Magnetorheological (MR) fluids are active materials that change their mechanical and electromagnetic properties in response to the application of a magnetic field. Renewed interest in these materials and in the subject of electromagnetic continua is motivated by the potential of providing relatively simple and quiet variable-stiffness devices as rapid-response interfaces between electronic controls and mechanical systems. A number of MR fluids and various MR fluid-based systems have been commercialized including a MR fluid brake system for use in physical exercise equipment, a controllable MR fluid damper for use in truck seat suspensions and a MR fluid damper for seismic application. In this talk we consider the MR medium as a homogenized single non-polar isotropic continuum and start with Pao's classical work summarizing the full system of equations. Then, we derive the basic system of constitutive equations for MR fluids using a phenomenological approach based on published data. The reduced system of constitutive equations is complemented by the system of initial and boundary conditions. We present the constitutive relation for non-Newtonian incompressible MR fluids and illustrate the usefulness of the derived mathematical model. Finally, we examine the basic operational system for controllable fluid devices by showing that the mechanical response changes with increasing magnetic field strength.
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