Development of a four-parameter phenomenological model for the nonlinear viscoelastic behaviour of magnetorheological gels

Magnetorheological gel (MRG) excels in the material properties in term of adjustability and sedimentation performance, which could upgrade the performances of the current magnetorheological fluid based adjustable devices for structural control and vibration mitigation. However, the characterization and modelling of the stress-strain hysteresis responses of MRG has not been reported in the past, which are fundamental steps towards engineering applications. In this study, the stress-strain hysteresis of polyurethane based MRG sample with 60% carbonyl iron particle weight fraction was characterized under sinusoidal shear excitations with broad ranges of strain amplitude (5%–100%), excitation frequency (0.1 Hz–2 Hz) and magnetic fields (0–0.91 T). Significant stress overshooting phenomenon were observed under the application of low magnetic fields (0.27 T). A structurally-simple and accurate phenomenological model has been established to capture this unique nonlinearity. By validating the experimental results, the proposed model accurately predicts the hysteretic behaviour and the overshoot of the MRG under the excitation scenarios and the magnetic fields considered. Finally, the support vector machine (SVM) was implemented to provide the solution to the model generalization. The SVM-assisted model showed good agreement with the experimental data and can benefit the efficiency and viability in developing controllable MRG-based devices and system.