Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session P30: Soft Mechanics via Geometry III |
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Sponsoring Units: DSOFT DPOLY Chair: Michael Czajkowski, Georgia Inst of Tech Room: 502 |
Wednesday, March 4, 2020 2:30PM - 2:42PM |
P30.00001: Geometrically-frustrated wrinkle patterns 1: Defects and mesoscale structure Joseph Paulsen, Oleh Tovkach, Monica Ripp, Junbo Chen, Teng Zhang, Benjamin Davidovitch Thin films readily buckle to relax compression, creating wrinkle patterns that can have considerable morphological complexity. Some of this complexity stems from a basic geometric conflict, arising when wrinkles that would otherwise prefer a fixed wavelength are formed in geometries where the lines of tension are splayed, for example when wrinkles emanate radially from a point. We study such frustrated states within an annular region of an elastic sheet subjected to unequal tensions at its inner and outer boundaries. Using experiments and simulations, we demonstrate two distinct solutions: (i) states with approximately constant wavelength, enabled by “defects” in the wrinkle pattern where new wrinkles begin, and (ii) “defect-free” states consisting of a fixed number of wrinkles of non-constant wavelength. We show how these two morphological types reflect distinct minima of a suitable coarse-grained elastic energy. We further predict a mesoscopic lengthscale for patches of nearly-parallel wrinkles separated by defect-rich regions, in agreement with our observations. This work unravels an organizing principle with analogs in liquid crystalline and superconducting states of matter. (This is part 1 in a 3-talk series). |
Wednesday, March 4, 2020 2:42PM - 2:54PM |
P30.00002: Geometrically-frustrated wrinkle patterns 2: cascades versus defects Meng Xin, Doireann O'Kiely, Benjamin Davidovitch, Dominic Vella Cascades and localized defects are characteristic motifs of wrinkle patterns in |
Wednesday, March 4, 2020 2:54PM - 3:06PM |
P30.00003: Geometrically-frustrated wrinkle patterns 3: Experimental realisation of defect patterns Lucie Domino, Doireann O'Kiely, Dominic Vella In the previous talks, the role of geometry in forcing the creation of defects in wrinkle patterns has been discussed. Here, we present a series of experimental systems that exhibit different mechanisms for introducing new wrinkles, including smooth cascades and localised defects. We discuss the influence of the underlying preferred wrinkle pattern on which of these mechanisms is observed in reality. (This is part 3 in a 3-talk series). |
Wednesday, March 4, 2020 3:06PM - 3:18PM |
P30.00004: Curvature in Compressed Thin Cylindrical Shells Approaching the Isometric Limit Nicole E Voce, Cassidy Anderson, Marcelo Dias, Klebert Feitosa We study the buckling of a thin cylindrical shell constrained to slide onto an inner non-deformable pipe. Our goal is to characterize the relationship between the shell thickness and the localization of stresses by using curvature measurements. First, we induce surface buckling by immobilizing one end of the shell and applying force to the other end. Then, we obtain a virtual reconstruction of the surface from 3D optical scanning and compute the Gaussian curvature for every point on the mesh. We find that as the shell gets thinner, the distribution of Gaussian curvatures becomes broader. However, surprisingly, the mean of the Gaussian curvature distribution increases. Furthermore, measurements of areas enclosed by the parabolic lines around protruding vertices from the buckled surface show that the transitions between regions of positive and negative Gaussian curvature are more localized. Finally, the Gaussian curvature reveals the formation of substructures within the lobes around the vertices. These results demonstrate that the evolution of the cylindrical shell towards the isometric limit represented by the well-known Yoshimura pattern is non-trivial. |
Wednesday, March 4, 2020 3:18PM - 3:30PM |
P30.00005: Topological Floppy Modes in Epithelial Tissue Network Harold Liu, Di Zhou, Leyou Zhang, David Lubensky, Xiaoming Mao The ordering, structure formation, and mechanical response in epithelial cells are essential to the functioning of many tissues. In this talk, we explore topological mechanics in a simple epithelial cell sheet starting described by a vertex model. We find that floppy modes in this model can become polarized based on the geometry of the cells, and domain boundaries with localized floppy modes can be observed. This simple model indicates a possible role for epithelial cell structure in directing mechanical responses. This topological mechanical polarization may be related to the mechanism of formation of Planar Cell Polarization (PCP), an intriguing phenomenon often seen in animal development, which is a polarization of a field of cells within the plane of a cell sheet to obtain directional information that is essential for diverse cellular processes. |
Wednesday, March 4, 2020 3:30PM - 3:42PM |
