Curvature-affected instabilities in membranes and surfaces: A review

Abstract

Instability of soft materials and membrane structures usually shows similar wrinkling patterns across length scales, which has aroused considerable interest in the past twenty years. Curvature and mechanics are intimately connected in thin-film structures, and curvature plays a key role in the critical threshold, mode selection, and post-buckling evolution. Here, we review the advancement of instability mechanics of thin-film structures in the past two decades, from planar to curved geometry, focusing on the curvature-affected instability of stretched membranes and film-substrate systems under various stimuli. Development of the theoretical models and numerical methods of finite strain plate/shell advances fundamental understanding, quantitative prediction, and tracking of multiple bifurcation transitions in morphology and shape of thin-film structures. It not only promotes the in-depth insight into instability mechanism but also guides wrinkle-resistant control and the effective design of morphology-related multifunctional surfaces and membrane structures via harnessing instability.