Inflationary routes to Gaussian curved topography

Abstract

Gaussian-curved shapes are obtained by inflating initially flat systems made of two superimposed strong and light thermoplastic impregnated fabric sheets heat-sealed together along a specific network of lines. The resulting inflated structures are light and very strong because they (largely) resist deformation by the intercession of stretch. Programmed patterns of channels vary either discretely through boundaries or continuously. The former give rise to faceted structures that are in effect non-isometric origami and that cannot unfold as in conventional folded structures since they present the localized angle deficit or surplus. Continuous variation of the channel direction in the form of spirals is examined, giving rise to curved shells. We solve the inverse problem consisting in finding a network of seam lines leading to a target axisymmetric shape on inflation. They too have strength from the metric changes that have been pneumatically driven, resistance to change being met with stretch and hence high forces like typical shells.