Dynamic response of poroelastic materials containing Bingham fluid: Application to electrorheological fluids

This work examines the dynamic response to harmonic loading of a disk of poroelastic material containing non-Newtonian Bingham fluid which exhibits a yield stress. Biot's poroelasticity equations and modified Darcy's law for non-Newtonian fluids exhibiting a yield stress are combined together to obtain the governing equations of the system for quasi-static case. Dissipation due to friction arising from the flow of fluid relative to the solid is taken into account but inertia effects are neglected. The response and the complex modulus of the system are calculated using the finite element method taking into account the nonlinear nature of Bingham fluid. As an application of the model developed, the behavior of electrorheological (ER) fluids in poroelastic media is investigated. The storage modulus and loss tangent are obtained for different electric field strengths. The results suggest that ER fluid-porous solid device can be tuned to provide optimum stiffness and damping as excitation or resonant frequencies change.