Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session L30: Soft Mechanics via Geometry IFocus

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Sponsoring Units: DSOFT DPOLY Chair: D. Zeb Rocklin, Georgia Inst of Tech Room: 502 
Wednesday, March 4, 2020 8:00AM  8:36AM 
L30.00001: Conformal elasticity of twodimensional dilational maximally auxetic materials Invited Speaker: Zeb Rocklin The elastic response of a structure depends not only on its material, but on its geometry, as when the thinness of a sheet gives rise to outofplane bending fundamentally distinct from the response of a thick slab. Such thinness is similarly exploited in mechanical metamaterials which permit counterrotations of stiff adjoining elements, ranging from cornersharing square or triangular pieces to disordered networks. Such behavior can be described via a micromorphic theory which includes these abrupt local rearrangements, giving rise to a longwavelength elastic theory which resembles conventional Cauchy elasticity with a dramatically reduced bulk modulus. The lowenergy deformations consist predominantly of local rotations, translations and dilations without shears and are hence exactly the conformal maps of complex analysis, which admit a simple analytical theory extending even into the nonlinear regime. Despite finitesize effects, bending resistance and disorder, this theory accurately captures response in both finiteelement simulations and experimental systems, opening new avenues for shapechanging, programmability and nonlinear response. 
Wednesday, March 4, 2020 8:36AM  8:48AM 
L30.00002: Control and design of response in disordered networks: Geometry and selfstresses. Anwesha Bose, Steven A. H. van Duijnhoven, Mathijs F.J. Vermeulen, Wouter G Ellenbroek, Cornelis Storm The mechanical response of elastic networks is not only controlled by the elastic properties of its constituents, but also by their architecture. This is evident for crystalline structures, but equally true for random networks. I share two recent examples where we use geometry to elicit nonstandard mechanical response from disordered networks. In the first, we design freestanding frames that are mechanically overconstrained, and demonstrate that by engaging their states of self stress (i.e., applying internal loads that produce no strain) we can tune the overall mechanical response and induce softness, bi and instabilities of purely geometric origin [1]. In the second example, we design random periodic lattices and structurally optimize them to exhibit specific responsiveness manifested, f.i., by extreme auxeticity (deeply negative Poisson's ratios). Together, these examples illustrate that the power of geometry may be harnessed to coax tailored, highly nongeneric response even out of fully disordered materials. 
Wednesday, March 4, 2020 8:48AM  9:00AM 
L30.00003: Coulomb Floppy Networks: from soft to hard matter. Alexei Tkachenko, Igor Zaliznyak Floppy Networks (FNs) play a prominent role in soft condensed matter physics, from polymeric gels and rubber to biomolecules, glasses, and granular materials. We demonstrate how the very same concept emerges in the context of a family of openframework ionic solids, e.g. ScF_{3}, which can be conceptualized as Coulomb FNs. They exhibit unusual properties, including quantum structural phase transition near ambient pressure and negative thermal expansion (NTE). We connect these phenomena to FNlike crystalline architecture, stabilized by the net electrostatic repulsion, playing a role similar to the osmotic pressure in a polymeric gel. Our theory provides an accurate quantitative description of NTE and structural transition. Entropic stabilization of criticality explains the observed phase behavior. In addition, a significant entropic contribution to elasticity accounts for the marked discrepancy between numerical and experimentally observed compressibilities. 
Wednesday, March 4, 2020 9:00AM  9:12AM 
L30.00004: Emergence of rigidity, microscopic rearrangements and viscoelastic response in soft particle gels Emanuela Del Gado, Bavand Keshavarz, Minaspi Bantawa, Michela Geri, Mehdi Bouzid, Thibaut Divoux, Gareth H McKinley

Wednesday, March 4, 2020 9:12AM  9:24AM 
L30.00005: Pseudomomentum balance in thin structures James Hanna, Harmeet Singh The balance of pseudomomentum is associated with material symmetry in continua. We will employ it in the context of thin, flexible structures, to explain conserved quantities in rotating conical membranes and propulsive forces on confined elastic rods. 
