A conduction model is developed for the dc electrorheological (ER) response of highly conducting particles (e.g., metal particles) suspended in a weakly conducting oil. The numerical analyses show that a surface film with some conductivity is desired, but not a completely insulating film as previously proposed. Increasing the film conductivity leads to an increase in the ER yield stress. However, too high a conductivity will give an unacceptable level of current density. The film should also have an intermediate thickness. A small thickness increases the possibility of electrical breakdown in the film; too large a thickness decreases the ER effect. Good agreement exists between the yield stress and the current density predicted by our model and those measured.

This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results.

Two sizes (6 and 100 μm average diameter) glass spheres suspended in silicone oil (volume fraction Ф=0.3) were used to investigate the influence of particle size on electrorheological response at a shear rate 2s-1. The larger particles gave a higher shear yield stress but a lower current density at zero shear than the smaller ones. When the two particle sizes were mixed together, the shear yield stress decreased, reaching a minimum when the volume fraction of the small particles equals that of the large particles. The minimum in the current density occurred when the ratio of the volume of small to large particles was ～1/3.

Hydrodynamic lubrication of a bilinear rheological fluid plays an important role in the so-called electrorheological (ER) smart' bearings. There may not. however, be a reliable and efficient algorithm for the non-Newtonian lubrication problem of bilinear rheological fluids. In this paper, a finite element trethod (FEM), together with a mathematical programming solution technique, are proposed for solving such a non-Newtonian lubrication problem. This method was used to study the hydrodynamic lubrication of a journal bearing lubricated by a bilinear rheological lubricant. The computed results were compared with Tichy's work for the Bingham rhcological model. It was shown that the Bingham model should be regarded as a limiting case of the bilinear rhcological model.