Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session P40: More Geometry and Dynamics: Wrinkling, Folding, Snapping, etc. |
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Sponsoring Units: GSNP GSOFT Chair: Dominic Vella, Oxford University Room: 343 |
Wednesday, March 16, 2016 2:30PM - 2:42PM |
P40.00001: Rolling Wrinkles on Elastic Substrates Michael Imburgia, Alfred Crosby The mechanics of rolling contact between an elastomer layer and a thin film present unique opportunities for taking advantage of elastic instabilities, such as surface wrinkling, to create patterned surfaces. Here we present a plate-to-roll(P2R) geometry to laminate a thin film onto an elastomer layer in order to induce surface wrinkling. First, a poly(dimethylsiloxane)(PDMS) layer is draped around a roller and pressed into contact with a poly(styrene)(PS) film supported on a plate. Once rolling begins, the PS film preferentially laminates onto the PDMS layer. During this process, the deformation of the PDMS layer can induce wrinkling when the contact load exceeds a critical value. Wrinkle feature size consists of amplitudes of $0.2-4{\mu}m$ and wavelengths of $15-20{\mu}m$. Wrinkle amplitude can be controlled by contact load and roller curvature, as well as the mechanical properties and thickness of the film and elastomer. We develop semi-empirical equations to describe the effect of contact load and roller curvature on the wrinkle aspect ratio. Finite-element modeling of an elastomer layer in rolling contact with a rigid plate is used to support experimental results. Using these models, wrinkle-based technologies such as optoelectronics and enhanced adhesives can be envisioned. [Preview Abstract] |
Wednesday, March 16, 2016 2:42PM - 2:54PM |
P40.00002: Slow frictional waves Koushik Viswanathan, Narayan Sundaram, Srinivasan Chandrasekar Stick-slip, manifest as intermittent tangential motion between two dry solid surfaces, is a friction instability that governs diverse phenomena from automobile brake squeals to earthquakes. We show, using high-speed in situ imaging of an adhesive polymer interface, that low velocity stick--slip is fundamentally of three kinds, corresponding to passage of three different surface waves --- separation pulses, slip pulses and the well--known Schallamach waves. These waves, traveling much slower than elastic waves, have clear distinguishing properties. Separation pulses and Schallamach waves involve local interface separation, and propagate in opposite directions while slip pulses are characterized by a sharp stress front and do not display any interface detachment. A change in the stick-slip mode from separation to slip pulse is effected simply by increasing the normal force. Together, these three waves constitute all possible stick-slip modes in adhesive friction and are shown to have direct analogues in muscular locomotory waves in soft bodied invertebrates. A theory for slow wave propagation is also presented which is capable of explaining the attendant interface displacements, velocities and stresses. [Preview Abstract] |
Wednesday, March 16, 2016 2:54PM - 3:06PM |
P40.00003: Poking around: how indentation reveals wrinkly isometries Dominic Vella, Hamid Ebrahimi, Joseph Paulsen, Ashkan Vaziri, Narayanan Menon, Benny Davidovitch When deforming extremely thin objects, deformation via stretching is relatively expensive. It is therefore natural to seek deformations that preserve lengths, or isometries. Two common examples of such isometries in mechanics are the `d'-cone (for a plate) and `mirror buckling' (for a shell). I will show two examples for which the presence of a weak tension means that these isometries are not obtained experimentally. Instead, the systems in question wrinkle and tend to new `wrinkly isometries': isometries that are only available to a wrinkled object. [Preview Abstract] |
Wednesday, March 16, 2016 3:06PM - 3:18PM |
P40.00004: Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets Narayanan Menon, JD Paulsen, Evan Hohfeld, Hunter King, Jiangshui Huang, Thomas Russell, Zhanlong Qiu, Benny Davidovitch, Dominic Vella Natural wrinkle patterns often inhabit surfaces of curved substrates, and typically are spatially nonuniform. However, the unified understanding of wrinkle wavelength [1] in terms of a competition between the bending energy of a sheet and the stiffness provided by the tension or potential energy of the supporting substrate, applies only to nearly-planar, parallel, and spatially uniform wrinkle patterns.~ We describe theory and experiment that extend this understanding in two major directions. The first is to show that the underlying curvature may be treated as a distinct term in the substrate stiffness. The second is to demonstrate in two very different settings that the local value of the wavelength is determined by the local stiffness of the subphase. Both results are encapsulated in a simple, local law for the wavelength that has greatly expanded applicability. We acknowledge support from the WM Keck Foundation 1. Cerda, E., {\&} Mahadevan, L. (2003). \textit{Physical review letters}, \textit{90}, 074302. [Preview Abstract] |
