Magnetorheological elastomer (MRE) is a kind of smart material prepared by filling magnetic particles into polymer matrix. Under the action of magnetic field, MRE exhibits instantaneous and reversible modulus magnetic stiffening effect. Due to this property, a great application prospect is shown for MRE in vibration control, soft robotics, acoustic metamaterials and other fields. Similar to filler rubbers, an obvious stress softening phenomenon (Mullins effect) exists in the loading and unloading of MRE. The softening phenomenon is an indispensable part of the mechanical behavior evolution of MRE. At present, most studies on the theoretical analysis of MRE focus on the magnetic stiffening behavior of the modulus, but few studies on the evolution law of stress softening. In addition, experimental results show that, besides the Mullins effect, an obvious magnetic dependent nonlinear viscoelastic behavior is exhibited for MRE. After the literature review, it is realized that the Mullins effect and the nonlinear viscoelastic behavior of filler rubbers are often studied independently. However, for practical application, the aforementioned inelastic behaviors of MRE occur simultaneously in a coupled manner. Therefore, a constitutive model which incorporates the Mullins effect and the magnetic dependent nonlinear viscoelastic behavior of MRE is needed.
In this work, firstly, MRE based on silicone rubber were prepared. Then, quasi-static loading-unloading tests, dynamic loading-unloading tests and stress relaxation tests were carried out for MRE. The results of the dynamic loading-unloading tests and stress relaxation tests are shown in Figure 1 and 2, respectively. Obviously, the experimental results show that MRE has obvious inelastic behaviors as mentioned above. Afterwards, a constitutive model used to describe these inelastic behaviors of MRE is established based on the theory of continuum mechanics. Following, the parameter identification of the model is conducted. The comparison between simulation results and experimental results is shown in Figure 1 and 2. Clearly, the simulation results fit well with the experimental results. The R-squared values of the dynamic loading-unloading tests and stress relaxation tests were 0.991 and 0.987, respectively. This indicates that the theoretical model can perfectly describe Mullins effect and nonlinear viscoelasticity behavior of MRE. Finally, this work can provide guidance for the design of MRE-based applications.

magnetorheological elastomer,Mullins effect,Magnetic-dependent nonlinear viscoelasticity,Constitutive modelling