The nonlinear dynamics of uncharged ideally polarizable spheres freely suspended in a viscous electrolyte in a uniform electric field are analysed using theory and numerical simulations. When a sphere polarizes under the action of the field, it acquires a non-uniform surface charge, which results in an electro-osmotic flow near its surface that scales quadratically with the applied field magnitude. While this so-called induced-charge electrophoresis yields no net motion in the case of a single sphere, it can drive relative motions by symmetry breaking when several particles are present. In addition, Maxwell stresses in the fluid also result in non-zero dielectrophoretic forces, which also cause particle motions. The combination of these two nonlinear electrokinetic effects, termed dipolophoresis, is analysed in detail by using numerical simulations. An efficient simulation method based on our previous analysis of pair interactions is presented and accounts for both far-field and near-field electric and hydrodynamic interactions in the thin-Debye-layer limit, as well as steric interactions using a novel contact algorithm. Simulation results in large-scale suspensions with periodic boundary conditions are presented. While the dynamics under dielectrophoresis alone are shown to be characterized by particle chaining along the field direction, in agreement with previous investigations, chaining is not found to occur under dipolophoresis, which instead causes transient particle pairings and results in a non-uniform microstructure with large number of density fluctuations, as we demonstrate by calculating pair distribution functions and particle occupancy statistics. Dipolophoresis is also found to result in significant hydrodynamic dispersion and velocity fluctuations, and the dependence of these two effects on suspension volume fraction is investigated.