Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session C48: Extreme Mechanical Instabilities, Defects, and Large Deformations IIFocus

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Sponsoring Units: GSNP GSOFT Chair: Shmuel Rubinstein, Harvard Univ Room: LACC 510 
Monday, March 5, 2018 2:30PM  3:06PM 
C48.00001: From turbulence transition to the buckling of a soda can Invited Speaker: Tobias Schneider Thinwalled cylindrical shells such as rocket walls (or soda cans) offer exceptional strengthtoweight ratios yet predicting at which load the structure becomes unstable and fails remains an unsolved problem. Shells buckle and collapse at loading conditions much below those predicted by linear stability theory. This failure of linear theory is traditionally ascribed to extreme sensitivity to unavoidable shell imperfections, which modify the linear thresholds and lead to unpredictable stochastic variations of buckling loads for nominally identical shell structures. 
Monday, March 5, 2018 3:06PM  3:18PM 
C48.00002: Smooth wrinkling patterns in strongly compressed shells Hadrien Bense, JeanBaptiste Gorce, Javier Contreras Pastenes, Benoit Roman, Jose Bico Changing the gaussian curvature of a plate or of a thin shell generally leads to compressive stresses and induces folding and crumpling instabilities. However, the localised folds first observed as a shallow shell is compressed between parallel plates progressiveley evolve into a smooth wrinkling pattern at high compaction. While azimutal wrinkles are observed in the case of a plain spherical cap, cutting a wide hole at center results in a different wrinkling pattern: radial wrinkles appear around the hole and are followed by circular wrinkles. The radius of the transition if found to be the geometric mean of the radius of the hole and the radius of the base of the shell. We show how the wavelength and, more generally, the global geometry of the wrinkles can be inferred from the stress distribution corresponding to the full compression of the shell, as previously demonstrated in the case of embossed plates. This description is not limited to axisymmetric shells and can be applied to complex topographies. 
Monday, March 5, 2018 3:18PM  3:30PM 
C48.00003: Surface wrinkling of a rigid capping layer on a freestanding thin elastic film John Niven, Gurkaran Chowdhry, Kari DalnokiVeress Periodic wrinkling of a rigid capping layer on a deformable substrate is a ubiquitous example of pattern formation in nature. Many experiments have studied wrinkle formation during the compression of thin rigid films on relatively thick soft elastic substrates. The resulting wrinkling wavelength and amplitude can be predicted theoretically by minimizing the bending energy of the rigid film and the deformation energy of the soft substrate. To date, most studies have focused on the regime where the substrate thickness can be considered semiinfinite relative to that of the rigid film. In this work we use optical and atomic force microscopy to study the wrinkling behavior of thin rigid films upon compression by a prestrained freestanding elastic substrates which cannot be considered semiinfinite. As the ratio of substrate to rigid film thickness is decreased, deviations from the typical semiinfinite behaviour are observed as periodic deformations of the entire substrate film become significant. 
Monday, March 5, 2018 3:30PM  3:42PM 
C48.00004: Mechanics of Wrinkled Structures Sijie Tong, Andrej Kosmrlj Surface wrinkling of thin films on soft substrates has been of great interest both in fundamental studies and in practical applications, such as tunable adhesion, wetting and drag coefficient. While the formation of wrinkles is well understood from the linear stability analysis, which can predict critical strains and buckled modes, we know much less how wrinkled structures respond to additional external forces. This is because postbuckled wrinkled surfaces are extremely sensitive and even small forces can lead to large deformations, which have to be described with the nonlinear elasticity. I will discuss how the corresponding nonlinear PDEs can be solved perturbatively, where the small parameter is the ratio between the magnitude of displacements (e.g. amplitude of wrinkles) with the wavelength of wrinkles (as determined from the linear elasticity). This way we can derive systematic estimates for the postbuckling response of wrinkled structures to external forces, such as a point indentation force or a point force directed in the plane of wrinkles. I will also comment how this formalism can be applied to analyze more complex interaction of the wrinkled structures with external environment, such as the effective wetting angle of liquid droplet on wrinkled surfaces. 
