Spontaneous Shear Strain Governed Bending of Dielectric Nematic Elastomer Sheets With In-Plane Director Orientation Gradients

Abstract In this study, the programmable bending behavior of dielectric nematic elastomer (DNE) sheets, which is mechanically governed by electric-field-induced spontaneous transverse shear strain, is theoretically investigated. This bending mechanism is particularly significant in the DNE sheets with in-plane director orientation gradients. To highlight the effect of the spontaneous transverse shear strain on bending, we focus on examining the axisymmetric bending of circular sheets. The governing equations and analytical solutions for bending are derived based on the classical Reissner–Mindlin plate theory. The solutions reveal that the bending curvature is entirely determined by the in-plane gradient of the spontaneous transverse shear strain that is encoded by the designable director orientation alignment. This enables the programmable control of bending shapes. Several representative programmable axisymmetric bending shapes are presented, including cone-like and wave-like shapes, as well as other piecewise bending shapes. For each of these bending shapes, the corresponding bending characteristics, such as deflection, curvature, and wave number, can be optimized or/and adjusted to some extent. Overall, the results offer useful insights into the electric-field-induced bending characteristics of the DNE sheets, which can provide theoretical guidance for boosting the application of DNEs as bending actuators and sensors.