Local versus global buckling of thin films on elastomeric substrates

Local buckling can form microcorrugations in thin films on elastomeric substrates, to yield an effective type of mechanical stretchability in otherwise rigid, brittle materials, with many application possibilities. For large area films or relatively thin substrates, however, global (Euler) buckling, as opposed to local buckling, can be observed in experiments. This paper describes analytically the mechanics of local and global buckling of one-dimensional thin films or two-dimensional thin membranes on elastomeric substrates. The critical condition separating these two buckling modes is obtained analytically, and it agrees well with experiments and numerical simulations.