A universal rheological constitutive equation of magnetorheological fluids with a wide shear rate range

[Display omitted] •The proposed ELM model is a new universal rheological model for non-Newtonian fluids.•The ELM model captures both nonlinearities of MRFs in small and large shear rates.•Model splitting efficiently identifies the model parameters with a physical background.•The ELM model can be reduced to the Bingham and Papanastasious models.•Application to the magnetic effect modeling and design simulation demonstrated. As an intelligent material, the magnetorheological fluid (MRF) has increased use in various fields, e.g., the semi-active suspension of vehicles. However, the efficient utilization and optimization of MRFs depend on a reliable constitutive relationship over a wide shear rate range, which existing models cannot fully and satisfactorily explain. This paper proposes a new non-Newtonian fluid constitutive equation that combines exponential and linear terms to describe the general characteristics of MRFs to tackle this problem. An effective parameter identification approach is realized by adopting model splitting to reduce the dimension of the optimized parameter space combined with a reasonable initial guess. A well-designed experiment for a commercial MRF is conducted to verify the proposed constitutive equation, indicating an improvement in accuracy of approximately 43 % compared with the Herschel-Bulkley model and its capability to reveal the rheological behaviors of MRFs in the wide shear rate range of 0.3–30000 s−1. The high compatibility between the proposed model and the Bingham model is supported by the high correlation coefficients of the dynamic yield stress and viscosity coefficient identified by this model and the existing data processing method based on the Bingham model, 0.9949 and 0.9160, respectively. Owing to its decoupled parameter structure, the extension to a multivariable framework has been implemented to consider the magnetorheological effect with good agreement. Finally, the application of magnetorheological device design has demonstrated the versatility and capacity of the proposed model for developing and utilizing a new generation of MRFs.