Wednesday, March 4, 2020 9:24AM  9:36AM 
L30.00006: Asymptotic isometry and wrinkletofold transition in a simplified Lamé problem Anshuman Pal, Thomas Witten Azimuthal wrinkling in the annular (Lamé) geometry serves as an archetype for understanding geometryinfluenced elastic response in thin sheets. In most experiments, the annulus is subjected to radial tension at both the inner and outer boundaries, generating compression and wrinkling in the azimuthal direction ([1]) . In our work, we study an even simpler version of this problem, using theory and simulations, where the annulus is subjected to only a radial pull at the inner boundary. This creates azimuthal wrinkling with a simpler, onedimensional phase space spanned by the dimensionless 'bendability' parameter, ε^{1}.We focus on the large ε^{1}(small thickness and/or large load) limit  here, in contrast to previous experiments, the sheet becomes asymptotically isometric, and the wavenumber coarsens and hits a lower limit set by the geometry of the sheet and the boundary conditions. If we now loosen the boundary condition, the wrinkles transition to a single fold that consumes all the excess length. Although purely numerical, to the best of our knowledge, this is the first realisation of a wrinkletofold transition ([2]) on an unsupported membrane. 
Wednesday, March 4, 2020 9:36AM  9:48AM 
L30.00007: Geometry, mechanics, and dynamics of leaves, flowers, and sea slugs Kenneth Yamamoto, Shankar Venkataramani Why are there intricate, selfsimilar wrinkles along the edges of growing leaves, blooming flowers, torn plastic sheets, and frilly sea slugs? We argue that the mechanics and dynamics of these nonEuclidean elastic sheets are governed by interacting nonsmooth geometric defects in the material. I will describe novel ideas stemming from characterizing and analyzing these defects using discrete differential geometry in order to uncover fundamental insights into the elastic behavior and properties of thin hyperbolic bodies. New theories based on the mechanics of nonsmooth defects may (i) explain biological phenomena, from the morphogenesis of leaves, flowers, etc. to the biomechanics of sea slugs, as well as (ii) introduce new paradigms for materials design and actuation in a variety of new technologies, e.g., soft robotics. 
Wednesday, March 4, 2020 9:48AM  10:00AM 
L30.00008: Mechanics and geometry of soft beams and shells Daniele Battista, Michele Curatolo, Paola Nardinocchi We investigate swellinginduced morphing in thin soft polymer based plates and shells. Starting from flat geometries, spherelike and nearly developable shapes are realized and the ability to control a specific shaping, shifting from one shape to another, under anisotropic swelling is investigated. Starting from nearly developable shapes, the effects on the geometry of swelling and shrinking is also studied. The mathematical model accounts for both diffusion and nonlinear mechanics (stressdiffusion model). It is implemented in a finite element code and a campaign of numerical experiments is planned. 
Wednesday, March 4, 2020 10:00AM  10:12AM 
L30.00009: Capture of particles by a flexible granular envelope Katharine Bancroft, Theodore Anthony Brzinski The capture of small particles by a flexible envelope can model many common phenomena. For example, in the rotating environment of a commercial dryer, large, flexible, nonconvex objects like fitted sheets and duvet covers often capture smaller items like socks that fail to dry as a result. Amoeba exploit a similar process for prey capture by extruding pseudopodia in which smaller organisms become trapped. We have developed a quasi2D granular system with qualitatively similar dynamics: a granular chain envelope composed of custom ball chain in a background dispersion of spherical grains inside a rotating drum. The particlescale geometry of the granular chain determines the available conformations of the envelope, leading to a biased convexity. We share the results of our investigation of the kinetics of particle capture for this novel model system. 
Wednesday, March 4, 2020 10:12AM  10:24AM 
L30.00010: Predicting the onset of disclination defects on curved open surfaces Siddhansh Agarwal, Sascha Hilgenfeldt Ordered structures on surfaces with Gaussian curvature are topologically constrained to contain a finite defect charge, while the positioning of these defects is determined by optimization of the surface's elastic energy. Open surfaces of sufficiently small curvature minimize energy without defects in the bulk, while stronger curvature favors the appearance of a disclination in the ground state; the presence of a boundary adds subtlety to the local screening of Gaussian curvature by defects. We find that, in contrast to previous heuristic arguments, the onset of transition is governed neither by local values of Gaussian curvature nor by its global integral. Starting from stringent energy minimization, we instead propose a weighted integral Gaussian curvature as an improved predictor for the transition  one that is universally valid for a large class of bounded rotationally symmetric surfaces. Our formalism also allows for analysis of the first or second order character of the transition, and how it is modified by boundary stresses and/or breaking symmetries of shape or material properties. These findings are of practical and fundamental importance in both engineering and biological cellular systems, such as the pattern of visual processing in invertebrate eyes. 
