Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session Y55: Shell Buckling IIFocus

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Sponsoring Units: GSNP GSOFT Chair: Pedro Reis, Ecole polytechnique federale de Lausanne Room: BCEC 254B 
Friday, March 8, 2019 11:15AM  11:27AM 
Y55.00001: Mechanics of turning a page Jihye Myeong, Anna Lee, HoYoung Kim A mundane activity of turning a page arises not only in reading, but also in production of paper and textile. Here we analyze the shape and stability of a thin sheet of paper, bound to a book in one side and compressed from the other side, to gain mechanical understanding of the page turning. We start with describing the shape of a sheet that is buckled between the bound end and gripping fingers, using the Euler elastica. Then we predict the fate of the bent page when the external load is removed, to determine the condition for the page to turn to the other side. Upon corroborating our theory with experiments of various geometry and materials of thin sheets, we suggest the shortest path of fingers to turn pages for both lazy readers and efficient manufacturing robots. 
Friday, March 8, 2019 11:27AM  11:39AM 
Y55.00002: Swimming through shell buckling Adel Djellouli, Philippe Marmottant, gwennou coupier, Catherine Quilliet, Henda djeridi Under pressure, a hollow elastic sphere becomes unstable and 
Friday, March 8, 2019 11:39AM  11:51AM 
Y55.00003: Buckled Bundles and Beyond Isaac Bruss, Gregory Grason Defects can elastically buckle 2D crystalline membranes (like graphene) into 3D shapes. Using a combination of numerical simulations and continuum elasticity theory we show how the same is true for columnar structures (like nanotubes or protein fibers). This discovery builds upon the recently uncovered mapping between the interfilament spacing in bundles and the metric properties of a curved surface. We show that shape instabilities are controlled by a single materialdependent parameter that characterizes the ratio of bending to cohesion energies. Along with a host of previously unknown shape equilibria—the filamentous analogs to the conical and saddlelike shapes of defective membranes—we find a profoundly asymmetric response to positive and negative disclinations in the infinite length limit that is without parallel to the membrane analog. 
Friday, March 8, 2019 11:51AM  12:03PM 
Y55.00004: Dynamic buckling of rings and annuli Ousmane Kodio, Finn Box, Doireann O'Kiely, Vincent Cantelli, Alain Goriely, Dominic Vella When an elastic ring is subject to an external pressure, it is known to buckle as a 'figure of 8'; similarly an annulus subject to a strong internal tension is known to form two folds. Here we explore how these examples of mode2 buckling change under dynamic loading. In particular, we show that the presence of inertia means that higher modes are observed at the onset of instability, and present results for the observed mode number as a function of the driving pressure. Our results are in accord with experiments in which an elastic ring is rapidly pulled inwards by surface tension. Surprisingly, we find that while inertia is required to observe higher modes, the actual selected mode does not depend on inertia. We explain this, and reconcile our observation of higher modes with earlier experiments that exhibited mode 2, by understanding the growth rate of instability. 
Friday, March 8, 2019 12:03PM  12:15PM 
Y55.00005: Membrane morphology beyond polyhedra HANG YUAN, Monica Olvera de la Cruz Conventional homogeneous or heterogeneous elastic crystalline membrane exhibits buckling transition from sphere to polyhedra. However, their morphologies do not go beyond polyhedra and cannot be externally controlled. We study the morphology of a closed crystalline membrane coassembled with superparamagnetic particles which is called magnetoelastic membrane. With additional competition from magnetic dipoledipole interaction on top of elasticity, magnetoelastic membrane shows novel morphology beyond polyhedra. By systematically changing two dimensionless control parameters, we find a rich class of membrane morphologies. The morphology of magnetoelastic membrane can be manipulated by external magnetic field, providing promising applications for membrane shape control, design of microcontainers and targeted drug delivery systems. 
