<title>Analysis of electro- and magneto-rheological flow mode dampers using Herschel-Bulkley model</title>

Electrorheological (ER) and magnetorheological (MR) fluid- based dampers are typically analyzed using Bingham-plastic shear flow analysis under quasi-steady fully developed flow conditions. An alternative perspective, supported by measurements reported in the literature, is to allow for post- yield shear thinning and shear thickening. To model these, the constant post-yield plastic viscosity in Bingham model can be replaced with a power law model dependent on shear strain rate that is known as the Herschel-Bulkley fluid model. Depending on the value of the flow behavior index number, varying degrees of post-yield shear thickening or thinning behavior can be analyzed. A nominal ER bypass damper is considered. Damping forces in the damper are analyzed by approximate parallel plate geometry. The impacts of flow behavior index on shear stress-strain relationship and velocity profile for variable electric field are also examined numerically. Then, analytical damping predictions of ER/MR flow mode dampers are compared using the nonlinear Bingham-plastic and nonlinear Herschel-Bulkley analyses.