Wednesday, March 4, 2020 10:24AM  10:36AM 
L30.00011: Facets and Folds: A model for fragmentation kinetics of crumpled thin sheets Jovana Andrejevic, Lisa M Lee, Shmuel Rubinstein, Christopher Rycroft As a confined thin sheet crumples, a unique arrangement of sharp ridges emerges, delineating approximately flat facets. Viewed collectively, this mosaic of ridges and facets exhibits striking statistical reproducibility  the total length traced out by ridges, for instance, has been shown to grow logarithmically with the number of crumpling and unfolding repetitions. Here, we explore the correspondence between crumpling and a general fragmentation process. We identify a physical model for the evolution of facet area distribution in crumpled sheets that captures a wide range of data samples with a single variable parameter. We then demonstrate the capacity of this model to reproduce experimental observations such as the characteristic logarithmic scaling of total ridge length, thereby supplying a missing physical basis for the observed phenomenon. 
Wednesday, March 4, 2020 10:36AM  10:48AM 
L30.00012: Stress Relaxation of Drying Colloids Zhiyu Jiang, Chong Shen, Lanfang Li, Megan Valentine, Ye Xu, H Daniel OuYang Stress relaxation during the drying of coatings is of interest due to its importance in the thin filmformation process that dictates the final properties of coatings. Using drying colloidal suspensions as a model system, this study examines how stresses in the colloidal matrix relax when particles are compacted during uniaxial drying in a microfluidics. Microscopic oil droplets cosuspended in the colloidals are used as probes for local stresses and strains as these droplets are deformed by the changing matrix of particles. Balance of the interfacial stress of the oil in the colloids and the stress produced by the compacting colloids dictates the shape evolution of the droplets. The evolution of the deformations of multiple droplets is recorded by confocal fluorescence microscopy. Images of the time evolutions of the droplet shapes and the positions of fluorescent tracer particles nearby the droplets are analyzed by digital image correlation. The talk will address questions on the roles of the viscous damping, interfacial tension between the oil and colloidal matrix, the anisotropy of the strain and stress distributions and the mechanical properties of compacting colloidal particles before the coating is fully dried. 
Wednesday, March 4, 2020 10:48AM  11:00AM 
L30.00013: Physics Behind the Snapping of a Twisted Balloon YuChuan Cheng, HungChieh Fan Chiang, HsinHuei Li, WeiChih Li, TzayMing Hong It is childhood experience to twist balloons and turn them into dogs and flower. In this talk we investigate the process that leads up to the snap of a cylindrical balloon. For a twisted short balloon (1<L/D<7 where L, D : length and diameter), its phase transits from (1) being sheared and wrinklefree while torque (τ) is linear to θ, (2) appearance of a neck without wrinkles, while radius and shear angle are found to obey r^{3}dθ/dx=const, (3) development of parallel wrinkles whose number ~12 is insensitive to L, D, and thickness. τ increases concavely with θ, to (4) wrinkles cross one another eventually and are followed by a sudden snap into two segments, as for a bended drinking straw. For a mediumsize balloon (7<L/D<15), (a) similar to (1), (b) skip (2, 3) to become curled with a lowamplitude oscillation in θ, (c) similar to (4). When the balloon is long (15<L/D), (i) similar to (1) (ii) similar to (b), but develop a supercoil while accompanied by a suddenly drop in τ, (iii) repeat (i, ii). Heuristic models are proposed to understand the physics behind different phases. MD simulation is also performed to reveal energetics. Furthermore, to verify whether the above properties are unique to a quasi1D object (balloons), a thread (real 1D) and ribbon (2D) are also studied. 
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