Non-Linear Finite Element Framework for Large-Strain Wrinkling of Thin-Layer Structures

Abstract

: Thin-walled lightweight structures begin to wrinkle when they are subjected to in-plane extension, and predicting this phenomenon is a challenging problem in engineering. This paper presents a study of finite-strain wrinkling of membranes using 2D strain gradient elasticity theory. Incorporating strain gradient theory instead of the classical continuum formulation is motivated by the conceptual aid it offers when dealing with size-dependent behavior or intrinsic length scale effects, to increase numerical stability, and to address the limitations of numerically solving classical wrinkling analysis. A nonlinear finite element formulation is derived for hyperelastic thin-walled membranes, which allows wrinkle patterns to occur naturally during the solution process without the need to perform a Buckingham analysis, several buckling modes, or creation of imperfections. The model proposed here has a better gradient solution and a physically consistent form than the classical understanding and is especially applicable to the study of large deformation wrinkling phenomena. The formulation is validated by comparing the membrane’s response with the published results, and the accuracy and reliability of the numerical results are checked by considering residual convergence and the sensitivity of the predicted wrinkle characteristics to mesh refinement.