Friday, March 8, 2019 12:15PM  12:27PM 
Y55.00006: Swelling and warpage of orthotropic plates Harrison Wood, James Hanna While isotropic inplane swelling problems for elastic sheets have been studied extensively in 
Friday, March 8, 2019 12:27PM  12:39PM 
Y55.00007: Transverse edge extension underlies compression, buckling and wrinkling in thin solids Meng Xin, Benjamin Davidovitch When a rectangular sheet whose short edges are clamped is stretched, elongated wrinkles appear, indicating the presence of transverse compression. So far, the mechanism by which longitudinal tension and edge clamping act jointly to generate transverse compression has not been clarified. Here we employ analytic tools and numerical simulations to compare this problem with a new variant, where instead of stretching and edge clamping one only imposes edgelocalized transverse strain, pulling the corners outward. We find that, despite the absence of longitudinal tension in the new variant, both models exhibit similar transverse stress profile in planar state, thus revealing that the generic origin of compression is the transverse extension of edges relative to the bulk. This similarity in planar stress profiles underlies similarity in the nearthreshold buckling patterns exhibited by the two models. In contrast, the two models are sharply distinct in their respective farfromthreshold regime: the deflection of the stretched sheet consists of small wavelength wrinkles whereas the edgeextended sheet does not develop wrinkles. This indicates the role of longitudinal tension in providing an effective substrate resistance, which is crucial for the emergence of wrinkle patterns. 
Friday, March 8, 2019 12:39PM  12:51PM 
Y55.00008: A geometric theory of wrinkling for confined shells: Part 1 Yousra Timounay, Ian Tobasco, Desislava V Todorova, Eleni Katifori, Joseph D Paulsen The problem of joining a planar sheet to a surface with a different metric is a familiar frustration. Flat bandages don’t stick as well to curved knuckles or elbows, and maps of the earth exaggerate areas near the poles. We study the deformations of ultrathin (∼100 nm) elastic shells, which we manufacture on sphericallycurved substrates and then transfer to a flat water bath. The sheets respond by forming distinct domains filled by smooth parallel wrinkles or by disordered buckled patterns. We show that the selection of these domains and the orientation of wrinkles within them depends sensitively on the shape of the boundary of the film. Remarkably, these complex patterns may be predicted by a theoretical model wherein the exposed surface area of the water bath is minimized. The derivation and solution of this model will be presented in the next talk. (This is part 1 in a 3talk series). 
Friday, March 8, 2019 12:51PM  1:03PM 
Y55.00009: A geometric theory of wrinkling for confined shells: Part 2 Ian Tobasco, Yousra Timounay, Desislava V Todorova, Joseph D Paulsen, Eleni Katifori Thin elastic shells readily take on shapes wildly different from their own. Motivated by the puzzle of determining the wrinkle patterns exhibited by shallow shells floating on a water bath, we obtain a fully rigorous asymptotic expansion of the energy (elastic and otherwise) valid in the highfrequency limit. After renormalizing by the typical energy of wrinkling, we derive a coarsegrained model in which an elastically compatible pattern is assigned energy proportional to the difference between its intrinsic undeformed area and its projected area in the plane. Energetically optimal patterns therefore maximize their projected area. Surprisingly, this limiting model turns out to be explicitly solvable in a large variety of cases, including for shells whose (possibly nonconstant) curvature is of a known sign. We demonstrate our methods in many cases of interest, offering an ansatzfree explanation for the geometry of wrinkle patterns seen in confined elastic shells. (This is part 2 in a 3talk series.) 
Friday, March 8, 2019 1:03PM  1:15PM 
Y55.00010: A geometric theory of wrinkling for confined shells: Part 3 Desislava V Todorova, Ian Tobasco, Yousra Timounay, Joseph D Paulsen, Eleni Katifori Materials engineered through surface patterning are used for a broad array of applications, including flexible electronic and microfluidic devices, electronic skin, and many others. Microfabrication techniques based on elastic instabilities have attracted much attention because of their relative simplicity and potential for technological innovation. We employ Gaussian curvature as a mechanism for pattern formation: when a shallow curved shell is placed upon a liquid surface, welldefined domains of unidirectional wrinkles are formed. In the third part of this series of talks, we use finite element simulations and a theoretical approach based on the minimization of the elastic energy, to probe how the global arrangement of the patterns and wrinkling amplitude depends on the shape and curvature of the shell. We finally consider cases of shells with highly nontrivial boundary geometries and we demonstrate how this setup can be employed to harness surface structures with complex, yet predictable and controllable, topography. (This is part 3 in a 3talk series). 
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