Multiscale modeling and simulation of magneto-active elastomers based on experimental data

In this contribution, we present a framework for the multiscale modeling and simulation of magneto-active elastomers (MAEs). It enables us to consider these materials on the microscopic scale, where the heterogeneous microstructure consisting of magnetizable particles and elastomer matrix is explicitly resolved, as well as the macroscopic scale, where the MAE is considered to be a homogeneous magneto-active body. On both scales, a general continuum formulation of the coupled magneto-mechanical boundary value problem is applied and the finite element method is used to solve the governing equations. Starting with an experimental characterization of the individual constituents, i.e. particles and matrix, microscopic constitutive models for both are formulated and adjusted to the experimental data separately. With that, properties of MAEs resulting from the microscopic constitutive behavior can be captured within the presented modeling approach. Secondly, to discuss general macroscopic properties of magnetically soft and hard MAEs, a computational homogenization scheme is used to calculate the composites’ effective behavior for different geometrical arrangements of the particles on the microscale. Finally, the calculated effective response of a magnetically soft composite system is used to identify the parameters of a macroscopic magneto-elastic model. Using the calibrated model, the behavior of macroscopic MAEs is simulated for different sample geometries.