Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session S21: Extreme MechanicsRecordings Available
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Sponsoring Units: DSOFT Chair: Lucia Stein-Montalvo, Princeton University Room: McCormick Place W-185D |
Thursday, March 17, 2022 8:00AM - 8:12AM |
S21.00001: Snapping of strings: singular or just really big? Abhinav R Dehadrai, James Hanna The whipping of the free end of a string, chain, or flexible cable, induced by generic initial and boundary conditions, is a rapid event featuring a tension spike and significant focusing of kinetic energy. It has been suggested that this "snapping" event is a regularized singularity. We examine the particular case where the system is driven by gravity and the initial conditions are a catenary, for which prior experimental data exist. We simulate an inextensible string by converting the usual partial-differential-algebraic system into a partial-ordinary-differential system and solving this with a finite difference scheme. This accurately reproduces the available experimental position data without any fitting parameters or ad hoc damping, and thus provides a more realistic estimate of forces, velocities, and accelerations. Our results reveal accelerations several orders of magnitude greater than the driving acceleration, associated with a very steep tension gradient near the free end of the body. By seeing how these quantities scale with the fineness of the numerical mesh, we conclude that while the amplification of some quantities is remarkably large, the event is only potentially singular when a geometric singularity is supplied by a perfectly folded vertical initial condition. Time permitting, we will comment on extensible cables and bungee jumping. |
Thursday, March 17, 2022 8:12AM - 8:24AM |
S21.00002: Packing of elastic rings with friction Silas D Alben We study the deformations of elastic filaments confined within slowly-shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall. |
Thursday, March 17, 2022 8:24AM - 8:36AM |
S21.00003: Shape-Shifting Structures by Jamming on a Deformable Manifold Arman Guerra, Douglas P Holmes
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Thursday, March 17, 2022 8:36AM - 8:48AM |
S21.00004: Twisting a thin cylindrical film: From wrinkles to kinematic constraints Pan Dong, Mengfei He, Nathan C Keim, Joseph D Paulsen Individual candies or lozenges may be wrapped by rolling a flat film into a cylinder, and then twisting the two ends to draw the sheet shut. Here we investigate the geometry and mechanics of this process by measuring torques and forces that occur when a thin cylindrical shell is manipulated between two flat plates. In one set of experiments, we compress a cylindrical film lengthwise and then twist it. The film shows a disordered crumpled pattern until it reaches a hard kinematic constraint, at which point an ordered pattern of wrinkles emerges and the measured torque rises rapidly. We develop a theoretical model of this process by modeling the film as an inextensible fabric that is free to compress in one direction via the formation of small-scale wrinkles. This model allows us to predict the rotation angle where the system becomes stiff, as well as the non-trivial orientation of the wrinkles. We map out these results in a phase diagram that delineates a region that may be accessed at low energetic cost, and an inaccessible region where there is macroscopic stretching. Ordered wrinkle patterns develop at the boundary between these regions, and we trace this boundary in experiments by applying a small tension force while gradually twisting the cylinder. |
Thursday, March 17, 2022 8:48AM - 9:00AM |
S21.00005: Expand into collapse: gross and fine structures of an inflated balloon Mengfei He, Vincent Démery, Joseph D Paulsen Inflatable structures such as balloons harbor the interplay among pressure driving, mechanical response and geometrical constraint. We study such inflation by stitching two flat circular membranes, subject to a hydrostatic pressure. Regardless of the complex surface configuration, we report a simple shape assumed by the system, which can be understood quantitatively using coarse graining with a geometrical model. At a finer scale, on the other hand, the balloon surface collapses into deep folds with an increasing pressure. Using laser scattering, we measure the fold shape and obtain good agreement with our analytical prediction. We further compare our measured balloon cross sections with a simple toy-simulation to qualitatively study the emerging two-dimensional behavior embedded in an intrinsically three-dimensional setting. Our work is potentially applicable in scientific ballooning, parachuting and industrial encapsulation. |