Wednesday, March 16, 2016 3:18PM - 3:30PM |
P40.00005: Geometry-driven folding transitions in floating thin films Joseph D. Paulsen, Vincent D\'emery, K. Bugra Toga, Zhanlong Qiu, Benny Davidovitch, Thomas P. Russell, Narayanan Menon When a thin elastic sheet is compressed, it forms wrinkles to gather excess material, while deforming the fluid or solid substrate by only a small amount. Upon further compression, the sheet may fold, in order to lower the mechanical energy of the system$^1$. Here we demonstrate a folding transition that is independent of the mechanical properties of the sheet. We study the deformations of a thin polymer film that has an annular shape, floating on a planar air-water interface. By controlling the concentration of a surfactant outside the film, we vary the tension pulling on the outer boundary of the annulus. The sheet spontaneously folds at a threshold ratio of inner to outer surface tension that depends on the geometry of the sheet, but is independent of its bending rigidity. Our results are consistent with a simple geometric principle: the sheet adopts the unstretched shape that minimizes the interfacial energy of the exposed liquid$^2$. Finally, we consider the application of this geometric principle to the folding of a floating indented film.\\\\ 1. Pocivavsek et al., Science 320, 912 (2008).\\ 2. Paulsen et al., Nature Materials, doi:10.1038/nmat4397 (2015). [Preview Abstract] |
Wednesday, March 16, 2016 3:30PM - 3:42PM |
P40.00006: Ribbon curling Anne Juel, Chris Prior, Julien Moussou, Buddhapriya Chakrabarti, Oliver Jensen The procedure of curling a ribbon by running it over a sharp blade is commonly used when wrapping presents. Despite its ubiquity, a quantitative explanation of this everyday phenomenon is still lacking. We address this using experiment and theory, examining the dependence of ribbon curvature on blade curvature, the longitudinal load imposed on the ribbon and the speed of pulling. Experiments in which a ribbon is drawn steadily over a blade under a fixed load show that the ribbon curvature is generated over a restricted range of loads, the curvature/load relationship can be non-monotonic, and faster pulling (under a constant imposed load) results in less tightly curled ribbons. We develop a theoretical model that captures these features, building on the concept that the ribbon under the imposed deformation undergoes differential plastic stretching across its thickness, resulting in a permanently curved shape. The model identifies factors that optimize curling and clarifies the physical mechanisms underlying the ribbon's nonlinear response to an apparently simple deformation. [Preview Abstract] |
Wednesday, March 16, 2016 3:42PM - 3:54PM |
P40.00007: Periodic Buckling Patterns On Constrained Elastic Shells. Joel Marthelot, Anna Lee, Pierre-Thomas Brun, Francisco Lopez Jimenez, Pedro M. Reis Thin spherical shells range from nanometer-sized viruses to space vehicles. A pressure differential between the inner and outer part of the shell can result in the buckling and catastrophic failure of the structure. We revisit this classic buckling problem, depressurizing thin elastic shells, which are arrested from within by a concentric spherical mandrel. As a result, buckling is constrained to occur within the gap between the two. Above a critical pressure, dimples appear sequentially on the surface of the shell to form a robust periodic pattern. We perform precision desktop experiments to construct the bifurcation diagram of the process, and explore a range of geometric and material properties. A scaling analysis enables us to rationalize the dependence of the size of the dimples on both the radius of the shell and the radial gap between the shell and the inner rigid mandrel. Moreover, we characterize the process of nucleation and progression of the dimpled pattern front. Particular emphasis is given to the patterns obtained in the strongly nonlinear post-buckling regime where a network of sharp ridges forms. [Preview Abstract] |
