For melt-compounded poly(lactic acid) composites containing graphene nanoplatelets (GNPs) at low volume fractions, phi(GNP) <= 0.34 vol. %, this study focused on correlation between the composite properties and a large-scale structure of GNPs formed by a strong alternating current electric field (with the frequency and intensity of 60 Hz and 1.75 kV/mm, respectively). The electric field was applied to the composite in a rheometer through the parallel plate fixture, so that the parallel plates served as the rheological measurement fixture as well as the electrodes. Optical microscopy, transmission electron microscopy, and two-dimensional wide-angle X-ray diffraction measurements revealed that almost randomly oriented, thin stacks of GNPs in the as-fabricated composites were aligned by the electric field in the field direction and further organized into an extended chain (or column) of stacks. This chained-stack structure bridged two parallel plate electrodes when phi GNP was above a threshold value, phi(GNP)*congruent to 0.17 vol. %. Corresponding to this structural change, the liquidlike rheological response of the as-fabricated composites, characterized by the storage modulus G' almost proportional to omega(2) at intermediate-to-low angular frequencies omega, became the solidlike response, G' similar to omega(0) at low omega (for the composites having phi(GNP) >=phi(GNP)*), after application of the electric field. In contrast, the loss modulus G" was insensitive to the electric field and remained almost proportional to omega at low omega, suggesting that the chained-stack structure formed by the electric field was an elastic structure bridging the parallel plates. This bridge also served as an electrically conductive path between the plates so that an insulator-conductor transition occurred when the composites with phi(GNP) >=phi(GNP)* were subjected to the electric field. Quantitative analysis of the equilibrium modulus and conductivity of the composites suggested that the chained-stack structure formed by the electric field was not a rigid single slab but included junctions being much softer and less conductive compared to the body of GNP (each graphene nanoplate). Moreover, analysis of the phi GNP dependence on the equilibrium modulus and static electrical conductance after the transition (phi(GNP) >= 0.17 vol. %) suggested that an elastically inert secondary structure was formed by the GNP stacks remaining out of the chained-stack structure (primary structure). This secondary structure appeared to be in soft contact with the primary structure to provide an extra conducting path. (C) 2017 The Society of Rheology.