- 2016 Elsevier Ltd This paper presents numerical analyses of elastic and viscoelastic smart flexible and foldable composite structures under electric field actuation. The studied composites comprise of multiple distributed piezoelectric patches bonded to the surfaces of in-active thin planar structures (substrates). Upon applications of electric field input, the planar structures can undergo three-dimensional large rotational deformations while their strains and stretches remain relatively small. A nonlinear time-dependent electro-mechanical coupling relation for the piezoelectric patches is considered to simulate more precisely response of piezoelectric materials when subjected to large magnitude of electric field. Co-rotational Lagrangian finite element approach is used for solving the governing equations of the deformations of flexible and foldable electro-active composite structures. Various three-dimensional shape changes of originally planar structures are achieved with different arrangements of integrated patches and subjected to different magnitude of electric fields. The effect of viscoelastic substrates and time-dependent electro-mechanical coupling of piezoelectric materials on the deformed shapes is also studied. This analysis can help designers in simulating desired deformed shapes and determining external stimuli to be prescribed prior to fabricating smart and flexible composites.