Programming curvilinear paths of flat inflatables
Significance Inflatable structures are flat and foldable when empty and both lightweight and stiff when pressurized and deployed. They are easy to manufacture by fusing 2 inextensible sheets together along a defined pattern of lines. However, the prediction of their deployed shape remains a mathematical challenge, which results from the coupling of geometrical constraints and the strongly nonlinear and asymmetric mechanical properties of their composing material: thin sheets are very stiff on extensional loads, while they easily shrink by buckling or wrinkling when compressed. We discuss the outline shape, local cross section, and state of stress of any curvilinear open path. We provide a reverse model to design any desired curved 2 dimensional shape from initially flat tubes. Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2 dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input.
Proceedings of the National Academy of Sciences