The rheological behaviors of suspension of ideally conductive particles in an electric field are studied using large-scale numerical simulations in the limit of the zero-shear-rate flow. Under the action of an electric field, the particles undergo the nonlinear electrokinetic phenomenon termed dipolophoresis, which is the combination of dielectrophoresis and induced-charge electrophoresis. For ideally conductive particles, the dynamics of the suspension are primarily controlled by induced-charge electrophoresis. To characterize the rheological properties of the suspension, the particle stress tensor and particle pressure are calculated in a range of volume fraction up to almost random close packing. The particle normal stress and particle pressure are shown to behave nonmonotonically with volume fraction, especially in concentrated regimes. In particular, the particle pressure is positive for volume fraction up to 30%, after which it becomes negative, indicating a change in the nature of the particle pressure. The microstructure expressed by the pair distribution function and suspension entropy is also evaluated. Visible variations in the local microstructure seem to correlate with the nonmonotonic variation in the particle normal stresses and particle pressure. These nonmonotonic behaviors are also correlated with the change in the dominant mechanism of particle pairing dynamics observed in our recent study [Mirfendereski and Park, J. Fluid Mech. 875, R3 (2019)]. Finally, the effects of confinement on the particle stress and particle pressure are investigated. It is found that the particle pressure changes its nature very quickly at high volume fractions as the level of confinement increases. This study should motivate control strategies to fully exploit the distinct changing nature of the pressure for rheological manipulation of such a suspension system.