Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers

Magnetorheological elastomers (MRE) are composite solids consisting of an elastomeric matrix and dispersed magnetic inclusions. Due to the composite nature of MREs, there is a demand for accurate techniques that allow for the determination of their effective properties. This task is complicated by the fact that the response of an MRE specimen is not only influenced by the properties of its constituents and the respective microscopic morphology, but also dependent on its shape. This is due to the fact that every MRE sample interacts with the magnetic fields it is exposed to and thus experiences shape-dependent boundary conditions. This makes it difficult to find adequate experimental procedures for material characterization. In the present contribution we analyze the effective response of several MRE specimens with respect to the individual impact of microscopic morphology and macroscopic shape. To closely link our investigations to experimental measurements we perform multiscale simulations of typical experimental scenarios in a two-dimensional setting. The underlying approach thereby fully resolves the magneto-mechanical problem on the specimen scale and accounts for the microscopic behavior via homogenization. In this way the approach allows for the multiscale computational characterization of magnetorheological elastomers with arbitrary shapes and microstructures. As prototype examples we analyze two-dimensional specimens with rectangular and elliptical shapes. Furthermore, we present a generic analytical approach to shape effects, which is based on magneto-mechanical tractions acting on the surface of MRE specimens. We show that the analytical approach is able to predict fundamental stress states and deformation trends, which were also observed in our numerical simulations.