Boundary curvature guided shape-programming kirigami sheets

Kirigami, an ancient paper cutting art, offers a promising strategy for 2D-to-3D shape morphing through cut-guided deformation. Existing kirigami designs for target 3D curved shapes rely on intricate cut patterns in thin sheets, making the inverse design challenging. Motivated by the Gauss-Bonnet theorem that correlates the geodesic curvature along the boundary with the topological Gaussian curvature, here, we exploit programming the curvature of cut boundaries rather than complex cut patterns in kirigami sheets for target 3D curved topologies through both forward and inverse designs. Such a new strategy largely simplifies the inverse design. We demonstrate the achievement of varieties of dynamic 3D shape shifting under both mechanical stretching and remote magnetic actuation, and its potential application as an untethered predator-like kirigami soft robot. This study opens a new avenue to encode boundary curvatures for shape-programing materials with potential applications in shape-morphing structures, soft robots, and multifunctional devices.