Field-stiffening effect of magneto-rheological elastomers

Magneto-rheological elastomers (MREs) are a class of soft active materials known for their tunable stiffness. Dispersed with magnetic particles, these polymer-based composites tend to be stiffer under a magnetic field. Such a stiffening effect is often attributed to the magnetic interaction among filler particles, but the well-acknowledged dipole-interaction model fails to explain the stiffening effect in tension/compression, which was observed in experiments. Other mechanisms, such as the effect of non-affine deformation, have been proposed, but there is no conclusive evidence on the dominating mechanism for the field-stiffening effect. This paper investigates various filler-chain structures, and seeks to identify the ultimate origin of the field-stiffening effect in MREs. Two different methods are used for cross verification: a dipole-interaction model and a finite-element simulation based on continuum field theories. This paper studies both the shear and axial deformation of the material, with a magnetic field applied in the particle-chain direction. It is found that while the magnetic interaction between particles is indeed the major cause of the stiffening effect, the wavy chain structure is the key to the modulus increase. Besides, chain–chain interaction and non-affine deformation are shown to be insignificant. In addition, the dependence of the stiffening effect on filler concentration is calculated, and the results qualitatively agree with experimental observations. The models also predict some interesting results that could be easily verified by future experiments.