Effect of magnetomechanical hysteresis on the field-induced oscillations of particles in a magnetoactive elastomer

A model is proposed for mesoscopic dynamics of a magnetoactive elastomer (MAE). The elementary cell comprises two spherical linearly magnetizing particles embedded in an elastoviscous medium of the Kelvin type. The forced oscillations of this system induced by an ac field are studied. Under a static field, this system is prone to bistability that entails the magnetomechanical hysteresis: being initially separated by a finite distance, the particles move jumplike to a tight contact. The initial configuration is restored under a field that is lower than that of its onset. It is shown that in the oscillatory regime, depending on the material parameters of the system and the characteristics of the oscillating field, the pair may display steady cycles of several types. Upon enhancing the frequency, the occurrence of the particle contact may be blocked or, on the contrary, they might be "quenched" in the vicinity of each other. The behavior of the pair at a high frequency is analyzed. Estimations are given for the energy dissipation caused by the hysteretic regimes of the particle oscillations.