A unified physics-based continuum theory for magnetorheological fluid deformation: Implications in magnetorheological fluid-based brake applications

Magnetorheological (MR) fluids are smart composites that can exhibit reversible behavior changes and quickly transit from a liquid state to a nearly solid state when exposed to magnetic fields. Existing theories, such as the Herschel–Bulkley (H-B) model and artificial neural network, are frequently employed to describe the deformation of MR fluids; however, these are limited to certain modes of deformation and have lagged in the physical interpretation of magneto–mechanical interaction. To address the limitations, this study provides an in-depth investigation of MR fluid behavior, highlighting its non-Newtonian characteristics and the occurrence of a yielding phenomenon under finite deformation. A unified framework is developed to describe solid and fluid characteristics using classical continuum mechanics and Ericksen's seminal work consistent with the second law of thermodynamics. To highlight the distinctive characteristics of MR fluids, the investigation explores different deformation modes, including shear, flow, and squeezing. This study comprehensively addresses essential phenomena in MR fluids, including yielding, rate-dependent viscosity, and the Weissenberg effect, by leveraging the physical insights from their interaction with magnetic fields. We performed experiments with a rheometer to validate these conclusions and contrasted the analytical findings with the experimental data. Additionally, we confirmed the theoretical predictions for flow mode deformation by comparing them with existing experiments, offering a thorough explanation of field-dependent flow properties. The presented theory is also used to analyze the breaking for the MR brake system analytically, which is then validated by comparing it with the experiment. The proposed framework serves as a valuable tool for understanding and predicting the behavior of MR fluids, enabling the realization of their full potential in practical applications, such as MR fluid-based clutches and vibration dampers.