Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session C40: Extra Mechanics: Fracking, Growing, Buckling, Defects, Stat Mech, and Bio 
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Sponsoring Units: GSNP GSOFT Chair: Dominic Vella, Oxford University Room: 343 
Monday, March 14, 2016 2:30PM  2:42PM 
C40.00001: Hydraulic fracture and toughening of a brittle layer bonded to a hydrogel Alessandro Lucantonio, Giovanni Noselli, Xavier Trepat, Antonio DeSimone, Marino Arroyo Brittle materials fracture under tensile or shear stress. When stress attains a critical threshold, crack propagation becomes unstable and proceeds dynamically. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure [1]. Here, we show that all these features of brittle fracture are radically modified when the material susceptible to cracking is bonded to a poroelastic medium, such as a hydrogel, a common situation in biological tissues [2]. In particular, we show that the brittle material can fracture in compression and can resist cracking in tension, thanks to the hydraulic coupling with the hydrogel. In the case of multiple cracks, we find that localized fracture occurs when the permeability of the hydrogel is high, whereas decreased permeability leads to toughening by promoting multiple cracking. Our results [3] may contribute to the understanding of fracture in biological tissues and provide inspiration for the design of tough, biomimetic materials. \newline \newline [1] Noselli et al., Int. J. Fracture, 183, 241258 (2013) \newline [2] Casares et al., Nat. Mater., 14, 343351 (2015) \newline [3] Lucantonio et al., Phys. Rev. Lett., 115, 188105 (2015) [Preview Abstract] 
Monday, March 14, 2016 2:42PM  2:54PM 
C40.00002: Geometry and Mechanics of Thin Growing Bilayers Matteo Pezzulla, Gabriel Smith, Paola Nardinocchi, Douglas Holmes We investigate how thin sheets of arbitrary shapes morph under the isotropic inplane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourth's the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. [Preview Abstract] 
Monday, March 14, 2016 2:54PM  3:06PM 
C40.00003: Buckling, driven by constrained phase separation, of toroidshaped hydrogels Michael S. Dimitriyev, YaWen Chang, Anton Souslov, Alberto FernandezNieves, Paul M. Goldbart We investigate the buckling process observed in connection with the temperatureinduced shrinking of an elastic toroid composed of hydrogel. Hydrogels are polymeric network media that become swollen when mixed with water, provided the temperature is low enough. As the temperature is increased beyond a certain point, such gels undergo a firstorder deswelling transition to a demixed state, in which the network segregates from the water, resulting in a shrunken phase. It is known that the rapid heating of swollen hydrogels beyond the deswelling transition results in the formation of a shrunkenphase boundary region, or shell. This shell hinders the expulsion of fluid associated with the equilibration of the sample interior, and gives rise to a prolonged period of coexistence between shrunken and swollen domains in the interior of the sample. In contrast with the spherical case, toroidal samples have been observed to undergo a constrained phase separation that is accompanied by a global buckling (or ``Pringling") deformation of the sample shape. We present a model of hydrogel toroid Pringling in which such deformations are driven by this phase separation process. [Preview Abstract] 
Monday, March 14, 2016 3:06PM  3:18PM 
C40.00004: Modeling and design of the selftwisting of hydrogel bilayer strips Authors: Jiayu Liu, Jingkai Guo, Tanvi Shroff, ChangKyu Yoon, David Gracias {\&} Thao D Nguyen Jiayu Liu, Jingkai Guo, Tanvi Shroff, ChangKyu Yoon, David Gracias, Thao Nguyen Selffolding of hydrogels via heterogeneous swelling can be used to create complex, 3D structures. A bilayer structure with a thermoresponsive hydrogel layer, that swells with decreasing temperature, and a nonswelling layer can respond to a temperature change by either bending into a ring or twisting into a helix. The equilibrium structure depends on the thickness ratio of the two layers, the ratio of the width to thickness of the bilayer, as well as the stiffness of the two layers and equilibrium swelling ratio of the hydrogel.~ These parameters can be controlled using lithographic photopatterning and multilayer deposition techniques.~ To guide the design of the bilayer structures, we developed a finite element model of the bilayer structure. The constitutive model of the hydrogel is described by a free energy density that includes a quasiincompressible NeoHookean component~for the strain energy density of the polymer network and a FloryHuggins component for the~freeenergy density of mixing of the polymer and solvent. We discussed how variations in the layer thickness, slenderness, stiffness, and equilibrium swelling ratio can be used to design selffolded rings of different curvatures and helices with different helix angle and diameters. [Preview Abstract] 
Monday, March 14, 2016 3:18PM  3:30PM 
C40.00005: Mechanics of a leaf detaching from tree Tim Zehnbauer, Sunghwan Jung Deciduous trees shed their leaves through an abscission process. The abscission zone is formed at the base of the petiole, and consists of a top layer with weak walls and a bottom layer that expands and breaks the walls of the cells in the top layer. Although this process is well understood biologically, the mechanical principles underlying this shedding have received little attention. In the present study, we characterize the stressstrain relation of the petiolebranch connection failure over the seasons. The testing is done with a 1kN load cell, where the stem is pulled directly from the branch to make a stressstrain curve. The slope of the stressstrain curve, Young’s modulus, is obtained using least squares linear regression of the curve. We show that Young’s modulus stays constant from spring to late fall, while the maximum tensile strength falls. We are investigating the role of the shape of a leaf’s petiole in this behavior. [Preview Abstract] 

