Localized Wrinkle Behavior near Fixed Boundaries in Flat and Cylindrical Membranes

Abstract

This study analyzes wrinkle behavior in both flat and cylindrical membranes undergoing shear displacement. The goal is to establish a relationship between the wrinkle behavior in the two types of membranes and understand how different geometric properties affect the behavior. The analysis is an equilibrium path-tracking analysis using the finite-element method. By applying cyclic boundary conditions to a flat membrane, a degree of similarity in the wrinkle behavior can be established between flat and cylindrical membranes. In both membranes, the initial wrinkles cover the entire membrane. These wrinkles are followed by smaller, localized wrinkles, referred to as collapsed sections. These collapsed sections form on existing wrinkles. The generation of new wrinkles, by splitting the existing wrinkles, is controlled by collapsed sections and is the same in both types of membranes. For the cylindrical membrane, the curved shape results in a more controlled wrinkle behavior. This is represented by fewer bifurcation points that require larger values of shear to occur. Second, the collapsed section frequency and position are fixed with respect to the wrinkle frequency and position. The cause of simplified and controlled wrinkle behavior is analyzed, and the control mechanism is explained.