Transition from isometric to stretching ridges in thin elastic films

Isometric deformations in thin elastic films easily form ridges to connect large flat regions or facets. Depending on the forces applied or the boundary conditions imposed, these ridges can be isometric, with no stretching or "stretching ridges" when bending and stretching are required to relax the elastic energy. Here we study a simple configuration to observe the transition between an isometric ridge to the well-known stretching ridge observed in crumpled films, and obtain the parameters that determine the ridge type. Specifically, we show that the transversal size of a stretching ridge acts as a cutoff length scale: a ridge is isometric if its width is greater than this characteristic length.