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.

This paper considers the design of electrorheological (ER) particles. Multi-coated particles suspended in insulating (very weakly conducting) oil are recommended for obtaining high-performance ER suspensions. Only the outer two coatings determine the ER strength. The outermost coating should be a material with high dielectric constant, high electrical breakdown strength and a reasonable level of conductivity. The coating immediately below should be a highly conducting material. The inner coatings, including the core (which can be void), can be of any material having such a density that the composite particle has substantially the same density as the host liquid. Our analysis gives that multi-coated particles can have an ER shear strength as high as 29kPa when the volume fraction of particles is 0.4 and the applied field is 5kV mm-1. Results in the literature provide support for the concept and analysis.

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.

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.