Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session C15: Extreme Mechanics of ShellsFocus

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Sponsoring Units: GSNP Chair: Francisco Jimenez, Massachusetts Institute of Technology Room: 274 
Monday, March 13, 2017 2:30PM  3:06PM 
C15.00001: Statistical mechanics of microscopically thin thermalized shells Invited Speaker: Andrej Kosmrlj Recent explosion in fabrication of microscopically thin free standing structures made from graphene and other twodimensional materials has led to a renewed interest in the mechanics of such structures in presence of thermal fluctuations. Since late 1980’s it has been known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli in a scaledependent fashion. However, much is still unknown about the mechanics of thermalized flat sheets of complex geometries and about the mechanics of thermalized shells with nonzero background curvature. In this talk I will present recent development in the mechanics of thermalized ribbons, spherical shells and cylindrical tubes. Long ribbons are found to behave like hybrids between flat sheets with renormalized elastic constants and semiflexible polymers, and these results can be used to predict the mechanics of graphene kirigami structures. Contrary to the anticipated behavior for ribbons, the nonzero background curvature of shells leads to remarkable novel phenomena. In shells, thermal fluctuations effectively generate negative surface tension, which can significantly reduce the critical buckling pressure for spherical shells and the critical axial load for cylindrical tubes. For large shells this thermally generated load becomes big enough to spontaneously crush spherical shells and cylindrical tubes even in the absence of external loads. I will comment on the relevance for crushing of microscopic shells (viral capsids, bacteria, microcapsules) due to osmotic shocks and for crushing of nanotubes. [Preview Abstract] 
Monday, March 13, 2017 3:06PM  3:18PM 
C15.00002: Variational elasticity of thin plates James Hanna I will discuss and compare approaches to thin plates that have arisen recently in the soft matter physics community. The main issues arise because of the presence of at least two metric tensors in descriptions of elasticity. Favoring one or the other metric affects, among other things, the definition of bending energy and the cleanliness of the equations. [Preview Abstract] 
Monday, March 13, 2017 3:18PM  3:30PM 
C15.00003: Bifurcation of Selffolded Planar Bilayers Arif Abdullah, K. Jimmy Hsia Stimuliresponsive curving of thin shells, also known as selffolding, is a topic of substantial technological importance due to its applicability toward a broad range of shape transforming structures. The morphing of shelllike structures in response to external stimuli, is often governed by geometric nonlinearities. One such example is the bifurcation buckling phenomenon of planar bilayers. When thin bilayers are subjected to external stimuli in the form of biaxial mismatch strain, they form shallow spherical caps at lower strains but bifurcate to cylindrical shapes at higher strains in an effort to minimize stretching, which is energetically less favorable. In this work, we investigated the bifurcation behavior of thin planar bilayers as they transform into threedimensional shapes in response to external stimuli. Through a combination of finite element analysis and experiments, we demonstrated how different structural parameters affect the bilayer behavior prior to bifurcation and also in the postbuckling regime. The insights obtained from this work will contribute toward the design of selffolding functional devices for sensing, robotics, and biomedical applications across multiple length scales. [Preview Abstract] 
Monday, March 13, 2017 3:30PM  3:42PM 
C15.00004: Instabilities In Dielectric Elastomer Plates Hadrien Bense, José Bico, Benoît Roman, Etienne Reyssat, Miguel Trejo Dielectric elastomers are soft capacitors whose electrodes undergo planar extension when stimulated by an electric voltage. Potential applications are numerous, ranging from sensors to actuators, displays or even energy harvesting systems. In most cases the elastomer is strongly stretched and clamped. Here, we investigate the effect of a spatially non uniform voltage on a non prestrained system. We find that the membranes under nonuniform load undergo mechanical instabilities. Such bucklinglike instabilities are not observed in other studies because of large tensile loading, but they are common in thin plates with internal stresses (such as nonuniform plastic deformation in a torn ductile plate or differential growth in hydrogels). As a first step, we propose to study simple geometries: a disk where only the central zone or a peripheral annulus is growing would be a first example. These systems, despite their apparent simplicity, display surprising features. Predicting the threshold of buckling and the main characteristics of the pattern (wavelength, extension) is complex, even in simple geometries. Nonlinear analysis is necessary to capture, at least qualitatively, the behavior of of such systems from the buckling threshold to the evolution of the observed patterns. [Preview Abstract] 
Monday, March 13, 2017 3:42PM  3:54PM 
