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...

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. However, attempts to leverage this programmability in objects that can change shape, or morph, have been limited by the tendency for the deformations induced by multiple elastic elements to be incompatible -deformation is frustrated by geometry. We study the root cause of this frustration in a particular system, the soft morphable sheet, which is caused by an azimuthal buckling instability of bistable elements embedded within a sheet. With this understanding we show that, for this system at least, the root of frustration can itself be frustrated by an appropriate design of the lattice on which bistable elements are placed.

No abstract

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.