Programming curvilinear paths of flat inflatables

Abstract

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.

Geometry and mechanics of inextensible curvilinear balloons

“…10 the evolution of the coiling factor λ as a function of the slenderness ratio S. Two series of specimens were made of 4 µm thick polyethylene and 16 µm thick polypropylene, respectively. In contrast with Siéfert et al [22], where the prediction failed for non slender rings (R * < 2), we obtain here a quantitative agreement between experiments and theory for a whole range of slenderness, the strain λ monotonically varying from 1.28 to 1.38.…”

“…1-a). This study generalizes a preliminary work presented in reference [22], where the families of cross section in open and closed configurations were assumed to be identical. Mylar balloons exhibit non-intuitive features that we wish to rationalize.…”

“…determining the initially flat template that will lead to any arbitrary 2D structure upon inflation. The case of a slenderness ratio close to unity has been presented in a previous study [22]. We propose here to extend this approach to any value of S.…”

“…The coiling angle has been estimated in reference [22] using the crude approximation that azimuthal tension was always reduced to a pair of (up-down symmetric) lines. However, this approximation fails for non-slender rings.…”

Shape Programming by Modulating Actuation over Hierarchical Length Scales

“…While printing at a given appropriate temperature, TPU matrix were welded together to obtain a strong bonding along the print path. [ 40,41 ] Upon inflation, the sheets bent perpendicular to the parallel seam lines to form a quasi‐circular cross section for sufficiently large pressure p . Owing to the quasi‐inextensibility of the fabric sheets, this cross‐section change implied an in‐plane contraction perpendicular to the channels with a magnitude λ ⊥ = 2/π and λ ∥ = 1.…”