kästner Markus
Institute of Solid Mechanics, Technische Universität Dresden, 01062 Dresden, Germany.
ICAMS, Ruhr-University Bochum, 44801 Bochum, Germany.
Materials (Basel). 2021 May 3;14(9):2380. doi: 10.3390/ma14092380.
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.
在本论文中，提出了一个关于磁活性弹性体中磁-机械耦合边值问题的新型基准问题。该问题源于对这些材料中磁感应相互作用的实验分析，通过一个仅包含少数影响因素的简单设置，使我们能够验证不同的建模策略。在此，针对简化的二维以及一般的三维情况，比较了基于在固定网格上应用谱求解器的尖锐界面拉格朗日有限元框架和扩散界面欧拉方法的结果。在分析了不同边界条件和样本尺寸的影响之后，对两种策略的结果进行了检验：对于所考虑的材料模型，发现它们具有良好的一致性，而所有差异都可归因于文献中描述的已知效应。因此，该基准问题可被视为未来与其他建模策略以及更精细材料模型进行比较的基础。