Wednesday, March 16, 2016 3:54PM - 4:06PM |
P40.00008: Defect-controlled buckling of depressurized elastic shells Anna Lee, Joel Marthelot, Francisco López Jiménez, Pierre-Thomas Brun, Pedro Reis We revisit the classic problem of buckling of spherical elastic shells under pressure loading, with an emphasis on determining the role that engineered imperfections have on the critical buckling pressure. Since the 1960’s numerous theoretical and computational studies have addressed this canonical problem in engineering mechanics, but there is a striking lack of precision experiments to corroborate these predictions. We perform an experimental investigation where thin shells of nearly uniform thickness are fabricated by the coating of hemispherical molds with a polymer solution, which upon curing yields the elastic structure. Moreover, our manufacturing technique allows us to introduce a single ‘dimple-like’ defect with controllable geometric properties. By systematically varying the amplitude of this defect (smaller than the thickness of the shell) we study the effect that these imperfections have on the buckling strength of our spherical shells. Small deviations from the spherical geometry result in large reductions in the buckling pressure and our experimental results agree well with the existing theories. We then perform a broader exploration for other classes of defects, for which theoretical predictions are yet to be developed. [Preview Abstract] |
Wednesday, March 16, 2016 4:06PM - 4:18PM |
P40.00009: Stress Localization in Elastic Shells Sarah Selden, Arthur Evans, Nakul Bende, Ryan Hayward, Christian Santangelo Upon indentation, thin shells react by localizing strain energy in polygonal structures as opposed to a uniform axisymmetric distribution. While the formation of these localized structures are well-characterized for perfect shells, a change in shell thickness or the introduction of a crease fundamentally changes the nature of the shell deformation. We perform finite element simulations, in tandem with experiments to explore the effect of different shell geometries on the energy landscape. We find that the crease induces a new symmetry-breaking localization that does not appear in perfect shells, and we explore the deformation characteristics of the creased shell over a wide range of crease radii, and crease orientations. [Preview Abstract] |
Wednesday, March 16, 2016 4:18PM - 4:30PM |
P40.00010: Regularizing rigidifying curves to understand the low-energy deformations of thin shells Salem Al Mosleh, Christian Santangelo It is much harder to stretch a piece of paper than bend it. We exploit this fact to simplify the elastic energy of a thin shell. We accomplish this by extending the linear isometric displacements, displacements that do not cause stretching to lowest order, to low energy Nambu-Goldstone modes. This approach fails in an interesting way in the vicinity of ``rigidifying curves,'' curves with zero normal curvature, because half of the linear isometries are divergent there. We use a renormalization group methods to show that nonlinearities in the strain regularize these divergences. We explore the relationship between these modes and folding along curves of zero normal curvature. [Preview Abstract] |
Wednesday, March 16, 2016 4:30PM - 4:42PM |
P40.00011: Hunting for ghosts in elastic snap-through Michael Gomez, Derek E. Moulton, Dominic Vella Elastic `snap-through' is a striking instability often seen when an elastic system loses bistability, e.g.~due to a change in geometry or external loading. The switch from one state to another is generally rapid and hence is used to generate fast motions in biology and engineering. While the onset of instability has been well studied, the dynamics of the transition itself remain much less well understood. For example, the dynamics exhibited by children's jumping popper toys, or the leaves of the Venus flytrap plant, are much slower than would be expected based on a naive estimate of the elastic timescales. To explain this discrepancy, the natural conclusion has been drawn that some other effect, such as viscoelasticity, must play a role. We demonstrate here that purely elastic systems may show similar `slow' dynamics during snap-through. This behaviour is due to a remnant (or `ghost') of the snap-through bifurcation underlying the instability, analogously to bottleneck phenomena in 1-D dynamical systems. This slowness is a generic consequence of being close to bifurcation --- it does not require dissipation. We obtain scaling laws for the length of the delay and compare these to numerical simulations and experiments on real samples. [Preview Abstract] |
