Mesomechanical Response of a Soft Magnetic Elastomer to AC Magnetization

The behavior of a pair of magnetizable spherical particles embedded in a viscoelastic elastomer is studied for the case, where an AC magnetic field is applied along the center-to-center line of the particles. This system is considered as a small-scale (mesoscopic) structure element of a magnetorheological elastomer. Under a quasistatic cycle of the field, the system in question is prone to hysteretic behavior. Namely, the particles initially positioned well apart, at some finite field strength, fall onto one another (cluster) and reside in this state until the field decreases well below the value at which the cluster has been formed. Under dynamic cycling of the field, the viscous friction interferes with the particle displacement process and impedes the occurrence of the magnetodeformational hysteresis of the element. Starting from small-amplitude overdamped oscillations and enhancing the role of magnetic forces over viscous ones, we show how the anharmonicity of the system grows while it approaches the transition threshold, above which the dynamics of the element includes the cluster state. The dynamic hysteresis of magnetization that accompanies the mechanical oscillations of the particles is presented as well.