Kirigami, a traditional 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 Gaussian curvature, here, we exploit programming the curvature of cut boundaries rather than the complex cut patterns in kirigami sheets for target 3D curved morphologies through both forward and inverse designs. The strategy largely simplifies the inverse design. Leveraging this strategy, we demonstrate its potential applications as a universal and nondestructive gripper for delicate objects, including live fish, raw egg yolk, and a human hair, as well as dynamically conformable heaters for human knees. This study opens a new avenue to encode boundary curvatures for shape-programing materials with potential applications in soft robotics and wearable devices.
Numerical Method for Direct Solution to Form-Finding Problem in Convex Gridshell
Abstract Elastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, more »
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- Journal of Applied Mechanics
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