Monday, March 5, 2018 3:42PM  3:54PM 
C48.00005: Buckling of an ultrathin shell on a flat liquid surface Alex Hartwell, Yousra Timounay, Graham Leggat, Vincent Demery, Joseph Paulsen Wrinkles are ubiquitous in biological materials such as flower petals and skin, and in everyday objects like window curtains or a rolledup shirt sleeve. Recently a farfromthreshold approach, in which wrinkles completely relax compressive stresses, has described wrinkle patterns in a variety of settings. However, the extension of this framework to a broader class of problems, including intrinsically curved films or situations with biaxial compression, remains open. We manufacture ultrathin (30 to 800 nm) polystyrene sheets on sphericallycurved substrates, varying the sheet thickness, width, and curvature, and transfer the films to a flat water bath. Above a threshold curvature, we observe a circular wrinkled core with a disordered pattern of wrinkles that is characteristic of biaxial compression. At higher curvatures the sheets fold. Our measurements of the onset of wrinkles and the size of the wrinkled core are in excellent agreement with our farfromthreshold calculations with no free parameters. Although the core size is governed by the curvature of the film, the wrinkle wavelength and folding threshold are surprisingly well described by simple onedimensional results for flat films. 
Monday, March 5, 2018 3:54PM  4:06PM 
C48.00006: A Diffuse Interface Model for the Analysis of Propagating Bulges in Cylindrical Balloons Basile Audoly, Claire Lestringant During the inflation of a cylindrical rubber balloon, it can be observed that the homogeneous cylindrical configuration quickly becomes unstable. A bulge is then formed while the pressure drops suddenly. Upon further inflation, the bulge propagates while the pressure remains constant. In earlier work, the value of the pressure at this plateau has been calculated based on Maxwell's construction for the coexistence of phases. In this talk, I will push the analogy between bulges in rubber balloons and phase transitions further. I will show that the details of the bulge formation and propagation can be captured accurately by a onedimension model similar to the diffuse interface model introduced by van der Walls in the context of liquidvapor phase transitions: in our model, the energy depends both on the tube radius and on its gradient. This model will be justified from a nonlinear membrane model by a formal expansion. I will also compare numerical solutions of this model with solutions of the original nonlinear membrane model, and show how our model can be used to make analytical predictions on the bifurcation loads and on the postbuckling behavior of the tube, while accounting for the finite tube length. 
Monday, March 5, 2018 4:06PM  4:18PM 
C48.00007: Stability landscape of cylindrical shell buckling Emmanuel Virot, Tobias Kreilos, Tobias Schneider, Shmuel Rubinstein What is the critical load required to crush a soda can or a space rocket shell? Surprisingly, there is no good way to estimate it, because of the presence of critical defects virtually impossible to characterize. Here we measure the response of soda cans to lateral poking and identify a generic stability landscape, which fully characterizes the stability of real imperfect shells in the case where one single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. Our results suggest that the complex stability of shells reduces to a low dimensional description and that tracking the ridge and the valley of this landscape defines natural coordinates for describing the stability of shells. 
Monday, March 5, 2018 4:18PM  4:30PM 
C48.00008: Highamplitude Ridge Structures Induced by Plastic Deformation Nasser Arbabi, Lihua Jin Ridging instability occurs in bilayer stiff film/compliant substrate systems where the elastomer substrate is subject to a large prestretch prior to attachment of the film. When the bilayer is then gradually compressed, sinusoidal wrinkles first form on the surface, and subsequently become unstable, giving way to localized ridges with high amplitudes. However, the large prestretch of the elastomer substrate during thin film attachment is not compatible with conventional thin film deposition methods. A new and simple method for constructing ridge structures is to deposit a plastic thin film on a stressfree elastomer, and stretch the resulting bilayer system. Upon the release of the stretching, the deformation of the elastomer is reversible, while the plastically deformed thin film stays elongated. The large length mismatch generates ridge structures. In this work, we study the mechanics of ridge instability formed by stretching and unloading a bilayer of plastic thin film on an elastomer substrate. The critical condition for the formation of ridges and the ridge morphology highly depend on the elastoplastic material properties, such as the yielding strain and hardening exponent of the film. A comparison between plastic and elastic ridges is also presented. 
