Stretch-induced wrinkling and post-buckling bifurcation in rectangular films: insights into energy barrier mechanisms

Theoretical understanding is essential for revealing wrinkling mechanisms, characterizing wrinkle behaviors, and guiding the design of thin films. However, existing studies on stretch-induced wrinkling in thin films still exhibit significant limitations in describing non-uniform wrinkle characteristics and post-buckling bifurcation evolution. This paper presents a novel wrinkle bifurcation theory based on energy methods. An energy model for a single wrinkle stripe is first constructed, and the concept of bifurcation points is introduced to describe the onset of wrinkle evolution. Specifically, the theory addresses typical nonuniform and localized instability modes in rectangular thin films under tension. By decomposing the axial boundary conditions and incorporating both mechanical and geometrical properties, this approach accurately captures spatial wrinkle variations and provides a detailed post-buckling bifurcation analysis. The concept of energy barriers, along with the decomposition of total energy into stretching and bending components, is employed to elucidate the evolution mechanism of wrinkle bifurcation throughout the loading process. This study offers valuable insights for the mitigation and control of wrinkles in rectangular thin film structures.