Abstract: Rayleigh identity based on a multipole expansion theory is extended to investigatethe mechanical properties of an ideal electrorheological fluid which consists of metal particles with insulating outer layer in a dielectricoil. Evaluation of the effective dielectric constant is emphasized.The dependence of the shear stress  on the shear strain and theshear modulus G for chains of particles arranged on a square lattice are presented.

Key words: Electrorheological fluids, Effective dielectric constant, Static yield stress, Shear modulus