Magnetoactive elastomers with periodic and random microstructures

We investigate the behavior of magnetoactive elastomers (MAEs) with periodic and random distributions of circular and elliptical fibers. For the MAEs with periodic microstructures, we develop finite element models and determine the local fields as well as the effective properties of MAEs with rectangular and quasi-hexagonal unit cells. For the MAEs with random microstructures, we derive a closed-form expression for the effective response making use of a recently developed theory (Ponte Castañeda and Galipeau, 2011). In particular, we determine the responses to pure shear loading in the presence of a magnetic field, both of which are aligned with the geometric axes of the fibers, and examine the roles of the deformation, concentration, particle shape, and distribution on the magnetostriction, actuation stress, and the magnetically induced stiffness of the composite. We show that the coupling effects are of second order in the concentration. This is consistent with the fact that these effects are primarily the result of the interaction between inclusions. We also demonstrate explicitly that the magnetomechanical coupling of these MAEs, when subjected to aligned loading conditions, depends not only on the magnetic susceptibility, but also, crucially, on its derivative with respect to the deformation. As a consequence, we find that the magnetoelastic effects may be quite different, even for composites with similar effective susceptibilities.