Modified Bouc−Wen model based on a fractional derivative for describing the hysteretic characteristics of magnetorheological elastomers

As a new type of magnetic sensitivity smart material, magnetorheological elastomers showing a good magnetorheological effect have been broadly applied in the field of intelligent structures and devices. A viscoelastic fractional derivative element was introduced into the stress−strain relationship of magnetorheological elastomers based on the Bouc−Wen model to accurately characterize the mechanical behavior of magnetorheological elastomers under a wide range of strain amplitude, excitation frequency, and magnetic field and to make it better applied in engineering practice. Further, a modified Bouc−Wen model based on a fractional derivative was proposed to describe the hysteresis characteristics of magnetorheological elastomers. The Bouc−Wen model has good universality and can accurately describe the hysteretic characteristics of the magnetorheological elastomer’s nonlinear viscoelastic region, but it cannot accurately simulate magneto-viscoelasticity and frequency dependence. The fractional derivative can express this characteristic with fewer parameters and higher accuracy. The micromorphology characteristics of isotropic and anisotropic magnetorheological elastomers were analyzed, and the performance tests of the magnetorheological elastomers were conducted. The storage and loss modulus of the magnetorheological elastomers initially remain unchanged and then decrease with an increase in strain amplitude (0–100%). Moreover, the storage and loss modulus of the magnetorheological elastomers increase with an increase in frequency (0–100 Hz) and magnetic flux density (0–545 mT). On this basis, a modified Bouc−Wen model was proposed based on the fractional derivative. The simulation model was established using the Simulink software, and the fractional derivative part of the modified model was approximately calculated using the Oustaloup filter algorithm. The effectiveness of the modified model was verified through a comparative analysis. The fitness values of simulation and experimental data under different loading conditions are higher than 98%. Results show that the modified Bouc−Wen model can accurately simulate the stress−strain hysteresis loops of the magnetorheological elastomers, and the fitting accuracy is significantly improved compared with that of the Bouc−Wen model. The modified model is accurate and effective in a wide range of strain amplitudes, frequencies, and magnetic fields, which can lay a foundation for the engineering application of magnetorheological elastomers.