Mathematical modeling of electrorheological materials

In this paper we derive governing equations for the motion of electrorheological fluids, where the complex interactions between the thermo-mechanical and electro-magnetic fields are taken into account. Starting point are the general balance laws of thermodynamics and electrodynamics. Based on simplifications, which reflect the nature of electrorheological fluids, and a non-dimensionalization, taking into account typical situations in applications, the final set of equations is derived, which is also tractable for mathematical and numerical analysis. Finally, we discuss the consequences of the second law of thermodynamics for various special constitutive relations for the Cauchy stress tensor.