Description of magnetorheological behavior with internal variables

The macroscopic theory of magnetorheological (MR) fluids is investigated by the use of the tensorial and vectorial internal variables. After both variables are defined, the balance equations, entropy inequality and evolution equations can be obtained. Under the consideration of physical phenomena of MR fluids (the existence of yield stress and the elasticity of MR solids), some parameters in the evolution equations are suitably chosen. The discussion is focused on the expression of stress tensor and the mechanism of energy dissipation. Comparisons among the vectorial internal variable, the tensorial internal variable, and the Cauchy's deformation tensor are made to explicate the connection among the different approaches. Finally, taking account of the effect of the gradient of the vectorial internal variable, modified expressions for entropy inequality and rotational invariant are also discussed.

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