P30.00006: Twisting, buckling, and tension in elastic helices with multiple perversions Adam Fortais, Kari Dalnoki-Veress A telephone cord and the coils of cucumber tendrils; these are two examples of elastic beam-like systems that take on the shape of soft, helical springs. By unwinding such a spring and holding its ends fixed, an elastic instability forms, causing the spring to form both chiralities of the helix, meeting at defects called perversions. We investigate this phenomenon in an idealized experiment using highly uniform, microscopic, elastic fibers with cylindrical cross-sections. We measure the force of extension as a function of geometry, material properties, and twist. Previous work has shown that multiple perversions may form as a result of a spring's prismatic cross-section. Here we observe that, surprisingly, multiple perversions still form, despite the uniform cylindrical cross-section of our fibers. |
Wednesday, March 4, 2020 3:42PM - 3:54PM |
P30.00007: Simulations of buckling and crumpling in twisted ribbons Madelyn Leembruggen, Jovana Andrejevic, Arshad Kudrolli, Christopher Rycroft A twisted ribbon exhibits at least five deformation phases, with transitions facilitated by tuning the tension applied or twist angle. When driven from one of these self-avoiding phases into a disordered regime of self-contact, the ribbon develops ridges as it folds or crumples. Here, we develop a computational model of this complex, dynamic process, which reproduces the transitions seen in experimental tests. Our simulations illuminate the details of folding and crumpling transitions induced via twisting; allow careful analysis of the ribbon's topography and curvature; and potentially reveal a state variable by which the disordered system may be quantified. |
Wednesday, March 4, 2020 3:54PM - 4:06PM |
P30.00008: Statistical mechanics of 2D sheets under uniaxial tension Mohamed El Hedi Bahri, Andrej Kosmrlj Atomically thin sheets, such as graphene, are widely used in nanotechnology. Recently they have also been used in applications including kirigami and self-folding origami, where it becomes important to understand how they respond to external loads. Motivated by this, we investigate how isotropic sheets respond to uniaxial tension by employing the renormalization group. Previously, it was shown that for freely suspended sheets thermal fluctuations effectively renormalize elastic constants beyond a characteristic thermal length scale (a few nanometers for graphene at room temperature), beyond which the bending rigidity increases, while the in-plane elastic constants reduce with universal power law exponents. Under uniaxial tension, we find that the bending rigidity along the axis of tension diverges with a different power law exponent beyond a stress-dependent length scale whereas the Young’s modulus in the orthogonal direction renormalizes to zero. As a consequence, for moderate tensions we find a universal nonlinear force-displacement relation and the universal Poisson’s ratio. For large tensions, in-plane fluctuations longitudinal with the axis of tension are suppressed and classical mechanics along this axis is recovered. |
Wednesday, March 4, 2020 4:06PM - 4:18PM |
P30.00009: Isigami: sheet reconfiguration driven by cone interactions Benjamin Katz, Vincent Crespi A novel class of surfaces holds the possibility of reversible reconfiguration into a large family of distinct, stable shapes. This property stems in part from their topological defects–they have equal numbers of cones and saddles. Exploring these surfaces with an example constructed out of a graphene monolayer with the defects arranged in a kagome-like superlattice, we model its mechanical response with semiclassical molecular dynamics. The cones possess a two-fold degree of freedom in their up/down orientation, yielding a reconfigurable surface with a large number of metastable shapes. Enumerating a complete 'zoo' of such shapes for a small patch of this material reveals that not only are the interactions between these degrees of mechanical freedom long-range enough to produce a gaussian-like 'density of states' for given cone orientations, but also that the surface possesses other hidden degrees of freedom in certain orientations–further increasing the number of stable shapes it can hold. These shapes cover a broad range of physical forms and a scale comparable to important biomolecules, raising the possibility of biological applications. |
Wednesday, March 4, 2020 4:18PM - 4:30PM |
P30.00010: Indentation of ellipsoidal and cylindrical shells: new insights from shallow-shell theory Wenqian Sun, Jayson Paulose Pressurized elastic shells are ubiquitous in nature, from pollen grains to the outer walls of yeast and bacterial cells. Indentation measurements provide a means of simultaneously probing the internal pressure and elastic properties of thin shells, which in turn can be relevant to understanding cellular function. We study the effects of geometry and pressure-induced stress on the indentation stiffness of ellipsoidal and cylindrical elastic shells using shallow shell theory. The key advance in our work lies in reducing the linear indentation response to a single integral with two dimensionless parameters which encode the asphericity and internal pressure. This integral can be numerically evaluated in all regimes, and is used to generate analytical expressions in various limits. Our results provide theoretical support for previous scaling and numerical results on the stiffness of ellipsoids, and give new insights to the linear indentation response of pressurized cylinders. |
