Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session H11: Focus Session: Extreme Mechanics I 
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Sponsoring Units: GSNP Chair: P. Reis, Massachusetts Institute of Technology Room: A107A109 
Tuesday, March 16, 2010 8:00AM  8:36AM 
H11.00001: Buckling thin films with inhomogeneous swelling Invited Speaker: Christian Santangelo The shapes of many leaves and flowers are determined, at least in part, by their inhomogeneous growth. Additional growth at the edges of leaves, for example, result in saddlesplay curvature and, ultimately, wrinkling. Recent experiments on thin, polymer films imprinted with a predefined pattern of inhomogeneous swelling provide a controlled, experimental playground for describing how swellinginduced buckling leads to a prescribed threedimensional shape. For example, one expects a sufficiently thin sheet to buckle into a shape that eliminates most of its inplane strain. Though this is always possible locally, a particular swelling pattern may be either globally frustrated, having no stressfree shapes even for vanishing thickness, or lead to a large degeneracy of stressfree shapes. In both cases, the bending energy remains important even for very thin sheets. I will describe theoretical work on disks and narrow ribbons with swellinginduced, negative Gaussian curvature. Perhaps surprisingly, when the prescribed Gaussian curvature is constant, there are families of stressfree and nearly stressfree shapes, none of which seem to appear in experiments. To understand this behavior, I will identify regimes in which the minimal energy ribbon shape can be determined and discuss the role of stretching and bending energies. We will consider both strips and closed ribbons. [Preview Abstract] 
Tuesday, March 16, 2010 8:36AM  8:48AM 
H11.00002: Conical surfaces and singularities in highly constrained elastic membranes Paula Mellado, Shengfeng Cheng, Andres Concha An elastic membrane that is forced to reside in a container of a slightly smaller size will deform and, upon further volume reduction, will eventually crumple. Previous studies have focused on the onset of the crumpled state by analyzing the mechanical response and stability of a developable conical surface (dcones) that can be described by a singlevalued function, while others have simulated the highly packed regime, neglecting the importance of connectivity of the membrane. Here we present a study in which experiments, numerical simulation and analytic work are used to show that the emergence of new regions of high stretching is a generic outcome when a self avoiding membrane is subject to a severe geometrical constraint. Consequently, an anomalous mechanical response, characterized by a series of peaks in the forcedeformation curve, appears as the membrane is squeezed. Our findings emphasize the role of selfavoidance, connectivity and friction as the key factors defining the morphology and response of a d cone from its formation to its final fate. [Preview Abstract] 
Tuesday, March 16, 2010 8:48AM  9:00AM 
H11.00003: Simple experiments in thin plates: Persistence length of curvature and Snapbuckling instability Yoel Forterre, Catherine Quilliet, L. Mahadevan, Denis Richard, Loic Tadrist We present two experiments in which the interplay between stretching and bending modes in thin elastic plates plays an important role. The first experiment is motivated by the understanding of plant leaf shape (e.g. Maize leaves, grass). During growth, many leaves unfold to become flat while their bottom is still attached to the cylindrical stem. We investigate the mechanical analogue of this unfold length and address the question: what is the persistence length of a curvature applied at one end of a flat elastic strip? Simple scaling arguments are compared to experiments and numerical simulations using Surface Evolver. The second experiment concerns the snapbuckling instability of highly deformed plates, in relation to the noise of crumpling. Using highspeed video and threedimensional shape reconstruction, we show that snapbuckling instabilities in thin plates are nonhomogeneous and occur via the very fast propagation of an elastic defect. The speed of the transition and the acoustic signature of the snap are mainly controlled by the defect size. [Preview Abstract] 
Tuesday, March 16, 2010 9:00AM  9:12AM 
H11.00004: A Sheet on a Drop Hunter King, Narayanan Menon We study experimentally the shapes that result when a circular sheet of polystyrene film (diameter~3mm, thickness t=75500 nm) is placed on the surface of an initially spherical water droplet. The competition between surface energies of the fluid interfaces and the elastic stresses in the sheet leads to interesting compromises between their energetically preferred shapes. We report the progression of features that result from continuously varying the droplet volume (and curvature) for various film thicknesses and sizes. For small droplet curvature, the sheet is smoothly stretched. It then develops smooth radial wrinkles at the edges. At larger drop volumes, the azimuthal symmetry is further broken as some wrinkles turn into focused dconelike points, and the droplet develops a faceted polygonal flat ``tabletop.'' [Preview Abstract] 
Tuesday, March 16, 2010 9:12AM  9:24AM 
H11.00005: Geometry of a sheet crumpled into a ball Narayanan Menon, Dominique Cambou We use Xray CT scanning to resolve in 3dimensions the conformation of aluminum sheets with thickness t=25 microns crumpled into spherical balls with average volume fractions, $\phi $ ranging from 0.06 to 0.22. We have previously reported an inhomogeneous distribution of mass in the volume: the volume fraction increases with radius so that the sphere is densest at its surface. We now report on the geometry of the sheet, in particular we report on the distribution of Gaussian and mean curvature in the sample, with a view to quantifying the arrangement of regions of stressfocusing. A new feature apparent in the images is an unusually strong degree of stacking into multilayered facets. We quantify layering in the sample by reporting on the local nematic ordering of the sheet normals. [Preview Abstract] 

H11.00006: ABSTRACT WITHDRAWN 
Tuesday, March 16, 2010 9:36AM  9:48AM 
