Shape Morphing of 2D Lattice Structures from Localized Contra-Rotations

The morphing of structure and materials from localized, self-equilibrated actuation loads is limited by SaintVenant's principle: Deformations typically decay rapidly from the actuation region, so that changes in shape for the entire structure are negligible. Materials and structures with unusual combinations of elastic properties may induce competitions between different deformation modes over longer decay distances, thereby overcoming this limitation. Here we push this principle to the extreme to generate shape morphing in large 2D lattice structures. We consider planar triangular lattice made of "meta-elements" with unusual combinations of axial, shear and flexural stiffness. We show, using finite element models, that localized contra-rotations on the center nodes can morph the entire structure in bending, provided that adequate combinations of elastic properties are selected. We use the global curvature as a measure of this deformation to establish precise design guidelines for morphing. We finally propose physical embodiments of these meta-elements and lattice structures which we fabricated using laser cutting, and which tested using servo-motors to impose contra-rotations on the two center nodes. The results validate our models and the design guidelines: planar lattice can morph in bending with significant curvatures, especially when the size of the structure is small. In comparison, similar lattice structures made of regular beams show no morphing, with all the deformation localized near the center nodes. These findings may lead to new strategies to actuate morphing materials and structures, with applications in aerospace or robotics.