Frequency Dependent Electrorheological Properties: Origin and Bounds

We present a unified framework for the first-principles calculation of the frequency dependent shear modulus, static yield stress, and structures of dielectric electrorheological systems. It is shown that a strong (applied field) frequency dependence of the static yield stress, in good quantitative agreement with those measured experimentally, can arise from Debye relaxational effects that are typical of poor insulators. Physical upper bounds on the yield stress and the shear modulus, as well as frequency-induced structural soft modes, are predicted.