Wednesday, March 16, 2016 4:42PM - 4:54PM |
P40.00012: One Bend, Two Bend: Stepping Towards a Complex Folded Object. Andrew Croll, Damith Rozairo Crumpled thin films form a very unique jammed state of matter. They are both lightweight and ridged, suggesting broad industrial relevance. While researchers have theorized over the origins of these properties, very little experimental work has been performed directly – collecting both structural and material properties in concert. Without testing the strength and interplay of the basic structures making up the larger object (bends, folds, and d-cones) it is difficult if not impossible to completely trust the origin of various material properties and processes (modulus, aging behaviour). Here we show that laser scanning confocal microscopy can be used to image geometry directly in concert with the recording of traditional macroscopic measurements (e.g. force vs displacement). Specifically, we examine the force/displacement behaviour in systems of 1 to N folds created with well understood polymeric materials. [Preview Abstract] |
Wednesday, March 16, 2016 4:54PM - 5:06PM |
P40.00013: Wrinkling Instability Induced by Imposed Gaussian Curvature in the Zero-tension Limit Yiwei Sun, Benny Davidovitch, Gregory Grason The adhesion of thin stiff films onto spherical substrates introduces compressive stresses, which cause the laminated film to buckle out of plane. Previous studies addressed the emerging wrinkle pattern in the limit of zero bending modulus and the presence of surface tension at the boundary, and found the radius of the inner unwrinkled zone scales with the tension. Here we study another fundamental limit: finite bending modulus and zero exerted tension. In this limit, subtlety will arise from the fact that the singular expansion, which previous studies relied on, becomes ill-defined. To reveal the morphology in the zero-tension limit, we employ numerical simulations based on bead-bond model. Surprisingly, we find that the scaling law for the radius of the unwrinkled zone can be generalized from the finite tension to the zero tension limit, by applying a bending modulus dependent term to the tension dominated scale. The simulation results also highlight the residual compressive hoop stress, which is scaled by bending modulus in the absence of tension. The findings suggest the existence of a new, yet unstudied process, by which the deformed shape of the sheet approaches isometry as the bending modulus vanishes, in the absence of boundary loads. [Preview Abstract] |
Wednesday, March 16, 2016 5:06PM - 5:18PM |
P40.00014: Geometry of Thin Nematic Elastomer Sheets Hillel Aharoni, Eran Sharon, Raz Kupferman A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods. [Preview Abstract] |
Wednesday, March 16, 2016 5:18PM - 5:30PM |
P40.00015: Unpredictable Motion and Post-chaotic Self-Organization of Flexible Structures. Nicholas Nechitailo Two physical phenomena, ``reverse buckling'' and ``post-chaotic self-organization'', were discovered by the author of this paper. The phenomena were analyzed using Newton's mechanics, Euler bifurcation and buckling theory, and Poincare's theory of chaotic motion when ``prediction becomes impossible.'' However, our experimental and theoretical findings revealed a more complex nonlinear physics with some predictability of final states. Geometric and material nonlinearities in flexible plates, beams and shells lead to transient chaos and unexpected final shapes. In one experiment, an axisymmetric transverse pressure pulse was applied to a circular metal membrane. It buckled, lost axial symmetry and formed a folded six-corner star. In another test, an impulsively stretched rod buckled and obtained a final shape similar to that of a rod under static axial compression. ``Reputable'' finite element and finite difference codes could not reliably predict deformation of an aluminum beam under a transverse pressure pulse. The anomalous responses were observed in a narrow region of the load amplitude and duration. These were described by simple analytical equations. Similar phenomena were seen in nonlinear equations of motion representing various non-mechanical systems. [Preview Abstract] |
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