Thursday, March 17, 2022 9:00AM - 9:12AM |
S21.00006: Failure behavior of polycarbonates subjected to ultra-high strain rates impact Kyle Callahan, Santanu Kundu, William Heard Understanding the failure behavior of materials subjected to extreme impact events can lead to the development of protective systems that can protect human life and critical infrastructure from those events. Here, we report the failure behavior of monolithic polycarbonate plates subjected to ultra high strain rates due to the impact of a 4 mm projectile traveling upto the velocity 6 km/s using a two-stage light gas gun (2SLGG). Commercial grade polycarbonates with two different molecular weights have been considered. The glass transition temperature (Tg) as determined by dynamic mechanical analysis (DMA) and dielectric thermal analysis (DETA) shifts to a higher temperature with increasing strain-rate. High-speed videos taken during the impact event captures the fluid-like flow of the ejecta material in the back-face debris clouds (BFDC). This behavior is different from PMMA, another glassy polymer, where glass-like failure with finely particulated BFDCs has been observed. Although Tg increases with increasing strain rate, the heating process during the perforation event leads to a liquid-like flow behavior. The change in failure behavior as a function of molecular weight and plate thickness will be presented. |
Thursday, March 17, 2022 9:12AM - 9:24AM |
S21.00007: Exploiting localized transition waves to tune sound propagation in soft materials Audrey A Watkins, Austin J Eichelberg, Osama R Bilal Programmable materials hold great potential for many applications such as deployable structures, soft robotics, and wave control; however, the presence of instability and disorder might hinder their utilization. Through a combination of analytical, numerical, and experimental analyses, we harness the interplay between instabilities, geometric frustration, and mechanical deformations to control the propagation of sound waves within self-assembled soft materials. We consider levitated magnetic disks confined by a magnetic boundary in-plane. The assemblies can be either ordered or disordered depending on the intrinsic disk symmetry. By applying an external load to the assembly, we observe the nucleation and propagation of different topological defects within the lattices. In the presence of instabilities, the defect propagation gives rise to time-independent localized transition waves. Surprisingly, in the presence of frustration, the applied load briefly introduces deformation-induced order to the material. By further deforming the lattices, new patterns emerge across all disk symmetries. We utilize these patterns to tune sound propagation through the material. Our findings could open new possibilities for designing exotic materials with potential applications ranging from sound control to soft robotics. |
Thursday, March 17, 2022 9:24AM - 9:36AM |
S21.00008: Curvature as an external field in Ising-like puckered cylinders Paul Z Hanakata, Abigail Plummer, David R Nelson Recently, free-standing puckered sheets with arrays of bistable units were introduced as a mechanical analog of an Ising antiferromagnet with, however, a strong coupling to flexural phonons [1]. At finite temperature, Ising-like phase transitions and anomalous thermal expansion can be observed. Here, we present evidence that geometry can be used to control the phase behavior of this model: curvature produces a radius-dependent “external field” that suppresses the ordered anti-alignment of neighboring mechanical “spins.” Molecular dynamics simulations of puckered sheets in cylindrical geometries are used to probe the effect of curvature on the stability of configurations at zero temperature as well as phase transitions at finite temperature. Continuum shallow-shell calculations support the mapping of curvature to a uniform magnetic field that couples to the staggered “magnetization”, defined as the average of the staggered buckled units. Furthermore, a simple phenomenological model predicts that the antiferromagnetic critical temperature decreases with increasing curvature, consistent with our simulation data. Our findings highlight the importance of curvature and temperature for designing meta-cylinders and motivates further study of highly compressible Ising models on curved surfaces. |
Thursday, March 17, 2022 9:36AM - 9:48AM |
