Cylinder morphology of a stretched and twisted ribbon

A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a transverse instability of the helicoid. Here, we propose a simple description for this cylindrical shape. By comparing its energy to the energy of other configurations, we are able to determine its location on the phase diagram. The theoretical predictions are in good agreement with our experimental results

How Geometry Controls the Tearing of Adhesive Thin Films on Curved Surfaces

Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.Comment: 6 pages, 5 figure

From cylindrical to stretching ridges and wrinkles in twisted ribbons

Twisted ribbons subjected to a tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. These shapes are intimately related to the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. In this paper, we focus on the tessellation patterns made of triangular facets. Our experimental observations are described within an "asymptotic isometry" approach that brings together geometry and elasticity. The geometry consists of parametrized families of surfaces, isometric to the undeformed ribbon in the singular limit of vanishing thickness and tensile load. The energy, whose minimization selects the favored structure among those families, is governed by the tensile work and bending cost of the pattern. This framework describes the coexistence lines in a morphological phase diagram, and determines the domain of existence of faceted structures.Comment: 5 pages, 4 figures; Supplemental material: 4 page

Exploiting the localized surface plasmon modes in gold triangular nanoparticles for sensing applications

In this study we investigate and exploit, for optical sensing, the surface plasmon excitation in gold triangular nanoparticles with high aspect ratios (i.e., the ratio of the edge length of the triangles with the height) prepared by nanosphere lithography. As shown previously, the shape and size of these nanoparticles were used to tune their optical properties, monitored by far field extinction spectroscopy. Interestingly, several localized surface plasmon resonances were detected in the visible and near infrared regions and were attributed to dipole and quadrupole modes. These modes, identified from numerical simulations, "red-shift'' as the aspect ratio of the particles increases. The plasmon modes observed for larger triangles exhibit unexpected sensitivity with a change in the refractive index. From experiments and numerical simulations, this higher sensitivity has been attributed to an increase of the local field enhancement for sharper tips. This new effect can provide important information for the design of particles as building blocks for sensing applications

A microscopic picture of erosion and sedimentation processes in dense granular flows

Gravity-driven flows of granular matter are involved in a wide variety of situations, ranging from industrial processes to geophysical phenomena, such as avalanches or landslides. These flows are characterized by the coexistence of solid and fluid phases, whose stability is directly related to the erosion and sedimentation occurring at the solid-fluid interface. To describe these mechanisms, we build a microscopic model involving friction, geometry, and a nonlocal cooperativity emerging from the propagation of collisions. This new picture enables us to obtain a detailed description of the exchanges between the fluid and solid phases. The model predicts a phase diagram including erosion, sedimentation, and stationary-flow regimes, in quantitative agreement with experiments and discrete-element-method simulations

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