Analysis of pulled axisymmetric membranes with wrinkling

Abstract

The nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed. The membrane is considered to be ideal in the sense that it cannot carry compressive stress resultants. If the membrane has a positive initial Gaussian curvature, the pulling gives rise to wrinkles which form over parts of the surface. The full nonlinear equations governing the membrane behavior in the doubly tense and in the wrinkled regions are formulated, and then solved using a numerical integration procedure. Solutions for various examples are presented, with Hookean and neo-Hookean constitutive behavior. These include a few examples of wrinkled membranes with positive initial Gaussian curvatures, and one example of a membrane with a negative initial Gaussian curvature, where no wrinkles are formed.