Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session F16: Geometrically-Frustrated Instabilities in Solid Mechanics IILive
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Sponsoring Units: GSNP DSOFT Chair: Douglas Holmes, Boston Univ |
Tuesday, March 16, 2021 11:30AM - 12:06PM Live |
F16.00001: On leaves, flowers, and sea slugs Invited Speaker: Shankar Venkataramani Leaves, flowers, fins, wings, and marine invertebrates are examples of the ubiquity of non-Euclidean plates (NEP), i.e. prestrained thin elastic objects whose intrinsic geometry does not allow for a stress-free embedding into 3-space. When the intrinsic geometry is hyperbolic, these objects often display intricate, hierarchical, “multi-scale” undulations and buckling patterns around their edges. I will discuss recent advances in the mathematics and mechanics of hyperbolic NEP, emphasizing the connections between the math and the ‘extreme’ mechanical properties of hyperbolic NEP that might explain their ubiquity in natural objects. |
Tuesday, March 16, 2021 12:06PM - 12:18PM Live |
F16.00002: Frustrated Euclidean ribbons: a new class of geometric frustration Emmanuel Siefert, Ido Levin, Cy Maor, Eran Sharon Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. It may indeed lead to mechanical instabilities, anomalous mechanics and shape-morphing abilities that can be harnessed in engineering systems. It is widely accepted that such frustration stems from violation of Gauss's Theorema Egregium, i.e. "Gauss frustration". Here we report on a new type of geometrical frustration, one that exists in sheets that satisfy Gauss's theorem. We show that the origin of the frustration is the violation of Mainardi-Codazzi-Peterson compatibility equations. Combining experiments, simulations and theory, we study the specific case of an Euclidean ribbon with radial and geodesic curvatures. Experiments, conducted using different materials and techniques, reveal shape transitions, symmetry breaking and spontaneous stress focusing. These observations are quantitatively rationalized using analytic solutions and geometrical arguments. We argue that this type of frustration is as general as the Gauss frustration and is, thus, expected to appear in natural and engineering systems, specifically in slender 3D printed sheets. |
Tuesday, March 16, 2021 12:18PM - 12:30PM Live |
F16.00003: Prediction of the buckling capacity of thin shells by using stability landscapes Kshitij Yadav, Nicholas Cuccia, Emmanuel Virot, Shmuel M Rubinstein, Symeon Gerasimidis The prediction of thin cylindrical shells’ buckling capacity is difficult, expensive, and time-consuming, if not impossible. This is because the prediction requires a priori knowledge about the imperfections that are present in the cylinders. As a result, thin cylindrical shells are nowadays designed conservatively using the knockdown factor approach to accommodate the uncertainties associated with the imperfections. A novel approach is proposed, which provides an accurate prediction of cylindrical shells’ buckling capacity without measuring the imperfections. The proposed approach is based on the stability landscape that is obtained by probing axially compressed cylinders in the radial direction. Computational and experimental implementation of the procedure yields accurate results when the probing is done in the location of the highest imperfection amplitude. However, we observe that the procedure over-predicts the capacity when the probing is done too far away from that point. Further, we investigate the effect of probing location, imperfection amplitude, and background imperfections on the accuracy of the prediction. This study demonstrates the crucial role played by the probing location in nondestructive predictions of the buckling capacity. |
Tuesday, March 16, 2021 12:30PM - 12:42PM Live |
F16.00004: Universal Features of Buckling Initiation in Thin Shells Nicholas Cuccia, Kshitij Yadav, Emmanuel Virot, Symeon Gerasimidis, Shmuel M Rubinstein Where, when, and how does a thin shell fail? Geometric imperfections are thought to play an essential part in the buckling of a thin shell, but how they interact to control the onset of failure remains unclear. We experimentally probe the initiation of shell buckling using coke cans as a model system. A large dimple is imparted onto the can's surface and is laterally probed with a poker to predict the can's axial capacity. By filming the can's surface with high-speed videography, the nucleation of buckling from axial loading is directly observed, revealing that larger dimples tend to set the initial buckling location. However, the influence of the can's background geometric imperfections can still occasionally dominate, causing nucleation to occur far from the dimple. In this situation, probing at the dimple leads to an overprediction of the axial capacity. Furthermore, when buckling does initiate at the dimple, a surprising universal feature emerges; even though different cans show a range of axial capacity, all cans whose buckling initiates at the prescribed dimple exhibit a similar critical deflection at the dimple. Together, these results hint that a better understanding of the initial buckling location may allow for better predictions of the onset of failure. |
