Stretch-induced wrinkling analysis of thin sheets with splines

Numerical simulation of stretch-induced wrinkling in thin elastic sheets is a challenging problem due to a vanishing bending stiffness and the coexistence of superabundant equilibrium solutions. In this work, we present a computational framework to capture the morphological evolution of stretch-induced wrinkles. The application of modified Foppl-von Karman plate model results in a fourth-order partial differential equation. The convergence of finite-element solutions necessitates C-1-continuous approximations. Herein, Powell-Sabin B-splines, which are based on triangles, are utilized for both the approximation of the field variables and the description of the geometry. To trace the wrinkling behavior in thin sheets, a path-following technique using asymptotic numerical method is considered. The advantage of this method is an adaptive step length, which works incredibly well near the bifurcation points and allows for the computation of the post-bifurcation diagrams with a quite small perturbation. The versatility and accuracy of the developed computational approach are assessed in three case studies, featuring wrinkling in highly stretched rectangular and annular thin sheets.