Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session T16: Focus Session: Extreme Mechanics: Buckling, Wrinkling, and Poking |
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Sponsoring Units: GSNP Chair: Dominic Vella, University of Oxford Room: 401 |
Thursday, March 6, 2014 11:15AM - 11:51AM |
T16.00001: Mechanics analysis and design of fractal interconnects for stretchable batteries Invited Speaker: Yonggang Huang An important trend in electronics involves the development of materials, mechanical designs and manufacturing strategies that enable the use of unconventional substrates, such as polymer films, metal foils, paper sheets or rubber slabs. The last possibility is particularly challenging because the systems must accommodate not only bending but also stretching. Although several approaches are available for the electronics, a persistent difficulty is in power supplies that have similar mechanical properties, to allow their co-integration with the electronics. Here we introduce a set of materials and design concepts for a rechargeable lithium ion battery technology that exploits thin, low modulus silicone elastomers as substrates, with a segmented design in the active materials, and unusual ``self-similar'' interconnect structures between them. The result enables reversible levels of stretchability up to 300{\%}, while maintaining capacity densities of $\sim$1.1 mAh cm$^{-2}$. Stretchable wireless power transmission systems provide the means to charge these types of batteries, without direct physical contact. [Preview Abstract] |
Thursday, March 6, 2014 11:51AM - 12:03PM |
T16.00002: Coiling rods onto moving substrates Mohammad Jawed, Fang Da, Eitan Grinspun, Pedro Reis We present results on the nonlinear patterns obtained when a thin elastic rod is deployed onto a moving substrate. Our experiments comprise an injector that deposits an elastomeric rod onto a conveyor belt, where it coils in a variety of nonlinear patterns, depending on the control parameters. The portion of the rod that is suspended between the injector and the point of contact with the belt can exhibit strong geometric nonlinearities that are a challenge for traditional analytical and numerical methods. We tackle this challenge by coupling our precision model experiments with cutting-edge simulation tools ported from the computer graphics community. By systematically exploring parameter space, we map out the basins of stability of the various nonlinear coiling patterns, which are then rationalized using a detailed energy balance. We give particular emphasis to the sinusoidal patterns that emerge from a straight-to-meandering instability that we find to be consistent with a Hopf bifurcation. Closed-form solutions are derived to describe the amplitude and wavelength of the meandering patterns. The excellent agreement between experiments, simulations and theory conveys the predictive ability of our tools to be used, upon scaling, in the original engineering applications that motivated this study: serpentines created from the coiling of carbon nanotubes (at the micron-scale) and the laying down of transoceanic undersea cables (at the kilometer-scale). [Preview Abstract] |
Thursday, March 6, 2014 12:03PM - 12:15PM |
T16.00003: ABSTRACT WITHDRAWN |
Thursday, March 6, 2014 12:15PM - 12:27PM |
T16.00004: Use of Buckling Instabilities in Micro Pumps, Valves, and Mixers Behrouz Tavakol, Aschvin Chawan, Douglas Holmes We use the buckling of thin, flexible plates for pumping fluids, controlling the flow rate, and mixing different media within a microfluidic channel. A dielectric elastomeric film with a confined geometry buckles out of the plane when exposed to an electric field. Solid or grease electrodes have traditionally been used as conductive materials to aid in voltage application to both sides of the film. In this work, we use an electrolytic fluid solution as the electrode to enable buckling at relatively low voltages, and to enhance the rate of deformation. We show that this mechanism can be implemented as a microvalve that controls flow rate, or as a micropump that operates over a range of frequencies. A similar mechanism can be used to aid diffusion between two adjacent laminar streams and improve mixing. These low-cost micropumps, microvalves, and micromixers rely on the reversible buckling of thin plates, are easily embeddable in a microfluidic chip, and can potentially be used in variety of applications to accurately control and manipulate fluid flow in a microchannel. [Preview Abstract] |
Thursday, March 6, 2014 12:27PM - 12:39PM |