Tuesday, March 16, 2021 12:42PM - 12:54PM Live |
F16.00005: Static equilibria and bifurcations of interlaced bigon rings Tian Yu, Lauren Dreier, Francesco Marmo, Stefano Gabriele, Sigrid Adriaenssens We propose a numerical framework to study mechanics of elastic strip networks. Each strip is modeled as a Kirchhoff rod, and the entire strip network is formulated as a two-point boundary value problem (BVP). We first study the buckling behavior of a bigon, which consists of two strips fixed with prescribed angles at the two ends. We find that both the end angles and the aspect ratios of the strip's cross section contribute to make a bigon buckle out of plane. Then we study a bigon ring that connects a series of bigons and forms a closed loop. A bigon ring is generally multistable. We find both experimentally and numerically that a bigon ring can fold into multiply-covered loops, similar to the folding of a bandsaw blade. Finally we explore the static equilibria and bifurcations of a 6-bigon ring, and identify several families of equilibria. Our numerical implementation can be applied to general elastic rod/strip networks that may contain flexible joints, naturally curved strips of different lengths, etc. The folding and multistable behaviors of a bigon ring may inspire the design of novel deployable and morphable structures. |
Tuesday, March 16, 2021 12:54PM - 1:06PM Live |
F16.00006: Delayed bifurcation in elastic snap-through Mingchao Liu, Michael Gomez, Dominic Vella Snap-through buckling is a striking instability in which an elastic object rapidly jumps from one state to another. Despite the ubiquity of snap-through in nature and engineering, its dynamics is not well understood. To explore the dynamic feature of elastic snap-through, here we study a model system: an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. By combining numerical simulation and asymptotic analysis, we investigate when and how the arch transitions between two stable states and show that the end-shortening at which the fast ‘snap’ happens depends on the rate at which the end-shortening is reduced. The results obtained here may have important consequences for understanding complex instabilities in both biological and engineering settings. They may also lead to new routes of controlling snap-through in applications. |
Tuesday, March 16, 2021 1:06PM - 1:18PM Live |
F16.00007: Delayed pressure buckling of viscoelastic spherical shells Lucia Stein-Montalvo, Douglas Peter Holmes, Gwennou Coupier With fast-switching devices in mind, we performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. However, unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures (i.e. below the experimentally-determined elastic critical load), often following a significant time delay. |
Tuesday, March 16, 2021 1:18PM - 1:30PM Live |
F16.00008: Mechanics and geometry of nonlinear cracks: A complex stress-function approach Oran Szachter, Michael Moshe, Eytan Katzav A central method for solving linear elastic problems in domains of low symmetry is by complexifying the elastic potential and using conformal maps to transform the domain of interest to a simpler one, e.g. from a crack to a circular hole. The elastic fields calculated at the vicinity of a crack in this approach are not small, and therefore question the validity of linear elasticity. Here we present a new method that allows us to generalise the complex function approach to nonlinear elasticity. We implement our method to solve the nonlinear problem of a crack, and upon comparing with earlier attempt to this problem we address open questions about the (un)ambiguity of this mechanical problem. |
Tuesday, March 16, 2021 1:30PM - 1:42PM Live |