C15.00005: Edge Effect of Strained Bilayer Nanofilms for Tunable Multistability and Actuation Zi Chen, Nan Hu, Xiaomin Han, Shicheng Huang, Hannah Grover, Xiaojiao Yu, Lina Zhang, Ian Trase, John X.J. Zhang, Li Zhang, Lixin Dong Multistability, the capability of a structure to exhibit more than one stable shape, has received increasing attention due to its applications in robotics, and energy harvesters, etc. Programming multistability into nanoelectromechanical systems allows for microscale manipulation, energy harvesting and robotic operation for biomedical applications. In a spontaneous scrolled Si/Cr bilayer, two stable shapes were achieved after detaching from the substrate. We employed both theoretical and computational models to study the multistable behavior of a Si/Cr microclaw and illustrated the mechanical principles involved. Besides the biaxial strain that serves as the primary driving force, we found residual edge stresses to be inducing bistability. In both models, individual Si/Cr microclaws consistently demonstrate either monostability or bistability as the magnitude of the edge effect is varied. Both macroscopic and microscopic experimental designs were studied, supported by analytical and finite element simulation results. The results from this study provide a means to guide the ondemand design of strained nanobelts and nanosheets with tunable multistability and actuating capability. [Preview Abstract] 
Monday, March 13, 2017 3:54PM  4:06PM 
C15.00006: A wrinkletofold transition in curved floating shells Desislava V. Todorova, Octavio Albarran Arriagada, Lucas Goehring, Eleni Katifori The generation of wrinkle patterns in thin elastic shells has attracted an increasing interest in both fundamental studies and practical applications. A spatially confined elastica or a flat elastic sheet exhibit regular sinusoidal wrinkles in response to an imposed small compressive confinement. For larger compression, the deformation energy becomes localized in small regions which ultimately develop folds. We consider the case where an elastic shell with a nonzero natural curvature, placed on a fluid substrate bends and wrinkles without compression. We discuss how the curvature can be viewed as an effective confinement and investigate how global constraints and local morphologies of the curved shells control the transition from regular wrinkles to composition of wrinkles and folds or foldlike structures. Further, we discuss various new strategies for creating and controlling patterns in thin elastic shells with natural curvature. [Preview Abstract] 
Monday, March 13, 2017 4:06PM  4:18PM 
C15.00007: Universal dynamics in the wrinkling of curved elastic bilayer systems Norbert Stoop, Joern Dunkel Wrinkling in curved bilayer systems is a ubiquitous phenomenon, occurring, e.g., in embryogenesis, biological tissue differentiation or structure formation in heterogenous thin films. Using a recently developed effective wrinkling theory, we previously showed that near the wrinkling transition, a hexagonal pattern is selected, which exhibits characteristic properties of generic 2D curved crystals, including curvaturedependent defect localization and orientation. Here, we show that under a finitetime quench from the unwrinkled to the crystalline phase, curved bilayer systems exhibit dynamic scaling properties consistent with universal predictions of the celebrated KibbleZurek mechanism (KZM). Specifically, by increasing the film stress at constant rates, we find that the system arrests its dynamics near the wrinkling transition, rendering the quench nonadiabatic. Once dynamics is resumed, topological defects appear and their densities follow powerlaws in the quench rate. Studying spherical and toroidal geometries, we find that the scaling exponent agrees with the KZM predictions and is independent of geometry and topology. Our results thus suggest that elastic bilayers provide a novel and accessible way to study universal aspects of dynamical phase transitions. [Preview Abstract] 
Monday, March 13, 2017 4:18PM  4:30PM 
C15.00008: On the mechanics of elastic lines in thin shells Eduard Benet, Franck Vernerey The deformation of soft shells in nature and engineering is often conditioned by the presence of lines whose mechanical properties are different from the shell. For instance, the deformation of tree leaves is conditioned by the presence of harder stems, and cell mitosis is driven by a stiffening line along its membrane. From an experimental standpoint, many groups have taken advantage of this feature to develop selfactuated shells with prescribed deformations. Examples include the polymerization of gels along certain lines, or the inclusion of stiffer lines via 3D printing. However, there is not yet a general continuum theory that accounts for this type of discontinuity within the membrane. Hence, we extend the general shell theory to account for the inclusion of a line that potentially induces jumps in stresses, couple stresses and moments, across its thickness. This is achieved via coupling the rod and the membrane deformations, and ensuring continuity of displacements. The model is then applied to three important problems: a constriction disc inside a shell of revolution, the induced twisting of a shell via the torsion of an embedded line, and the effect of an helicoidal line on the uniaxial deformation of a cylindrical shell. [Preview Abstract] 
Monday, March 13, 2017 4:30PM  4:42PM 
