Morphology of telephone cord buckles in films lying perpendicular to a thickness gradient: A finite element numerical study

We present a finite element method study of the morphology of telephone cord buckles in compressed thin films with a thickness gradient oriented perpendicular to the main buckle axis. Despite extensive studies on buckling in thin films, the influence of a transverse thickness gradient across the width of a confined telephone cord buckle remains unexplored. The analysis focuses on two morphological parameters defined as edge to peak distances asymmetry and height asymmetry evaluated over a wide range of internal stresses and thickness ratios within a confined stripe width. The results show that both in-plane and out-of-plane asymmetries exhibit only a weak dependence on internal stress and stripe width, while being strongly influenced by the thickness gradient. Increasing the gradient intensity leads to a skewing of the buckle profile toward the thinner region, consistent with the decrease of the local bending stiffness. These findings offer a new predictive scaling law for in-plane and out-of-plane asymmetry in TCBs of delaminated thin films with non-uniform thickness.