Modeling the non-linear rheological behavior of magnetorheological gel using a computationally efficient model

Magnetorheological (MR) gel is a novel generation of smart MR material, which has the inherent hysteretic properties and strain stiffening behaviors that are dependent on applied excitation, i.e. magnetic field. The main challenge for the application of the MR gel is the accurate reproduction of the above characteristics by a computationally efficient model that can predict the dynamic stress-strain/rate responses. In this work, parametric modeling on the non-linear rheological behavior of MR gel is conducted. Firstly, a composite MR gel sample was developed by dispersing carbon iron particles into the polyurethane matrix. The dynamic stress-strain/rate responses of the MR gel are obtained using a commercial rheometer with strain-controlled mode under harmonic excitation with frequencies of 0.1 Hz, 5 Hz and 15 Hz and current levels of 1 A and 2 A at a fixed amplitude of 10%. Following a mini-review on the available mathematical models, the experimental data is utilized to fit into the models to find the best candidate utilizing a genetic algorithm. Then, a statistical analysis is conducted to evaluate the model's performance. The non-symmetrical Bouc-Wen model outperforms all other models in reproducing the non-linear behavior of MR gel. Finally, the parameter sensitivity analysis is employed to simplify the non-symmetrical Bouc-Wen model and then the parameter generalization is conducted and verified for the modified non-symmetrical Bouc-Wen model.