Two-particle element of a magnetorheological elastomer under a cyclic magnetic field

Abstract

The results of modelling the behaviour of a pair of magnetisable spherical particles embedded in a viscoelastic elastomer with Kelvin rheology are presented for the case, where an ac magnetic field is exerted along the intercenter line of the particles. This system is considered as a small-scale (mesoscopic) structure element of a magnetorheological elastomer. The system in question is known to be able for hysteretic behaviour under the quasistatic cycle of the field. The particles initially positioned well apart, at some finite field strength, fall onto one another (cluster) and dwell 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 the particle displacement process and impedes 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 magnetisation that accompanies the mechanical oscillations of the particles is presented as well.