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