Symmetry breaking and high-order instability of telephone cord buckles triggered by in-plane gradients of thin films

Abstract

Buckle delaminations are ubiquitous in natural and artificial systems including tectonic plates, biological tissues, film structures, and two-dimensional materials. Although the formation and manipulation of various buckle delaminations have been extensively investigated in the past few decades, understanding complex buckle delamination patterns is still a challenge. Here we report on the symmetry breaking and high-order instability of telephone cord (TC) buckles triggered by in-plane gradients of thin films, including strain gradient and thickness gradient. Our experimental observations reveal the unique morphological profile of the asymmetric TC buckle due to the strain gradient. Impact of in-plane strain gradient on morphological changes of TC buckles is elucidated by simulations of buckling and delamination of the thin film. Phase diagrams for five buckle delamination morphologies, i.e., symmetric TC buckle, asymmetric TC buckle, symmetric bilateral branched buckle, asymmetric bilateral branched buckle, and unilateral branched buckle with respect to average strain and strain gradient (or thickness gradient) have been numerically established. This work could promote a better understanding of complex buckle delamination patterns with symmetry breaking and high-order instability and controllable fabrication of ordered buckle delamination patterns by regulating in-plane gradients of thin films.