H11.00007: Shape Selection in NonEuclidean Plates John Gemmer, Shankar Venkataramani We present a theoretical study of free nonEuclidean plates with a disc geometry and a prescribed metric that corresponds to a constant negative Gaussian curvature. We take the equilibrium configuration taken by the these sheets to be a minimum of a F\"{o}ppel VonK\`{a}rm\`{a}n type functional in which configurations free of any in plane stretching correspond to isometric embeddings of the metric. We show for all radii there exists low bending energy configurations free of any in plane stretching that obtain a periodic profile. The number of periods in these configurations is set by the condition that the principle curvatures of the surface remain finite and grows approximately exponentially with the radius of the disc. [Preview Abstract] 
Tuesday, March 16, 2010 9:48AM  10:00AM 
H11.00008: Pattern Driven Stress Localization Andrew Croll, Alfred Crosby The selfassembly of patterns from isotropic initial states is a major driver of modern softmatter research. This avenue of study is directed by the desire to understand the complex physics of the varied structures found in Nature, and by technological interest in functional materials that may be derived through biomimicry. In this work we show how a simple striped phase can respond with significant complexity to an appropriately chosen perturbation. In particular, we show how a buckled elastic plate transitions into a state of stress localization using a simple, selfassembled variation in surface topography. The collection of topographic boundaries act in concert to change the state from isotropic sinusoidal wrinkles, to sharp folds or creases separated by relatively flat regions. By varying the size of the imposed topographic pattern or the wavelength of the wrinkles, we construct a state diagram of the system. The localized state has implications for both biological systems, and for the control of nonlinear pattern formation. [Preview Abstract] 
Tuesday, March 16, 2010 10:00AM  10:12AM 
H11.00009: How do singularities fade away? From stressfocusing zones to smoothly deformed regions of elastic sheets Benny Davidovitch, Lee Walsh Confining elastic sheets often results in the formation of singular, stressfocusing structures: ridges and vertices in which strain is localized, allowing the sheet to reach a developable shape in the limit of vanishing thickness. The formation of such developable shapes through a network of singularities may become impossible, however, when certain types of geometric constraints are imposed on the sheet. One may ask: Are there other fundamental types of stress distribution that govern patterns on elastic sheets under such conditions? In particular  what is the nature of transition zones between singular and smoothly bent structures that may emerge in separate parts of a stressed sheet? We will address these questions through simple model systems that demonstrate the emergence of nontrivial shapes under such conditions. [Preview Abstract] 
Tuesday, March 16, 2010 10:12AM  10:24AM 
H11.00010: Experimental Study of Shape and Energy Scaling in Hyperbolic NonEuclidean Plates Yael Klein, Efi Efrati, Eran Sharon Hyperbolic elastic NonEuclidean plates are plates whose two dimensional target metric prescribes a negative Gaussian curvature. The equilibrium configurations of such, axisymmetric, bodies are known to consist of multiscale wave cascades. Using environmentally responsive gels, we experimentally study the change of the wavy patters with the thickness of the discs and with their radius. We provide the scaling of the number of nodes with respect to these parameters and show that, as the disc thickness decreases, the bending content of the discs sharply increases. This increase is compensated by a reduction of stretching content, due to the refinement of scales. [Preview Abstract] 
Tuesday, March 16, 2010 10:24AM  10:36AM 
H11.00011: The shapes of twocomponent crystalline shell Graziano Vernizzi, Rastko Sknepnek, Monica Olvera de la Cruz We consider an elastic shell with two coexisting components having different bending rigidities and elastic constants. We explore the lowenergy configuration of the shell when the relative fraction of the two components and their elastic constants vary. We analyze different domain patterns associated with the shape of the shell. We also study the effect of a line tension term between the two components. We show how the relation between the morphology of the shell and the domain patterns lead to a rich variety of structures. In particular we discuss the role of the buckling instability in this model with heterogeneous components. [Preview Abstract] 
Tuesday, March 16, 2010 10:36AM  10:48AM 
H11.00012: Buckling and crumpling of a compressed thinwalled box Tuomas Tallinen, Jan {\AA}str\"om, Jussi Timonen Vertical compression of an elastic thinwalled box is explored. Such a compression displays three successive regimes: linear, buckled and collapsed. Analogy of the buckled regime to thinfilm blisters is demonstrated. The compression force is shown to reach its maximum at the end of that regime, after which the box collapses displaying features (e.g. ridges) typical of crumpling of thin sheets. These qualitative findings are confirmed by numerical simulations based on a discrete element method, and implications are drawn on the box compression strength. [Preview Abstract] 
Tuesday, March 16, 2010 10:48AM  11:00AM 
H11.00013: Draping Films: A Wrinkle to Fold Transition Douglas Holmes, Alfred J. Crosby This work focuses on the wrinkletofold transition in glassy and elastomeric thin films. In biological systems, the process of folding is critical to morphogenesis, defining such features as the neural folds in embryonic development. In this paper, we examine the deformation of an axisymmetric sheet and quantify the force required to generate a fold. A thin film draping over a point of contact will wrinkle due to the strain imposed by the point and the underlying substrate. The wrinkle wavelength is dictated by a balance of material properties and geometry, and scales with film thickness to the threefourths power. At a critical strain the stress in the film will localize, causing hundreds of wrinkles to collapse into several discrete folds. We measure the energy of formation for a single fold and observe that it scales linearly with film thickness. We predict that the onset of folding, from a critical force or displacement, scales as the thickness to the onefifth power. The folds act as disclinations in the film causing the stress in the film to increase, thereby decreasing the wavelength of the remaining wrinkles. The number of folds that form from wrinkle collapse appears to be constant over several orders of magnitude in film thickness and elastic modulus. [Preview Abstract] 
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