Shear stresses in magnetorheological fluids: Role of magnetic saturation

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Abstract
The interparticle forces and resulting shear stresses in a magnetorheological fluid are calculated. The field due to a linear chain of particles in a fixed average magnetic induction Bave is determined from a finite element analysis in which the nonlinearity and saturation of the particle magnetization are incorporated. The shear stresses are then computed from the field using Maxwell’s stress tensor. The stresses obtained for all but the lowest magnetic inductions are controlled by the saturation of the magnetization in the contact regions of each particle. Identifying the maximum shear stress as a function of shear strain with the yield stress gives values in agreement with results reported for typical fluids. For high magnetic inductions the yield stress plateaus due to the complete saturation of the particle magnetization; the stress scales as the square of the saturation magnetization in this regime.