A quantitative comparison of two‐ and three‐dimensional modeling approaches for magnetorheological elastomers

In this contribution, a qualitative and quantitative comparison of two‐ and three‐dimensional finite element simulations for magneto‐rheological elastomers is presented. Based on a continuum formulation, a microscopic modeling approach is applied. To understand basic deformation mechanisms, the differences between simplified two‐dimensional and realistic three‐dimensional simulations are initially shown for the example of chain‐like structures with different arrangements of the particles. Subsequently, a numerical homogenization is used to connect microscopic and macroscopic quantities: different two‐ and three‐dimensional microstructures are compared with regard to their effective magneto‐mechanical behavior.