S21.00009: Scale Effects on the Perforation Resistance of Soft Materials Edwin P Chan, Katherine M Evans, Christopher L Soles, Stephan Stranick, Amanda Souna, Sanat K Kumar, Mayank Jhalaria From animal and insect bites to drug delivery and ballistics, puncture by a fast-moving projectile into soft materials is an event that occurs in everyday life. Although common, the projectile size and incident velocity of the various puncture events can vary by over several orders of magnitude thus making it challenging to relate the puncture resistance of materials to the scale and conditions of the impact test. Using a microprojectile puncture test, we study the relationship between the minimum puncture velocity (V0), microprojectile size, and impacted material thickness for two different polymer systems (polycarbonate and polymethylacrylate nanocomposite) with significantly different mechanical properties. By applying a Buckingham-Π dimensional analysis to our results, as well as published data on similar materials from macroscale projectile tests, we present a universal scaling relationship that correlates the size-scale of the system and material properties of the impacted materials to V0 that spans over two decades. Our results have important implications in predicting and understanding fast puncture events on a variety of length scales, velocities, and test methods for different material systems. |
Thursday, March 17, 2022 9:48AM - 10:00AM |
S21.00010: On local kirigami mechanics Souhayl Sadik, Marcelo A. Dias, Martin G Walker Kirigami offers unexplored ways to tailor the morphology of thin elastic sheets. By exploiting the fundamental principles of this art and carefully tuning the geometry of the cuts, it unlocks a great potential to control the mechanical properties of thin sheets across multiple scales. In this work, we explore the emergent local non-linear effects in Kirigami by focusing on the basic building block of Kirigami: a thin sheet with a single radial cut. We consider its deformation following the opening of the slit by a given excess angle and the rotation of its lips. As the thickness of the disk approaches zero, there is no stretching contribution and the shape of the disk is governed by the bending energy as it approaches that of an e-cone: a conical solution where all the generators remain straight and intersect at a singularity on its apex. We solve the geometrically nonlinear problem for a Saint Venant-Kirchhoff constitutive plate model to find the geometry of the e-cone as well as closed-form expressions for its surface stresses and couple-stresses. We further investigate the post-buckling stability of the e-cone and map out its phase space for symmetric boundary conditions. For a plate of finite thickness, one may not neglect the stretching contribution. We solve this case by proposing a stretchable creased e-cone model: a discretised e-cone made of a series of rigid panel connected by radial creases allowing for relative rotation and separation of the panels as a model for bending and stretching, respectively. Admissible equilibrium configurations are obtained by penalising these deformations using elastic springs with stiffness constants derived from compatible continuum plate deformations. We are hence able to solve for plates with finite thickness and find the full range of post-buckling behaviour as well as initial buckling instability. |
Thursday, March 17, 2022 10:00AM - 10:12AM |
S21.00011: Crumpled Kirigami Wathsala Jayawardana, Yangchao Liao, Zhaofan Li, Wenjie Xia, Andrew B Croll
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Thursday, March 17, 2022 10:12AM - 10:24AM |
S21.00012: Guided Tearing: What is the best way to cut a sheet of paper with a ruler? Benoit Roman, Francisco Melo, Alejandro Ibarra, Juan-Francisco Fuentealba, Jose Bico We all know how to cut a piece of paper : hold it on a table firmly with a ruler, and |
Thursday, March 17, 2022 10:24AM - 10:36AM |
S21.00013: TOPOLOGICALLY OPTIMISED METAMATERIALS FOR FRACTURE CONTROL Lucie Domino, Corentin Coulais, Alejandro M Aragón, Shahram Janbaz Fracture paths are very difficult to control, apart from idealised cases. Here we design metamaterials from building blocks that are topologically optimised to have a very strong anisotropy in the energy release rate : they break more easily in a direction than another. We 3D print, and tile periodically this building block to create materials that exhibit controlled crack path when broken under tensile stress. With this we create crack paths unachievable in homogeneous materials, which opens promising routes for material design and for new strategies for shock absorption. |
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