Out-of-plane buckling of architected sheets with non-periodic cut patterns

We investigate the out-of-plane shape morphing capability of elastic sheets with architected cut patterns. These cuts result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause a sheet to buckle into three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. This phenomenon stems from the geometric incompatibilities between regions that are designed to undergo different amounts of strain. Global buckling modes observed in experiments are rationalized by an in-plane kinematic analysis, and are reproduced in simulations of homogenized shell models implemented in the open-source finite-element platform FEniCS. Our work illustrates a scalable route towards the fabrication of three-dimensional objects with nonzero Gaussian curvature from initially-flat sheets.