Wrinkles and folds in a fluid-supported sheet of finite size

Abstract

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength λ. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length L, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We find that a second-order transition between these two states occurs at a critical confinement F = λ 2 /L.

Crumples as a Generic Stress-Focusing Instability in Confined Sheets

“…7 to sufficiently small ∆ where such folds do not appear. For the case of a flat bath (α = 0), there is a well-studied wrinkle-to-fold transition that results from a competition of bending and gravitational energies [31,51,52], but this folding threshold depends on ∆ rather than ∆, so we do not denote it in Fig. 7.…”

Microfluidic probing of the complex interfacial rheology of multilayer capsules

“…To rationalize the formulation of capsules it is necessary to understand the link between the composition of the protecting membrane, its mechanical properties and the performances of the capsules, which requires model polymer membranes as well as experimental techniques to determine capsule mechanical properties. New experimental techniques have been developed to characterize elastic polymer membranes at liquid interfaces [14][15][16][17][18] . The rheology of such membranes has been studied in model geometries 15,17,[19][20][21][22][23] and also on real capsules in viscous flows to mimic real conditions of fabrication and use, through various experiments 16,[23][24][25][26] , theories [27][28][29] and simulations [30][31][32] .…”

Fluid-supported elastic sheet under compression: Multifold solutions

“…These experiments have stimulated several efforts at modeling this sequence of transitions [2][3][4][5]. The equilibrium configurations are described by a fourth-order equation for the deformation angle as a function of arclength.…”

“…However, the problem also admits a vast array of multifold states consisting of both identical and nonidentical folds at different locations along the sheet. We compute here both single fold and multifold states using numerical continuation techniques that have proved invaluable in the studies of the Swift-Hohenberg equation, as well as weakly nonlinear theory of the type first employed in the present context in [5] and discuss the stability properties of these distinct states.…”