Development of a field dependent Prandtl-Ishlinskii model for magnetorheological elastomers

Highlights: • Experimental characterizations of a magnetorheological elastomer (MRE) in the shear mode; • Formulation of the classical Prandtl-Ishlinskii (PI) model for predicting hysteretic stress-strain behavior of the MRE; • Verification of classical PI model using measured data under different loading conditions and magnetic field; • Generalization of the PI model. -- Abstract: Magnetorheological elastomers (MREs) offer real-time controllable stiffness and damping properties, and strong hysteresis in the stress-strain responses that depends on magnetic field intensity, strain amplitude and strain rate in a highly nonlinear manner. Prediction of hysteretic stress-strain behavior is essential for effective designs of controllable MRE-based devices. This study presents a stop operator-based Prandtl-Ishlinskii (PI) model for predicting nonlinear hysteresis properties of MREs as functions of the strain amplitude, excitation frequency and magnetic flux density. The stress-strain properties of a MRE fabricated with 40% volume fraction iron particles were experimentally characterized in the shear mode under broad ranges of strain amplitude (2.5–20%), excitation frequency (0.1–50 Hz) and magnetic flux densities (0–450 mT). Subsequently, a stop operator-based classical PI model was formulated considering only 10 hysteresis operators, which required identification of only four parameters. The validity of the classical PI model was assessed using the laboratory-measured data. The proposed classical model is further generalized to enable predictions of MRE dynamic behavior independent of the loading conditions, which would be beneficial for developments in controllable MRE-based adaptive devices. The results demonstrated that the generalized model could accurately characterize nonlinear hysteresis properties of the MRE under the ranges of loading conditions and magnetic field considered.