Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session J9: Focus Session: Elasticity and Geometry of Thin Objects II |
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Sponsoring Units: GSNP Chair: Pedro Reis, Massachusetts Institute of Technology Room: 303 |
Tuesday, March 17, 2009 11:15AM - 11:51AM |
J9.00001: The self assembly of closed surfaces from flat sheet Invited Speaker: We will discuss theoretical and some experimental work to understand the conditions which a flat sheet with embedded permanent magnets can spontaneously fold into a closed surface. The critical question is understanding how to design the system -- both the cut of the sheet and the position of the magnets -- to maximize the yield of assembling into a closed surface without misfolding. This problem also raises novel and interesting questions in thin plate elasticity, which will be highlighted. [Preview Abstract] |
Tuesday, March 17, 2009 11:51AM - 12:03PM |
J9.00002: Simulating Striped Phases on Curved Surfaces Robin L. B. Selinger, Jonathan V. Selinger Ordered phases on curved surfaces often exhibit geometrical frustration: if the order is incompatible with the curved geometry, the phase must form a complex pattern of defects. Many recent theoretical and experimental studies have explored the relationship between curvature, order, and defects in crystalline, nematic, and striped (smectic or columnar) phases. In earlier work, we developed a new approach for simulating the orientational order of nematic phases on curved surfaces. We now present an analogous approch for simulating striped phases. This approach is based on a lattice gas, in which the Ising spin represents the local density variable. Long-range antiferromagnetic interactions between the spins induce the formation of a striped phase, with a wavelength proportional to the interaction range. This model can be simulated on a random mesh, which can be defined on any arbitrary curved geometry. Through these simulations, we determine how striped phases respond to curvature on spheres, tori, and other geometries. [Preview Abstract] |
Tuesday, March 17, 2009 12:03PM - 12:15PM |
J9.00003: Simulating Complex Modulated Phases Through Spin Models Jonathan V. Selinger, Lena M. Lopatina, Jun Geng, Robin L. B. Selinger We extend the computational approach for studying striped phases on curved surfaces, presented in the previous talk, to two new problems involving complex modulated phases. First, we simulate a smectic liquid crystal on an arbitrary mesh by mapping the director field onto a vector spin and the density wave onto an Ising spin. We can thereby determine how the smectic phase responds to any geometrical constraints, including hybrid boundary conditions, patterned substrates, and disordered substrates. This method may provide a useful tool for designing ferroelectric liquid crystal cells. Second, we explore a model of vector spins on a flat two-dimensional (2D) lattice with long-range antiferromagnetic interactions. This model generates modulated phases with surprisingly complex structures, including 1D stripes and 2D periodic cells, which are independent of the underlying lattice. We speculate on the physical significance of these structures. [Preview Abstract] |
Tuesday, March 17, 2009 12:15PM - 12:27PM |
J9.00004: Slow Stress-Relaxation of Thin Sheet Folds Jens Feder, Simon de Villiers, Anders Malthe-Sorenssen We measure the slowly relaxing force required to maintain a fold in thin sheets of aluminum, copper, Mylar, and paper. The relaxation is found to be best described by a Weibull distribution of relaxation times. The exponent $\beta$ of the Weibull distribution characterizes two distinct classes of relaxation observed in metallic ($\beta\simeq 2$) and polymeric materials ($\beta \simeq 1$) respectively. [Preview Abstract] |
Tuesday, March 17, 2009 12:27PM - 12:39PM |
J9.00005: Nanomechanical properties of few-layer graphene membranes Menno Poot, Herre van der Zant Graphene is a one-atom thick layer of graphite and has only recently been discovered. It combines unique electronic properties with an extremely high Young's modulus of 1 TPa. We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. Both the bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. Both parameters show a strong thickness-dependence. Surprisingly, flakes with down to only eight atoms thick can still be described by continuum mechanics. Measurements on single layer graphene could resolve the long standing question whether a one-atom thick membrane can have a finite bending rigidity. Finally we predict that these nanodrums have resonance frequencies in the GHz range. These high frequencies combined with their low mass make them ideal components for quantum electromechanical systems. [Preview Abstract] |
Tuesday, March 17, 2009 12:39PM - 12:51PM |
J9.00006: Adhesion Transition of Flexible Filaments Arthur Evans, Eric Lauga As forays into fabrication and self-assembly venture to increasingly small length scales, the role of adhesion events between material elements of the system must be closely scrutinized. This area of study is typically dominated by investigations into capillary adhesion, but relatively recent interest in carbon nanotubes and biomimetic devices have spurred interest in intermolecular forces as another source of micro- and nano-scale adhesion. We present here a far-field model for ``dry'' adhesion. We consider a small number N of flexible beams interacting with each other via a typical Lennard-Jones 6-12 potential, and describe the behavior of the system as the ratio of bending rigidity to beam-beam attraction is reduced. Applications ranging from fibrillar systems to the comparatively stiff carbon nanotubes are discussed. [Preview Abstract] |
Tuesday, March 17, 2009 12:51PM - 1:03PM |
