剛体平面に置かれたシートの隆起パターンとメカニクス

抄録

Extended thin sheets, such as clothes and papers, easily deform under gravity and form a variety of patterns, including wrinkles, draping, and folding, as we observe on a daily basis. The equilibrium shapes of those sheets are determined by the balance between the elasticity, gravity, and external contact forces. To clarify the mechanism of the formation of undulating patterns in a heavy sheet, we investigate a so-called “blister test’’, in which a thin sheet on a rigid flat substrate is pushed at its center from below, by combining mechanical testing, optical measurements, and theory. As the vertical displacement is increased, we observe a formation of a circular delaminated region, then a wrinkled pattern, and radial crack-like delaminated patterns that are asymptotically close to the draping. We also observe an anomalous force response, such as a discontinuous change of the vertical force when the crack front reaches an edge of the sheet. We rationalize our experimental findings with a scaling argument based on the Föppl–von Kármán’s equations.