Elastocapillarity: adhesion and large deformations of thin sheets

Abstract

This thesis is concerned with the deformation and adhesion of thin elastic sheets that come into contact with an underlying substrate. The focus of this work is on the interplay between material and geometric properties of a system and how this interplay determines the equilibrium states of sheet and substrate, particularly in the regime of geometrically nonlinear deformations.

We first consider the form of an elastic sheet that is partially adhered to a rigid substrate, accounting for deflections with large slope: the Sticky Elastica. Starting from the classical Euler Elastica we provide numerical results for the profiles of such blisters and present asymptotic expressions that go beyond the previously known, linear, approximations. Our theoretical predictions are confirmed by desktop experiments and suggest a new method for the measurement of material properties for systems undergoing large deformations.

With the aim to gain better understanding of the initial appearance of blisters we next investigate the deformation of a thin elastic sheet floating on a liquid surface. We show that, after the appearance of initial wrinkles, the sheet delaminates from the liquid over a finite region at a critical compression, forming a delamination blister. We determine the initial blister size and the evolution of blister size with continuing compression before verifying our theoretical results with experiments at a macroscopic scale.

We next study theoretically the deposition of thin sheets onto a grooved substrate, in the context of graphene adhesion. We develop a model to understand the equilibrium of the sheet allowing for partial conformation of sheet to substrate. This model gives phys- ical insight into recent observations of ‘snap-through’ from flat to conforming states and emphasises the crucial role of substrate shape in determining the nature of this transition.

We finally present a theoretical investigation of stiction in nanoscale electromechanical contact switches. Our model captures the elastic bending of the switch in response to both electrostatic and van der Waals forces and accounts for geometrically nonlinear deflections. We solve the resulting equations numerically to study how a cantilever beam adheres to a fixed bottom electrode: transitions between free, pinned and clamped states are shown to be discontinuous and to exhibit significant hysteresis. The implications for nanoscale switch design are discussed.