J9.00007: Elastic theory of unconstrained non-Euclidean plates and shells Efi Efrati, Raz Kupferman, Eran Sharon Non Euclidean bodies possess no stress free configuration, thus exhibit residual stress and a rich variety of non-trivial equilibrium configurations in the absence of external constraints. An appropriate hyper-elastic treatment of such bodies is achieved by measuring strain with respect to a reference metric rather than a reference configuration. Applying this formalism to thin sheets, we derive a reduced 2D elastic theory, which enables us to treat thin bodies which are neither plates nor shells in the classical sense. In this reduced theory the elastic energy is given as a function of the mid-surface properties (first and second fundamental forms). We show how prescribing a reference metric for a three-dimensional thin body, corresponds to setting a reference first fundamental form (2D metric) and a reference second fundamental form (curvatures) on the mid-surface. When the prescribed reference curvatures and 2D metric do not comply with one another, the system is frustrated (non-Euclidean). Such systems exhibit various phenomena such as spontaneous buckling and the emergence of a boundary layer. [Preview Abstract] |
Tuesday, March 17, 2009 1:03PM - 1:15PM |
J9.00008: Experimental Study of Energy Scaling in Non-Euclidean Plates Yael Klein, Eran Sharon We present an experimental study of the three-dimensional (3D) configurations that result from non-uniform lateral growth/shrinking of thin elastic sheets. We construct environmentally responsive hydrogel plates that shrink no uniformly when heated above 33C0. This process prescribes a non-Euclidean ``target'' metric on the sheets. In order to reduce their energy, the plates buckle into 3D configurations associated with their target metric. We study the variations in sheet configurations with decreasing thickness. We observe two types of behaviors: sheets with imposed positive Gaussian curvature have weak thickness dependence, their bending content is bounded and their total bending energy scales like thickness cube. On the other hand, sheets with imposed negative Gaussian curvature undergo a set of bifurcations, as they obtain configurations with increasing number of nodes as thickness decreases. As a result their bending content increases with decreasing thickness, causing the bending energy to scale like the square of the thickness. [Preview Abstract] |
Tuesday, March 17, 2009 1:15PM - 1:27PM |
J9.00009: The Elastochrone: the descent time of a sphere on a flexible beam Jeffrey Aristoff, Christophe Clanet, John Bush We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favorably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is compared to the classical brachistochrone, the shortest time between two points in a gravitational field. [Preview Abstract] |
Tuesday, March 17, 2009 1:27PM - 1:39PM |
J9.00010: Wrinkles/Folds and the Role of Interfacial Thermodynamics Luka Pocivavsek, Brian Leahy, Enrique Cerda, Binhua Lin, Ka Yee Lee We recently developed a general model for studying instabilities like wrinkling and folding in interfacial membranes on fluid substrates. The dominant length scales describing the instability are set by the elastic response of the membrane (primarily bending) and the ``stiffness'' of the substrate. These length scales, like the wrinkle wavelength and fold amplitude, are independent of the particular interfacial molecular interactions for micron thick membranes where typical system energies like the membrane bending stiffness are thousands of times larger than intermolecular potentials. However, as the membranes become thinner and thinner and eventually approach molecular membranes only a couple of nanometers thin, the chemical interactions between the membrane and the fluid substrate strongly influence the wrinkling and folding length scales. We present data for two such systems (a lipid monolayer and a gold nanoparticle layer) on different hydrogen bonding fluids and discuss possible mechanisms and modifications of our wrinkle-to-fold scaling laws to account for this new degree of freedom. [Preview Abstract] |
Tuesday, March 17, 2009 1:39PM - 1:51PM |
J9.00011: Universal Shapes of Interacting Mode-I Cracks Melissa Fender, Frederic Lechenault, Pedro Reis, Benoit Roman, Karen Daniels We experimentally investigate the interaction between two parallel cracks propagating towards each other under uniaxial traction in quasi-2D slabs of gelatin. A single crack would propagate perpendicular to the direction of traction. However, after they pass each other, the two cracks rotate and ultimately meet, leaving behind a lens-shaped remnant. We find a universal length-to-width ratio for this remnant, independent of the pulling speed and initial crack separation; the same phenomenon is observed in a variety of elastic materials. Moreover, the overall dimensions of the lens-shaped remnant are set by the initial crack separation. [Preview Abstract] |
Tuesday, March 17, 2009 1:51PM - 2:03PM |
J9.00012: The Life and Times of a Ruck in a Rug Dominic Vella, Mokhtar Adda-Bedia, Arezki Boudaoud We study the familiar problem of a ruck in a rug. Under lateral compression, a rug bends out of the plane forming a ruck - a localised region in which it is no longer in contact with the floor. We consider the equilibrium of such a ruck. Once the external force that caused the compression is removed, experience tells us that the ruck may either remain or flatten out under its own weight. We quantify the conditions under which each of these two scenarios occurs. We also consider how the propagation of a ruck along the carpet facilitates large-scale sliding. [Preview Abstract] |
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