Pham Dinh Huy, Démery Vincent, Davidovitch Benny, Brau Fabian, Damman Pascal
Laboratoire Interfaces Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium.
Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France.
Phys Rev Lett. 2016 Sep 2;117(10):104301. doi: 10.1103/PhysRevLett.117.104301. Epub 2016 Sep 1.
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.
处于张力下的扭曲带呈现出极其丰富的形态，从光滑和有褶皱的螺旋面到圆柱形或多面体形图案。这种复杂性源于系统自然螺旋对称的不稳定性，它会产生纵向和横向应力，从而导致带的屈曲。在这里，我们关注由三角形小面构成的镶嵌图案。我们的实验观察结果是在一种将几何与弹性结合起来的“渐近等距”方法中进行描述的。几何结构由参数化的曲面族组成，在厚度和拉伸载荷消失的奇异极限下与未变形的带等距。能量在这些曲面族中通过最小化来选择有利的结构，它由图案的拉伸功和弯曲成本决定。这个框架描述了形态相图中的共存线，并确定了多面体形结构的存在域。
