Hierarchical folding of elastic membranes under biaxial compressive stress
Résumé
Mechanical instabilities that cause periodic wrinkling during compression of layered materials find applications in stretch- able electronics1-3 and microfabrication4-7 , but can also limit an application's performance owing to delamination or cracking under loading8 and surface inhomogeneities during swelling9. In particular, because of curvature localization, finite defor- mations can cause wrinkles to evolve into folds. The wrinkle- to-fold transition has been documented in several systems, mostly under uniaxial stress10-13. However, the nucleation, the spatial structure and the dynamics of the invasion of folds in two-dimensional stress configurations remain elusive. Here, using a two-layer polymeric system under biaxial compressive stress, we show that a repetitive wrinkle-to-fold transition generates a hierarchical network of folds during reorganization of the stress field. The folds delineate individual domains, and each domain subdivides into smaller ones over multiple gen- erations. By modifying the boundary conditions and geometry, we demonstrate control over the final network morphology. The ideas introduced here should find application in the many situa- tions where stress impacts two-dimensional pattern formation.