The mechanism of the giant unipolar strain recently observed in a lead-free piezoceramic, 0.92(Bi0.5Na0.5)TiO3-0.06BaTiO(3)-0.02(K0.5Na0.5)NbO3 [S.-T. Zhang, A. B. Kounga, E. Aulbach, H. Ehrenberg, and J. Rodel, Appl. Phys. Lett. 91, 112906 (2007) was investigated. The validity of the previously proposed mechanism that the high strain comes both from a significant volume change during the field-induced phase transition, from an antiferroelectric to a ferroelectric phase and the domain contribution from the induced ferroelectric phase was examined. Monitoring the volume changes from the simultaneously measured longitudinal and transverse strains on disk-shaped samples showed that the phase transition in this specific material does not involve any notable volume change, which indicates that there is little contribution from a volume change due to the phase transition to the total strain response. Temperature dependent hysteresis measurements on unpoled samples of a nearby ferroelectric composition, 0.93(Bi0.5Na0.5)TiO3-0.06BaTiO(3) -0.01(K0.5Na0.5)NbO3 demonstrated that the origin of the large strain is due to the presence of a nonpolar phase that brings the system back to its unpoled state once the applied electric field is removed, which leads to a large unipolar strain.