Delamination from an adhesive sphere: Curvature-induced dewetting versus buckling.

Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates-what is a petty frustration when placing a sticky band aid onto a knee is a more serious matter in the coating and painting industries. Irrespective of their resistance to bending, a key driver of such phenomena is Gauss' Theorema Egregium, which implies that naturally flat sheets cannot conform to doubly curved surfaces without developing a strain whose magnitude grows sharply with the curved area. Previous attempts to characterize the onset of curvature-induced delamination, and the complex patterns it gives rise to, assumed a dewetting-like mechanism in which the propensity of two materials to form contact through interfacial energy is modified by an elastic energy penalty. We show that this approach may characterize moderately bendable sheets but fails qualitatively to describe the curvature-induced delamination of ultrathin films, whose mechanics is governed by their propensity to buckle and delaminate partially, under minute levels of compression. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination accounting for the two buckling motifs that underlie partial delamination: shallow "rucks" and localized "folds". We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experiments. Beyond gaining control on the use of ultrathin adhesives in cutting-edge technologies such as stretchable electronics, our analysis is a significant step toward quantifying the multiscale morphology that emerges upon imposing geometrical and mechanical constraints on highly bendable solid objects.

Tapered elasticæ as a route for axisymmetric morphing structures.

Transforming flat two-dimensional (2D) sheets into three-dimensional (3D) structures by combining carefully made cuts with applied edge-loads has emerged as an exciting manufacturing paradigm in a range of applications from mechanical metamaterials to flexible electronics. In Kirigami, patterns of cuts are introduced that allow solid faces to rotate about each other, deforming in three dimensions whilst remaining planar. In other scenarios, however, the solid elements bend in one direction. In this paper, we model such bending deformations using the formulation of an elastic strip whose thickness and width are tapered (the 'tapered elastica'). We show how this framework can be exploited to design the tapering patterns required to create planar sheets that morph into desired axisymmetric 3D shapes under a combination of horizontal and vertical edge-loads. We exhibit this technique by recreating miniature structures with positive, negative, and variable apparent Gaussian curvatures. With sheets of constant thickness, the resulting morphed shapes may leave gaps between the deformed elements. However, by tapering the thickness of the sheet too, these gaps can be closed, creating tessellated three-dimensional structures. Our theoretical approaches are verified by both numerical simulations and physical experiments.