Shape Morphing of Closed Stiff Frames by Targeted Internal Angle Reduction

Stiff convex polygonal frames composed of stiff rods and flexible joints of a singular material can undergo drastic 2D to 3D shape morphing via reduction of individual internal angles using any stimuli-responsive shrinking materials. Utilizing the conservation of the sum of internal angles, we show that any attempt to reduce the sum of internal angles can destabilize the 2D configuration of a polygon. Experiments on thermoplastic polyurethane-based 3D printed frames and monodomain liquid crystal elastomer sleeves exhibit significant shape changes in regular polygons. Computational methods show that the number of angle reduction sites affects the extent of shape morphing and concave polygons face major difficulties in 3D shape morphing. Complex structures formed by tessellations, nesting, and stacking of simple convex polygons give rise to several non-conventional shape-morphing configurations which can be used for microscopic as well as macroscopic applications.