Wednesday, March 4, 2020 4:30PM - 4:42PM |
P30.00011: Statistical mechanics of dislocation pileups Grace Zhang, David R. Nelson Dislocations experiencing applied stress in two dimensions can order when trapped in a single glide plane with aligned Burgers vectors. These dislocation queues, called dislocation pileups, are critical in the initiation and propagation of deformations in materials. We study the static and dynamical properties of this class of defect ordering, where the dislocations themselves form inhomogeneous quasilattices in one dimension, with spatially varying lattice spacings whose spatial profile depends on the form of the applied stress. We study these dislocation pileup lattices using an intriguing connection with recent generalizations of random matrix ensembles, and examine the crystallization of these dislocations at low temperatures. We use random matrix theory to probe the equilibrium statistical mechanics, which allows us to extract the spatial correlation functions and structure factors of two distinct types of dislocation pileups, those in uniform stress fields and those in stress fields linear in space. Our formalism provides an analytical formulation for these correlations generalizable to other inhomogeneous crystals in one dimension. Finally, we analyze the low temperature excitation spectrum of these dislocation pileups and the spatial properties of their excitation modes. |
Wednesday, March 4, 2020 4:42PM - 4:54PM |
P30.00012: Statistical ensemble inequivalence for flexible polymers under confinement in various geometries Panayotis Benetatos, Sandipan Dutta The problem of statistical ensemble inequivalence for single polymers has been the subject of intense research. In a recent publication, we show that even though the force-extension relation of a free Gaussian chain exhibits ensemble equivalence, confinement to half-space due to tethering to a planar substrate induces significant inequivalence [S. Dutta and P. Benetatos, Soft Matter, 2018, 14, 6857-6866]. In this talk, we extend that work to the conformational response to confining forces distributed over surfaces. We analyze in both the Helmholtz and the Gibbs ensemble the pressure-volume equation of state of a chain with free ends in rectangular, spherical, and cylindrical confinement. We especially consider the case of a directed polymer in a cylinder. We also analyze the case of a tethered chain in various geometries. In general, confinement causes significant ensemble inequivalence. Remarkably, we recover ensemble equivalence at the limit of squashing confinement. Our work may be useful to the interpretation of single molecule experiments and caging phenomena. |
Wednesday, March 4, 2020 4:54PM - 5:06PM |
P30.00013: Soft actively contractile cylinders and spheres Michele Curatolo, Paola Nardinocchi, Luciano Teresi In the last years, contractile gels have been the subject of intense research activity. Active gel microtubules have been produced to investigate how the dynamics of diffusion can be enhanced when gel activity is driven by molecular motors (Phil.Trans.R.Soc. A 372, 2014). Likewise, buckling shapes of thin sheets made of active polymers have been presented and discussed (Nature Communications 9, 2018). On a different side, microfluidic applications based on polymer microtubules have been investigated (Lab on a Chip 18, 2018). |
Wednesday, March 4, 2020 5:06PM - 5:18PM |
P30.00014: Non trivial deformation structures in confined elastic membrane under stretching Debankur Das, Jürgen Horbach, Surajit Sengupta, Tanusri Saha-Dasgupta Two dimensional elastic networks when stretched, deform plastically by producing pleats; system |
Wednesday, March 4, 2020 5:18PM - 5:30PM |
P30.00015: Mechanical response of wrinkled structures Sijie Tong, Andrej Kosmrlj Wrinkling instability of compressed stiff thin films bound to soft substrates has been studied for many years and the formation and evolution of wrinkles is well understood. Recently, the wrinkling instability has been exploited to create structures with tunable drag, wetting and adhesion. While these studies successfully demonstrated the proofs of concepts, the quantitative understanding is still lacking, because we don’t know how wrinkled surfaces deform in response to interactions with environment. To address this issue, we systematically study how wrinkled structures respond to infinitesimal surface forces both in the vertical and horizontal directions. We find that the linear response diverges near the onset of wrinkling instability and then decays away from this critical threshold. The mechanical response near the critical threshold is dominated by the characteristic mode of wrinkles. In analogy with the critical phenomena in ferromagnets, we can introduce the critical exponents for the response of the characteristic mode of wrinkles, which are consistent with the Landau theory. Our theory can be further used to study the response of wrinkled structures to more complicated distributions of external forces and can thus provide insights for the above-mentioned applications. |
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