Boundary curvature guided shape-programming kirigami sheets

Kirigami sheets can morph from 2D to 3D by deforming along cut patterns, but designing cuts to reach a desired 3D curved shape is difficult. This study proposes a different design route: instead of focusing on intricate cut patterns, it programs the curvature of the cut boundaries. The approach is motivated by the Gauss-Bonnet theorem, linking boundary geodesic curvature to topological Gaussian curvature. Using this idea, the authors describe both forward and inverse design strategies to target 3D curved topologies. They report dynamic 3D shape shifting under mechanical stretching and remote magnetic actuation. They also suggest an application as an untethered predator-like kirigami soft robot and position the method as a route to boundary-curvature-encoded shape-programming materials for shape-morphing structures and multifunctional devices.