Thermodynamics provides a convenient framework to analyze the electrorheology of suspensions of non-Brownian, noncolloidal particles in Newtonian carriers. Aided by simple constitutive relations Linking suspension architecture to its electrical response, we examine the evolution of the microstructure upon cessation of flow and the linear-elastic behavior in the preyield region. In the case where the particles and the fluid are both nonconducting, a rigorous proof can be worked out to show that, upon cessation of flow, the suspension microstructure will evolve towards a "pillared" configuration, whereby chains of particles spanning the flow gap are formed. Also, a maximum in the linear-elastic shear modulus as a function of solid concentration is predicted in this case, under certain conditions. For finite solid and carrier conductivities, where Maxwell-Wagner-Sillar polarization can occur, the results are less rigorous; although some necessary conditions for stability of the pillared structure can still be inferred.