Electrorheological (ER) and magnetorheological (MR) fluids are characterized by an increase in dynamic yield stress upon application of a magnetic field. The Bingham plastic model has proven useful in modeling flow mode dampers utilizing ER and MR fluids. However, certain MR fluids can exhibit shear thinning behavior, wherein the fluid's apparent plastic viscosity decreases at high shear rates. The Bingham plastic model does not account for such behavior, resulting in overprediction of equivalent viscous damping. We present a Bingham biplastic model that can account for both shear thinning and shear thickening behaviors. This approach assumes a bilinear postyield viscosity, with a critical shear rate specifying the region of high shear rate flow. Furthermore, the model introduces nondimensional terms to account for the additional parameters associated with shear thinning and thickening. A comparison is made between Bingham plastic and Bingham biplastic force responses to constant velocity input, and equivalent viscous damping is examined with respect to nondimensional parameters.

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Magnetorheological (MR) fluids are characterized by dynamic yield stress with the application of a magnetic field. The Bingham plastic model has proven useful in modeling MR fluid properties, as in flow mode dampers. However, certain MR fluids can exhibit shear thinning behavior, wherein the fluid's apparent plastic viscosity decreases at high strain rates. The Bingham plastic model does not account for such behavior, resulting in over-prediction of equivalent viscous damping. This paper proposes a Bingham biplastic model to account for shear thinning or shear thickening. This approach assumes a bilinear post-yield viscosity, with a critical strain rate specifying the region of high strain rate flow. Furthermore, the model introduces non-dimensional terms to account for the additional parameters associated with shear thinning and thickening. A comparison is made between Bingham plastic and Bingham biplastic force responss to sinusoidal input, and equivalent viscous damping is examined with respect to nondimensional parameters.

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