Stability of anisotropic magnetorheological elastomers in finite deformations: A micromechanical approach

We study the stability of magnetorheological elastomers (MREs) undergoing finite deformations in the presence of a magnetic field and derive a general condition for the onset of macroscopic instabilities. In particular, we focus on anisotropic MREs with magnetoactive particles that are aligned along a particular direction, forming chain-like structures. We idealize the microstructure of such anisotropic magnetosensitive elastomers as a multilayered structure and derive an analytical model for the behavior of these materials. The analytical model, together with the derived condition for the onset of instabilities, is used to investigate the influence of magnetomechanical finite deformations on the stability of the anisotropic MREs. While the formulation is developed for generic hyperelastic magnetosensitive elastomers, the results are presented for a special class of soft materials incorporating a neo-Hookean hyperelastic response. The influence of material properties and loading conditions is investigated, providing a detailed picture of the possible failure modes.