Curvature tunes wrinkling in shells

Abstract

Transverse wrinkles usually emerge in a uniaxially stretched elastic film and can be suppressed upon further tension, which is an instability-restabilization behavior due to the nonlinear competition between stretching energy and bending energy. Here, we show that curvature can effectively and precisely tune the wrinkling localization and amplitude. To quantitatively explore curvature effect on the wrinkling response, we develop a finite strain shell model with varying curvatures, e.g., S-shaped and C-shaped surfaces, based on the general differential geometry and nonlinear elasticity theory. Distinguished from the central wrinkling observed in a stretched cylindrical film with constant curvature, we reveal that wrinkles tend to move toward the region with lower curvature. Notably, localized wrinkles can be remotely influenced by the curvature of neighbouring region. Understanding morphological pattern evolution and in particular the dependence of wrinkling behavior on curvature, e.g., 3D phase diagram of stability boundaries, is crucial for the effective use of wrinkling as a tool for realizing multifunctional wrinkle-tunable surfaces.