F16.00009: Snap buckling in overhand knots Dezhong Tong, Mohammad Khalid Jawed We report a snap buckling process in overhand knots: when an overhand knot tied in elastic rods is tightened, it can undergo a sudden change in shape. We study this buckling process through a combination of discrete differential geometry (DDG)-based simulations and tabletop experiments. The onset of snap buckling is explored as a function of the topology of the knot, the rod geometry, and friction. In our setup, the two open ends of the overhand knot are slowly pulled which eventually leads to snap buckling in the closed-loop of the knot. We call this phenomenon “inversion” since the loop appears to dramatically move from its current position to the other side of the knot. A numerical framework is implemented with a combination of discrete elastic rods and a constraint-based method for frictional contact to explore the inversion in overhand knots. The numerical simulation can robustly capture the inversion in the knot and is found to be in good agreement with experimental results. In order to gain physical insight into the process, we employ scaling analysis on elastic energies and investigate the role of various physical ingredients on inversion. |
Tuesday, March 16, 2021 1:42PM - 1:54PM Live |
F16.00010: Bifurcation of pre-buckled bands under lateral transverse shear Weicheng Huang, Mohammad Khalid Jawed We combine experiments and simulations to study the supercritical pitchfork bifurcation of a pre-compressed band under lateral end translation, from narrow to wide. Based on the ratio among length, width, and thickness, the elastic structures in our study fall into three different categories: rods, ribbons, and plates. To capture their geometrically nonlinear deformations, we develop several discrete differential geometry-based numerical frameworks. The one dimensional rod model can predict the mechanical response when the plate is narrow, while it is unable to match with experiments as the width of the band increases. A two dimensional approach (plate model) can accurately predict the deformations of bands with different geometries. The ribbon model of Sadowsky, surprisingly, fails to capture the mechanics of strips at inflection points. Our study provides guidelines on the choice of the appropriate models – rod, ribbon, and plate – in simulation of slender structures. |
Tuesday, March 16, 2021 1:54PM - 2:06PM Live |
F16.00011: Snap buckling of active bistable beams under magnetic actuation Arefeh Abbasi, Dong Yan, Pedro M Reis Bistable structures featuring two distinct stable configurations are central in the design of many functional devices, both in nature and in technology. Here, we investigate the snap buckling of a bistable beam made of magnetorheological elastomer (MRE) prepared by incorporating micron-sized magnetic particles into a polymer matrix. We demonstrate that the snap buckling of our magnetic beams can be triggered in the presence of an external uniform magnetic field. We make use of precision experiments to quantify how the critical field strength required for buckling depends on both the imposed end-to-end shortening and the beam geometry. In parallel to the experiments, we perform finite element simulations. The experimental and numerical results are rationalized through a magneto-elastic beam model. Using magnetic fields to actuate the snap-through of bistable beams could enable a new class of devices with contactless actuation, across length scales; from MEMS to robotic applications. |
Tuesday, March 16, 2021 2:06PM - 2:18PM On Demand |
F16.00012: Stabilization of a heavy particle on a vibrating soft ribbon Anaïs Abramian, Suzie Protière, Arnaud Lazarus When sand is sprinkled on a vibrated plate, it accumulates near the vibration nodes of the plate forming the famous "Chladni patterns" [1]. These patterns, which vary with the forcing frequency, provide an easy visualization of a musical instrument when it needs to be tuned, for example. However, if the plate is soft enough, as an elastic membrane, grains can deform it and then change in turn the modes’ pattern and frequency. |
Tuesday, March 16, 2021 2:18PM - 2:30PM On Demand |
F16.00013: Diffusion stimulated snap-through inversion of an elastic hemispherical shell Ji Sung Park, JunSeong Kim, Anna Lee, Ho-Young Kim Vigorous snap-through buckling instability of shell structures is adopted by a variety of biological (Venus flytrap, Sphaerobolus) and artificial systems (jumping popper) as an efficient strategy for rapid transmutation between different geometrical configurations. Here we explore the snap-through buckling inversion of an elastomeric bilayer shell stimulated by diffusion induced differential swelling. Hemispherical bilayer shells of two different elastomers are fabricated layer-by-layer by pour coating on acrylic molds. The prepared shells are then fully immersed in organic solvents to swell. We characterize the dynamics of snap-through inversion through total response time and energy released, using both an analytical elastic energy model and Abaqus simulations. Upon combining our theory with experiments of various geometry of thin shells, we suggest a novel model for snap-through inverting shells for both biologists and toy enthusiasts. |
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