T16.00005: Wrinkling Crystallography on Curved Surfaces Pedro Reis, Miha Brojan, Denis Terwagne, Romain Lagrange We present results on an experimental analysis of the morphology of wrinkling patterns on curved surfaces. Our experimental hemispherical samples are fabricated using rapid prototyping and consist of a thin-stiff shell adhered to a soft-thick substrate, both made out of silicone-based rubbers. Pressurizing an inner spherical air cavity enables compression of the samples, thereby morphing the outer thin shell from its initially smooth configuration into a wrinkled state. A variety of patterns with different morphologies can be observed depending on the combination of the sample's geometric and material properties. We focus our attention on the specific pattern mode of hexagonal-like dimples, which we characterize by analyzing their surface profile using a digital 3D scanner. Through digital image processing, we skeletonize these patterns by identifying both the location of the ridges and determining the positions of the dimples. We give emphasis to the effect of curvature on the morphology and topology of these wrinkled patterns and focus on the tiling of the wrinkling units and their statistics of defects. Our results are contrasted with other crystalline planar and curved systems. [Preview Abstract] |
Thursday, March 6, 2014 12:39PM - 12:51PM |
T16.00006: Capping spheres with scarry crystals: Organizing principles of multi-dislocation, ground-state patterns Amir Azadi, Gregory M. Grason Predicting the ground state ordering of curved crystals remains an unsolved, century-old challenge, beginning with the classic Thomson problem to more recent studies of particle-coated droplets. We study the structural features and underlying principles of multi-dislocation ground states of a crystalline cap adhered to a spherical substrate. In the continuum limit, vanishing lattice spacing, $a \to 0$, dislocations proliferate and we show that ground states approach a characteristic sequence of patterns of $n$-fold radial grain boundary ``scars,'' extending from the boundary and terminating in the bulk. A combination of numerical and asymptotic analysis reveals that energetic hierarchy gives rise to a structural hierarchy, whereby the number of dislocation and scars diverge as $a\to 0$ while the scar length and number of dislocations per scar become remarkably independent of lattice spacing. We show the that structural hierarchy remains intact when $n$-fold symmetry becomes unstable to polydispersed forked-scar morphologies. We expect this analysis to resolve previously open questions about the optimal symmetries of dislocation patterns in Thomson-like problems, both with and without excess 5-fold defects. [Preview Abstract] |
Thursday, March 6, 2014 12:51PM - 1:03PM |
T16.00007: Edge curling that has plagued scrolls for millenniums Ming-Han Chou, Wei-Chao Shen, Yi-Ping Wang, Sun-Hsin Hung, Tzay-Ming Hong Qi-Wa refers to the up curl on the lengths of handscrolls and hanging scrolls, which has troubled Chinese artisans and emperors for as long as the art of painting and calligraphy exists. This warp is unwelcome not only for aesthetic reasons, but its potential damage to the fiber and ink. Although it is generally treated as a part of the cockling and curling due to moisture, consistency of paste, and defects from the mounting procedures, we demonstrate that the spontaneous extrinsic curvature incurred from the storage is in fact more essential to understanding and curing Qi-Wa. In contrast to the former factors whose effects are less predictable, the plastic deformation and strain distribution on a membrane are a well-defined mechanical problem. We study this phenomenon by experiments, theoretical models, and Molecular Dynamics Simulation, and obtain consistent scaling relations for the Qi-Wa height. This knowledge enables us to propose modifications on the traditional mounting techniques, that are tested on real mounted paper to be effective at mitigating Qi-Wa. By experimenting on polymer-based films, we demonstrate possible relevance of our study to the modern development of flexible electronic paper. [Preview Abstract] |
Thursday, March 6, 2014 1:03PM - 1:15PM |
T16.00008: Transitions in a compressible finite elastic sheet on a fluid substrate Oz Oshri, Haim Diamant A thin elastic sheet, supported on a fluid substrate and uniaxially compressed, exhibits two critical transitions: From a flat state to sinusoidal wrinkles and from wrinkles to a localized fold. Previous theoretical studies treated the system in the limits of incompressible and infinite sheets. Both assumptions are relaxed in the current work to obtain details of the transitions and the phase diagram. Deriving an amplitude equation and using a variational approach, we show that the flat-to-wrinkle transition is second-order, whereas the wrinkle-to-fold one is first-order. The pressure-displacement relation is linear above the first transition and becomes parabolic after the second one, in agreement with numerical results. [Preview Abstract] |
Thursday, March 6, 2014 1:15PM - 1:27PM |
T16.00009: From viscous fingering to bulk elastic fingering in soft materials Baudouin Saintyves, John Biggins, Zhiyan Wei, Serge Mora, Olivier Dauchot, L Mahadevan, Elisabeth Bouchaud Systematic experiments have been performed in purely elastic polyacrylamide gels in Hele-Shaw cells. We have shown that a bulk fingering instability arises in the highly deformable confined elastomers. It shares some similarities with the famous Saffman-Taylor instability, but a systematic study shows that surface tension is not relevant. This instability is sub-critical, with a clear hysteretic behavior. Our experimental observations have been compared very favorably to theoretical and finite element simulations results. In particular, the instability wavelength and the critical front advance have been shown to be proportional to the distance between the two glass plates constituting the cell. We have also shown that in Maxwell viscoelastic fluids, one crosses over continuously from a viscous to an elastic fingering instability. \\[4pt] [1] B. Saintyves, O. Dauchot, E. Bouchaud, PRL 2013 \\[0pt] [2] J. Biggins, B. Saintyves, Z. Wei, E. Bouchaud, L. Mahadevan, PNAS 2013 [Preview Abstract] |