C15.00009: Spherical shells buckling to the sound of music Anna Lee, Joel Marthelot, Pedro Reis We study how the critical buckling load of spherical elastic shells can be modified by a fluctuating external pressure field. In our experiments, we employ thin elastomeric shells of nearly uniform thickness fabricated by the coating of a hemispherical mold with a polymer solution, which upon curing yields elastic structures. A shell is submerged in a water bath and loaded quasistatically until buckling occurs by reducing its inner volume with a syringe pump. Simultaneously, a plunger connected to an electromagnetic shaker is placed above the shell and driven sinusoidally to create a fluctuating external pressure field that can excite dynamic vibration modes of the shell. These dynamic modes induce effective compressive stresses, in addition to those from the inner pressure loading, which can modify the critical conditions for the onset of buckling. We systematically quantify how the frequency and amplitude of the external driving affects the buckling strength of our shells. In specific regions of the parameter space, we find that pressure fluctuations can result in large reductions of the critical buckling pressure. This is analogous to the classic knockdown effect in shells due to intrinsic geometric imperfections, albeit now in a way that can be controlled externally. [Preview Abstract] 
Monday, March 13, 2017 4:42PM  4:54PM 
C15.00010: Periodic buckling of constrained cylindrical elastic shells Joel Marthelot, PierreThomas Brun, Francisco Lopez Jimenez, Pedro M. Reis We revisit the classic problem of buckling of a thin cylindrical elastic shell loaded either by pneumatic depressurization or axial compression. The control of the resulting dimpled pattern is achieved by using a concentric inner rigid mandrel that constrains and stabilizes the postbuckling response. Under axial compression, a regular lattice of diamondlike dimples appears sequentially on the surface of the shell to form a robust spatially extended periodic pattern. Under pressure loading, a periodic array of ridges facets the surface of the elastic cylindrical shell. The sharpness of these ridges can be readily varied and controlled through a single scalar parameter, the applied pressure. A combination of experiments, simulations and scaling analyses is used to rationalize the combined role of geometry and mechanics in the nucleation and evolution of the diamondlike dimples and ridges networks. [Preview Abstract] 
Monday, March 13, 2017 4:54PM  5:06PM 
C15.00011: Global Curvature Buckling and Snapping of Spherical Shells. Matteo Pezzulla, Norbert Stoop, Mark Steranka, Abdikhalaq Bade, Miguel Trejo, Douglas Holmes A spherical shell under external pressure will eventually buckle locally through the development of a dimple. However, when a free spherical shell is subject to variations in natural curvature, it will either buckle globally or snap towards a buckled configuration. We study the similarities and differences between pressure and curvature instabilities in spherical shells. We show how the critical buckling natural curvature is largely independent of the thinness and halfangle of the shell, while the critical snapping natural curvature grows linearly with the halfangle. As a result, we demonstrate how a critical halfangle, depending only on the thinness of the shell, sets the threshold between two different kinds of snapping: as a rule of thumb, shallow shells snap into everted shells, while deep shells snap into buckled shells. As the developed models are purely geometrical, the results are applicable to a large variety of stimuli and scales. [Preview Abstract] 
Monday, March 13, 2017 5:06PM  5:18PM 
C15.00012: Buckling shells are also swimmers Catherine Quilliet We present an experimental and numerical study on the displacement of shells undergoing deformations in a fluid. When submitted to cycles of pressure difference between outside and inside, a shell buckles and debuckles, showing a succession of shapes and a dynamics that are different during the two phases. Hence such objects are likely to swim, including at low Reynolds (microscopic scale). We studied the swimming of buckling/debuckling shells at macroscopic scale using different approaches (force quantization, shape recording, displacement along a frictionless rail, study of external flow using PIV), and showed that inertia plays a role in propulsion, even in situations where dimensionless numbers correspond also to microswimmers in water. Different fluid viscosities were explored, showing an optimum for the displacement. Interestingly, the most favorable cases lead to displacements in the same direction and sense during both motor stroke (buckling phase) and recovery stroke (debuckling phase). This work opens the route for the synthesis with high throughput of abusively simple synthetic swimmers, possibly gathered into nanorobots, actuated by a scalar field such as the pressure in echographic devices. [Preview Abstract] 
Monday, March 13, 2017 5:18PM  5:30PM 
C15.00013: Motion of a rigid sphere through an elastic tube with a lubrication film Marie TANI, Thomas CAMBAU, Jose BICO, Etienne REYSSAT The transport of soft objects through small rigid channels is a common problem in the biological world; red blood cells are deformed when passing through small capillaries and polymer coils can make their way through minute pores. We study the opposite model problem of a rigid sphere through a narrower elastic tube. The frictional force is measured while the sphere is pulled in the elastic tube at constant velocity. In addition to the dry case, we test the same system but we lubricate the spheretube contact with a viscous liquid. Friction generally decreases compared to the dry case owing to the lubrication film, but it depends on viscosity and velocity. As a result, geometry, mechanical properties of the tube, friction or lubrication mechanisms, and wetting properties determine the dynamics of the entrapped sphere. We present experimental results on this problem, together with scaling law analysis. [Preview Abstract] 
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