This paper is concerned with the optimisation of the actuation response of electro-elastic, rank-two laminates obtained laminating a core rank-one composite with a soft phase which constitutes the shell. The analysis is performed for two classes of composites that are subjected to traction-free boundary-value problems. The results are compared with those computed in a previous study where the optimisation was carried out at small strains. The non-linear approach allows a better estimation of the geometric layout of the reference configuration to enhance the maximum stretch or shear strain at the operative applied voltage. The optimum layouts are in general characterised by a very low volume fraction of the shell while in the core the two components are almost equally distributed. The amplification of the electric field in each phase of the laminate in the actuated state is also estimated to provide an indication of the effective local electro-mechanical response..