Thursday, March 6, 2014 1:27PM - 1:39PM |
T16.00010: High Aspect Ratio Wrinkles Yu-Cheng Chen, Alfred J. Crosby Wrinkles occur when a compressive strain is imposed on a bilayer system composed of a stiff thin top film and a soft substrate. Wrinkle aspect ratio (wrinkle height divided by wavelength) is perhaps the most critical parameter for many promising wrinkle-based technologies; however, the current accessible range of aspect ratio has been restricted from 0 to 0.35. Within this range, wrinkle aspect ratio is known to increase with increasing compressive strain until a critical strain is reached, at which point wrinkles transition to localizations, such as folds or ridges. Here, we demonstrate the ability to delay this transition and ultimately expand the range of aspect ratios. Building upon recently developed models which link this transition to the asymmetric traction forces between the wrinkle crests and valleys for non-linear strain energy functions, we experimentally quantify the critical strain for both ridge and fold localizations as a function of the substrate material properties, initial stretch ratio, as well as film properties and geometry. Collectively, we demonstrate the ability to achieve wrinkle aspect ratios as large as 0.8, demonstrating significant promise for future wrinkle-based applications. [Preview Abstract] |
Thursday, March 6, 2014 1:39PM - 1:51PM |
T16.00011: Scaling laws for the wavelength of tensional wrinkle patterns Zhanlong Qiu, Benny Davidovitch Thin sheets under uni-axial tension often exhibit periodic patterns of wrinkles parallel to the tension lines, that are characterized by small wavelength and relax the induced compression in the direction perpendicular to the exerted tension. As the sheet gets thinner, it becomes more and more bendable, signifying the emergence of an asymptotically compression-free state in the singular limit of vanishing thickness. What is the dependence of the wrinkle wavelength on the sheet's thickness, characteristic lateral scales, and exerted tensile loads? In simple set-ups, such as a stretched rectangular sheet, simple scaling law is available. However, a general law, which can be implemented also to more complex set-ups, is still lacking. In this talk, we will use the Lame set-up, an annular sheet subjected to radial tension gradient, as a prototypical example to address this problem. We analyze various characteristic parameter regimes and obtain analytic scaling laws for the wrinkle wavelength, which may be generalizable to describe more complex problem. [Preview Abstract] |
Thursday, March 6, 2014 1:51PM - 2:03PM |
T16.00012: Poking a floating sheet Benny Davidovitch, Jiangshui Huang, Narayanan Menon, Thomas P. Russell, Dominic Vella Poking of liquid surface leads to a simple deformation of the surface, whose characteristic scale is nothing but the capillary length. In contrast, the poking of a circular solid sheet floating on a liquid bath demonstrates a surprisingly complex phenomenology, with numerous distinct length scales that are determined by the capillary length as well as by the poking amplitude and the stretching modulus of the sheet. The fundamental physical mechanism that underlies this complex response is intimately related to the emergence of an highly anisotropic stress, whose radial component is tensile and its hoop component is asymptotically compression-free. In this talk I will discuss the various parameter regimes that describe this problem and will identify the characteristic patterns of the poked sheet in these regimes. Experimental results will be presented and compared to theoretical predictions. [Preview Abstract] |
Thursday, March 6, 2014 2:03PM - 2:15PM |
T16.00013: An effective substrate stiffness induced by curvature and its consequences in wrinkling problems Evan Hohlfeld, Benjamin Davidovitch Thin elastic plates will wrinkle to relax compressive stress. The wavelength of the wrinkle pattern is set by a combination of the plate's bending stiffness and an ``effective substrate'' stiffness, e.g. due to an elastic foundation or as a consequence of tension in the plate. We discuss another, previously unrecognized effective stiffness due to macroscale, out-of-plane curvature of the plate. In applications, this stiffness often dominates the elastic and tensile stiffnesses, and so controls the wrinkle wavelength. The energy of the resulting wrinkle pattern directly depends on the macroscale curvature-unlike in the elastic and tensile cases--and we argue that this dependence can lead to a breakdown of Tension Field Theory. [Preview Abstract] |
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