title: From Cylindrical to Stretching Ridges and Wrinkles in Twisted Ribbons.
abstract: Twisted ribbons under tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. This complexity emanates from the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. Here, 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.
authors.affiliation: Laboratoire Interfaces Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium.
authors.forename: Huy
authors.initials: H
authors.lastname: Pham Dinh
authors.affiliation: Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France.
authors.forename: Vincent
authors.initials: V
authors.lastname: Démery
authors.affiliation: Department of Physics, University of Massachussetts, Amherst, Massachussetts 01003, USA.
authors.forename: Benny
authors.initials: B
authors.lastname: Davidovitch
authors.affiliation: Laboratoire Interfaces Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium.
authors.forename: Fabian
authors.initials: F
authors.lastname: Brau
authors.affiliation: Laboratoire Interfaces Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium.
authors.forename: Pascal
authors.initials: P
authors.lastname: Damman