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Abstract We introduce a new mechanism for self‐actuating deployable structures, based on printing a dense pattern of closely‐spaced plastic ribbons on sheets of pre‐stretched elastic fabric. We leverage two shape‐changing effects that occur when such an assembly is printed and allowed to relax: first, the incompressible plastic ribbons frustrate the contraction of the fabric back to its rest state, forcing residual strain in the fabric and creating intrinsic curvature. Second, the differential compression at the interface between the plastic and fabric layers yields abilayer effectin the direction of the ribbons, making each ribbon buckle into an arc at equilibrium state and creating extrinsic curvature. We describe an inverse design tool to fabricate low‐cost, lightweight prototypes of freeform surfaces using the controllable directional distortion and curvature offered by this mechanism. The core of our method is a parameterization algorithm that bounds surface distortions along and across principal curvature directions, along with a pattern synthesis algorithm that covers a surface with ribbons to match the target distortions and curvature given by the aforementioned parameterization. We demonstrate the flexibility and accuracy of our method by fabricating and measuring a variety of surfaces, including nearly‐developable surfaces as well as surfaces with positive and negative mean curvature, which we achieve thanks to a simple hardware setup that allows printing on both sides of the fabric. 

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom. 

We describe a new meta-material for fabricating lightweight architectural models, consisting of a tiled plastic star pattern layered over pre-stretched fabric, and an interactive system for computer-aided design of doubly-curved forms using this meta-material. 3D-printing plastic rods over pre-stretched fabric recently gained popularity as a low-cost fabrication technique for complex free-form shapes that automatically lift in space. Our key insight is to focus on rods arranged into repeating star patterns, with the dimensions (and hence physical properties) of the individual pattern elements varying over space. Our star-based meta-material on the one hand allows effective form-finding due to its low-dimensional design space, while on the other is flexible and powerful enough to express large-scale curvature variations. Users of our system design free-form shapes by adjusting the star pattern; our system then automatically simulates the complex physical coupling between the fabric and stars to translate the design edits into shape variations. We experimentally validate our system and demonstrate strong agreement between the simulated results and the final fabricated prototypes.