Wrinkling and smoothing of a soft shell

Abstract

Transverse wrinkles usually occur in a uniaxially tensile elastic membrane and will be smoothed upon excess stretching. This instability-restabilization response (isola-center bifurcation) can originate from the nonlinear competition between stretching energy and bending energy. Here, we find a crucial factor, the curvature, which can control effectively and precisely the wrinkling and smoothing regimes. When the sheet is bent, the regime of wrinkling amplitude versus membrane elongation is narrowed, with local wrinkling instability coupled with global bending. There exists a critical curvature, where no wrinkles appear when the value is beyond this threshold. The curvature effects on wrinkling-smoothing behavior have been quantitatively explored by our theories, computations and experiments. The models developed in this work can describe large in-plane strains of soft shells to effectively capture this transition behavior, which build on general differential geometry and thus can be extended to arbitrarily curved surfaces. Our findings may shed light on designs of wrinkle-tunable membrane surfaces and structures.