Magnetoelastic instabilities in soft laminates with ferromagnetic hyperelastic phases

We investigate the microscopic and macroscopic instabilities developing in magnetoactive elastomer (MAE) composites undergoing large deformations in the presence of an external magnetic field. In particular, we consider the MAEs with bi-phasic layered microstructure, with phases exhibiting ferromagnetic behavior. We derive an explicit expression for the magnetic field-induced deformation of MAEs with hyperelastic phases. To perform the magnetoelastic instability analysis, we employ the small-amplitude perturbations superimposed on finite deformations in the presence of the magnetic field. We examine the interplay between the macroscopic and microscopic instabilities. We find that the layered MAEs can develop microscopic instability with antisymmetric buckling modes, in addition to the classical symmetric mode. Notably, the antisymmetric microscopic instability mode does not appear in a purely mechanical scenario (when a magnetic field is absent). Furthermore, our analysis reveals that the wavelength of buckling patterns is highly tunable by the applied magnetic field, and by the properties and volume fractions of the phases. Our findings provide the information for designing materials with reconfigurable microstructures. This material ability can be used to actively tune the behavior of materials by a remotely applied magnetic field. The results can be utilized in designing tunable acoustic metamaterials, soft actuators, sensors, and shape morphing devices.