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Morphogenesis, Self-Organization and Fracture in Elastic Thin Sheets
When a curtain is suspended, a periodic deformation, having a given mean wavelength, is usually applied at one of its edges. This deformation relaxes along the curtain producing a cascade of folds characterized by an increase of the mean wavelength. We will show that this pattern can be understood as a self-organization of transition zones where the folds merge. When the skin of the back of the hand is compressed between thumb and forefinger, regularly spaced ripples appear spontaneously. Similar patterns are also emerging in the formation of geological folds or wrinkles on the surface of dried fruits. These morphologies can be described by considering the compression of an elastic thin plate attached to a compliant substrate. The influence of the substrate on these structures, as it is a dense fluid or elastomer, will be discussed. When an adhesive film is peeled by pulling a partially detached flap, the two fractures at each side of the flap converge linearly toward each other. When they meet, a triangular piece of film is released. The influence of the curvature of the substrate on the crack trajectories will be discussed. The limit where adhesion is negligible will be analyzed.