programming the shape of inflated flat ribbons

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.

See our article in PNAS and the Supplementary Information.