AFM, Maison de la Mécanique, 39/41 rue Louis Blanc, 92400 Courbevoie, France(FR)
Abstract
Curling deformation of thin elastic sheets appears in numerous structures in nature, such as membranes of red blood cells, epithelial tissues or green algae colonies to cite just a few examples. However, despite its ubiquity, the dynamics of curling propagation in a naturally curved material remains still poorly investigated. Here, we present a coupled experimental and theoretical study of the dynamical curling deformation of naturally curved ribbons. Using thermoplastic and metallic ribbons molded on cylinders of different radii, we tune separately the natural curvature and the geometry to study curling dynamics in air, water and in viscous oils, thus spanning a wide range of Reynolds numbers. Our theoretical and experimental approaches separate the role of elasticity, gravity and hydrodynamic dissipation from inertia and emphasize the fundamental differences between the curling of a naturally curved ribbon and a rod described by the classical Elastica. Ribbons are indeed an intermediate class of objects between rods, which can be totally described by one-dimensional deformations, and sheets. Since Lord Rayleigh, it is known that a thin sheet can easily be bent but not stretched. As a result, large deformations in thin sheets usually lead to the localization of deformations into small peaks and ridges as observed by crumpling a simple piece of paper. These elastic defects induce critical buckling situations studied in detail statically in the literature, while experimental and theoretical studies on their dynamics are scarce. Our work shows evidence for the propagation of such a single instability front, selected by a local buckling mechanism. Finally, we show that depending on gravity, and both the Reynolds and the Cauchy numbers, the curling speed and shape are modified by the large scale drag and the local lubrication forces, shedding a new light on microscopic experiences where curling is observed
