A nonlinear magnetorheological elastomer model based on fractional viscoelasticity, magnetic dipole interactions, and adaptive smooth Coulomb friction

Abstract Magnetorheological elastomers (MRE) are emerging as smart materials for application in the field of the intelligent devices and structures. In order to design MRE-based vibration control devices, their dynamic behavior should be mathematically represented with respect to broadband excitation frequency, amplitude, and the applied magnetic field. In this study, a nonlinear MRE model consisting of three parts – a fractional viscoelasticity model, magnetic dipole model, and an adaptive smooth Coulomb friction model – is developed. The fractional Maxwell model with only three parameters was introduced to simulate the dynamic behavior of MRE in a wide frequency range. A magnetic interaction model for adjacent particles was investigated and the magnetic force corresponding to the particle volume was calculated. We found that the interaction force not only affects the shear modulus, but also affects slipping at the interface between the particle and matrix. The adaptive smooth Coulomb friction used to model the magnetic field-dependent properties of the MRE accurately described the behavior of the material over a wide range of amplitudes at different magnetic field strengths. The model parameters were estimated by a simple procedure and the proposed model was found to represent MRE characteristics accurately. Therefore, the new model is expected to be advantageous for designing MRE-based vibration devices.