Abstract
Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower. Anticipating and controlling these morphologies is crucial to a variety of applications involving textiles, synthetic skins, and inflatable structures. Here we show that a "wrinkle-to-crumple" transition, previously observed in specific settings, is a ubiquitous response for confined sheets. This unified picture is borne out of a suite of model experiments on polymer films confined to liquid interfaces with spherical, hyperbolic, and cylindrical geometries, which are complemented by experiments on macroscopic membranes inflated with gas. We use measurements across this wide range of geometries, boundary conditions, and lengthscales to quantify several robust morphological features of the crumpled phase, and we build an empirical phase diagram for crumple formation that disentangles the competing effects of curvature and compression. Our results suggest that crumples are a generic microstructure that emerge at large curvatures due to a competition of elastic and substrate energies.
Highlights
When unrolling plastic wrap, handling a large flimsy poster, or watching a fluttering flag, we witness a multitude of deformations available to thin sheets
We generalize an empirical threshold from previous work [25] to give an approximate criteria for the transition, and we show that a full account of the crumpling threshold must include the fractional in-plane compression
We have shown that wrinkles are unstable to another buckled morphology at large curvatures, namely, sharp localized crumples
Summary
When unrolling plastic wrap, handling a large flimsy poster, or watching a fluttering flag, we witness a multitude of deformations available to thin sheets. Much progress has been made to describe a wide range of deformations and patterns, a general understanding of the transition from smooth to sharp topographies under featureless confinement remains a major challenge Such an understanding promises broad practical implications from controlling surface patterning through buckling [8,9] to anticipating material degradation due to the focusing of stresses at elastic singularities [10,11,12]. We study the transition from smooth to sharp deformations in general geometries, and we find a common response whereby wrinkles are replaced at large imposed curvatures by a generic buckling motif, termed “crumples.” The realization that both wrinkles and crumples can form sequentially under gradual confinement is the outcome of recent work by King et al [25,26]. Our experimental measurements and phenomenological description provide a foothold for a theoretical understanding of this ubiquitous transition
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