Monday, March 5, 2018 4:30PM  4:42PM 
C48.00009: For Better or For Worse: Selftuning of the buckling strength of active bilayer shells Dong Yan, Anna Lee, Matteo Pezzulla, Francisco Lopez Jimenez, Joel Marthelot, Douglas Holmes, Pedro Reis We study a new class of composite shells that can selfrepair or selfaggravate existing imperfections, thereby tuning their buckling strength. Our bilayer polymeric shells, containing a precise geometric defect, are fabricated through a customizable coating technique. Upon curing, the diffusion of uncrosslinked residual polymer chains across the two layers induces swelling, causing the natural curvature of the bilayer structure to evolve. This natural curvature can be made positive or negative depending on the order of the layers. Through precision experiments, we quantify the timedependence of both the geometry and buckling strength of the shells. We find that the critical buckling pressure of the shells with negative natural curvature can increase with time, as long as the defect amplitude exceeds a critical value, hence, causing the shells to selfheal. This healing trend is reversed for defects with an amplitude below the threshold. By contrast, the shells with positive natural curvature always exhibit a selfdestructive behavior. We combine the experiments with finite element simulations and a reduced analytical model to rationalize our results on how an evolving geometry and residual stresses can selftune the buckling strength of bilayer shells, for better or for worse. 
Monday, March 5, 2018 4:42PM  4:54PM 
C48.00010: Exploiting Structural Buckling: A MechanicsDriven Approach to 3D Microscale Functional Scaffolds Xin Ning In this talk I will present a novel method of designing and fabricating 3D microscale functional scaffolds. Buckling is often considered as structural failure; however, in our method we use compressive buckling to assemble complex threedimensional structures from twodimensional precursors. This approach is able to achieve simple to complex structures and is compatible with many functional materials, including devicegrade singlecrystal silicon and highperformance inorganic piezoelectric materials. I will also show some representative applications enabled by this approach. 
Monday, March 5, 2018 4:54PM  5:06PM 
C48.00011: Passive Elastic Structures Interacting with Grains in Motion Martin Brandenbourger, Alex Hindelang, Wyatt Perry, Douglas Holmes Recent publications have shown how nonlinear interactions between elastic structures and granular media lead to unique behaviors (complex bending transition, nonsymmetric buckling, etc..) that can be described by characteristic elastogranular lengths. Studies have been focused on passive granular media activated by an elastic structure or passive elastic structures interacting with grains in motion. 
Monday, March 5, 2018 5:06PM  5:18PM 
C48.00012: Image Charges in 2D Linear Elasticity Siddhartha Sarkar, Andrej Kosmrlj The analogy between electrostatics and 2D linear elasticity enables us to describe the deformation of two dimensional solid structures with holes (or inclusions) in terms of “elastic multipoles”. Just like external electric field induces polarization (dipoles, quadrupoles, etc.) of conductive objects, external stress induces elastic multipoles inside holes. Previously, we demonstrated how one can predict complex deformation patterns of structures with many holes that are far away from structure boundaries by considering interactions between induced elastic multipoles. However, when holes are near the structure boundaries, their deformation is affected by the boundary conditions. In electrostatics, the boundary effects can be dealt with the method of image charges. Here we employ the concept of image charges in 2D elasticity to discuss how deformation of holes is affected near flat edges and near wedges. 
Monday, March 5, 2018 5:18PM  5:30PM 
C48.00013: The Emergence of Small Scales in Vortex Ring Collisions Shmuel Rubinstein, Ryan McKeown, Rodolfo Ostilla Monico, Alain Pumir, Michael Brenner When two vortex rings collide headon, the initially smooth flow structures rapidly become unstable as they develop complex threedimensional dynamics that result in the vortex cores either reconnecting or breaking down into a turbulent cloud. We use highspeed flow visualization techniques with a scanning laser sheet to reconstruct the intricate, threedimensional dynamics of the interacting vortex cores. We show that the breakdown of the vortex cores is caused by the local flattening of the cores into vortex sheets, which break down into smaller vortex filaments. These secondary filaments break down again in an iterative manner to produce finescale turbulent “smoke.” This iterative cascade could be indicative of a possible mechanism by which kinetic energy is conveyed to small scales in turbulent flow. 
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