Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the transition zone in the merging of two wrinkles, as building-blocks of the global pattern. Contrary to the case of crumple paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work. This formalism is validated from hundreds of nm for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.Comment: 7 pages, 4 figures, added references, submitted for publicatio

Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy. Here, we study the energy distribution for highly confined membranes and show the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic self-organized focalization of the deformation energy is observed provided an up-down symmetry breaking, induced by the intrinsic nonlinearity of the elasticity equations, occurs. The physical model, exhibiting an analogy with parametric resonance in nonlinear oscillator, is a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues, e.g., wrinkled skin, internal structure of lungs, internal elastica of an artery, brain convolutions or formation of fingerprints. Moreover, it opens the way to new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography via self-organization.Comment: Submitted for publicatio

Stretchable electronic structures formed of thin films integrated with soft heterogeneous substrate

Stretchable electronic structure comprising one intrinsically fragile thin film integrated on or within a soft heterogeneous substrate. The invention also relates to a process for manufacturing such a structure

In situ tuning the optical properties of a cavity by wrinkling

In this letter we propose an original, in situ, approach to tune the optical properties of an optical cavity, based on the wrinkling of compressed metal/polymer multilayer thin films. This phenomenon is conceptually described, simulated, and experimentally confirmed. The main idea is to use wrinkling to modulate the effective refractive index of the upper interface. This modulation induces a spectral shift of the cavity modes. The work presented here constitutes a first step to the development of stretchable and curved photonics

Hierarchical wrinkling patterns

International audienceThis paper reports a simple and flexible method for generating hierarchical patterns from wrinkling instability. Complex features with gradually changing topographies are generated by using the spontaneous wrinkling of a rigid membrane (titanium) on a soft foundation (polystyrene) compressed via the diffusion of a solvent. We show that the morphology of these unreported wrinkled patterns is directly related to the rheological properties of the polymer layer and the geometry of the diffusion front. Based on these ingredients, we rationalize the mechanism for the formation of hierarchical wrinkling patterns and quantify our experimental findings with a simple scaling theory. Finally, we illustrate the relevance of our structuration method by studying the mechanosensitivity of fibroblasts