Cross-sections of doubly curved sheets as confined elastica

Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. However, it remains unclear how the selection of an overall shape constrains the behavior of smaller-scale wrinkles or folds. We have investigated a prototypical system consisting of a thin-membraned balloon that is partially filled with water and pressurized with air. We have shown that a geometrical, which considers the sheet as inextensible yet free to compress, predicts the overall shape of the balloon. We have proposed a quasi-two-dimensional model that captures an array of features seen in the experiments, from the shapes of individual folds to how the membrane morphology changes with pressure.

Authors: Mengfei He, Vincent Démery and Joseph D. Paulsen

Publication: PNAS 2023, Vol. 120 No. 11 e2216786120

https://doi.org/10.1073/pnas.2216786120

Arxiv