ANM analysis of a wrinkled elastic thin membrane

Abstract

In this work, we have investigated numerically the disappearance of wrinkles from a tended membrane by the Asymptotic Numerical Method (ANM) using the finite-element DKT18. The ANM is a path-following technique that has been used to solve bifurcation problems. We show numerically the influence of the terms corresponding to the membrane displacement gradient in the Föppl-von Kármán (FvK) theory on the bifurcation curves in the case of a stretched elastic membrane. We will also study numerically, by using the ANM algorithm, the influence of the thickness and of the aspect ratio on the restabilization of a rectangular elastic membrane during stretching. The results obtained by our model are compared with those obtained using the industrial code ABAQUS.

Mechanics of tension-induced film wrinkling and restabilization: a review

“…In 2009, Zheng [45] uncovered the restabilization phenomenon in a highly stretched sheet, showing that wrinkles appear first, then decrease, and eventually disappear with the continuous increase of applied stretching. To consider large deformations of soft films, some plate/shell theories accounting for finite in-plane strain [62][63][64][65] and advanced numerical methods [32,[66][67][68][69][70] for capturing multiple bifurcations in nonlinear post-buckling paths were developed. General mechanics models to characterize large deformations of thin films can be placed into three categories: extended Föppl-von Kármán plate model (EFvK) [32][33][34], finite-strain plate model derived from three-dimensional nonlinear elasticity [71][72][73][74], and consistent finite-strain plate model [64,65,70,75].…”