C40.00006: ABSTRACT WITHDRAWN 
Monday, March 14, 2016 3:42PM  3:54PM 
C40.00007: The role of deformable structured surfaces on viscous forces during peeling Charles Dhong, Joelle Frechette It is known that tree frogs are able to adhere well in flooded environments, presumably due to their interconnected network of drainage channels formed by hexagonal epithelial cells in their toe pads. To investigate this effect, a patterned surface of hexagonally arranged cylindrical posts was brought close to a stationary substrate in a submerged, viscous fluid via a normal load, and then peeled off to measure a retraction force. Because these structured surfaces were made from PDMS, they are able to deform throughout the process. We find that these deformable surfaces further reduce the work required to peel apart the two surfaces, even when compared to previous studies in the same system with rigid structures, and we isolated these contributions independent of conservative forces. We then conducted experiments to compare the effect of deformation on the viscous forces and conservative forces. We find that there are several regimes where deformation either increases or decreases the retraction force since we have found that elasticity decreases retraction forces when considering viscous contributions but is also known to increase adhesion in the context of conservative forces. [Preview Abstract] 
Monday, March 14, 2016 3:54PM  4:06PM 
C40.00008: Bioinspired microfluidics: The case of the velvet worm Andres Concha, Paula Mellado, Bernal MoreraBrenes, Cristiano SampaioCosta, L. Mahadevan, Julian MongeNajera The rapid squirt of a proteinaceous slime jet endow velvet worms (Onychophora) with a unique mechanism for defense from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date neither qualitative nor quantitative descriptions have been provided for this unique adaptation. We have investigated the mechanism that allows velvet worms the fast oscillatory motion of their oral papillae and the exiting liquid jet that oscillates with frequencies $f\sim 3060$ Hz. Using anatomical images and high speed videography, we show that even without fast muscular action of the papilla, a strong contraction of the slime reservoir and the geometry of the reservoirpapilla system suffices to accelerate the slime to speeds up to $v\sim 5$ m$/$s in about $\Delta t\sim 60$ ms. A theoretical analysis and a physical simulacrum allow us to infer that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. We propose several applications that can be implemented using this instability, ranging from highthroughput droplet production, printing, and micronanofiber production among others. [Preview Abstract] 
Monday, March 14, 2016 4:06PM  4:18PM 
C40.00009: Nonlinear adhesion dynamics of confined lipid membranes Tung To, Thomas Le Goff, Olivier PierreLouis Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha \footnote{T. Le Goff, P. Politi and O. PierreLouis, PRE {\bf 90}, 032114 (2014).}$^\textrm{,}$\footnote{T. Le Goff, P. Politi and O. PierreLouis, PRE {\bf 92}, 022918 (2015).}$^\textrm{,}$\footnote{T. Le Goff, O. PierreLouis and P. Politi, J. Stat. Mech. {\bf P08004}, 1742 (2015).}. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems \footnote{T. B. T. To, T. Le Goff, O. PierreLouis, preprint.}. [Preview Abstract] 
Monday, March 14, 2016 4:18PM  4:30PM 
C40.00010: Statistical Mechanics of Sliced Graphene Ribbons. Mark Bowick, Emily Russell, Rastko Sknepnek, David Nelson Twodimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly change the effective mechanical properties of these membranes, renormalizing both bending rigidity and elastic moduli so that thermal membranes are stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine the further effect of topology and geometry on the properties of thermal membranes, and find that the introduction of a slit suppresses the scale of thermal fluctuations. [Preview Abstract] 
Monday, March 14, 2016 4:30PM  4:42PM 
C40.00011: Statistical mechanics of thin spherical shells Andrej Kosmrlj, David R. Nelson We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells via renormalization group calculations. It is well known that for flat solid membranes thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local inplane stretching modes and the local outofplane undulations leads to novel phenomena. In spherical shells thermal fluctuations effectively produce negative surface tension, which is equivalent to applying external pressure. We find that small spherical shells are stable, but for sufficiently large shells this thermally generated “pressure” becomes big enough to crush spherical shells. Such shells can be reinflated by increasing internal pressure, where the effective shell size grows nonlinearly as a function of internal pressure with a power law exponent characteristic for thermally fluctuating flat membranes under uniform tension. [Preview Abstract] 
Monday, March 14, 2016 4:42PM  4:54PM 
C40.00012: Phyllotactic transformations as plastic deformations of tubular crystals with defects Daniel Beller, David Nelson Tubular crystals are 2D lattices in cylindrical topologies, which could be realized as assemblies of colloidal particles, and occur naturally in biological microtubules and in singlewalled carbon nanotubes. Their geometry can be understood in the language of phyllotaxis borrowed from botany. We study the mechanics of plastic deformations in tubular crystals in response to tensile stress, as mediated by the formation and separation of dislocation pairs in a triangular lattice. Dislocation motion allows the growth of one phyllotactic arrangement at the expense of another, offering a lowenergy, stepwise mode of plastic deformation in response to external stresses. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, dislocation glide. The crystal's bending modulus is found to produce simple but important corrections to the tube's deformation mechanics. [Preview Abstract] 
Monday, March 14, 2016 4:54PM  5:06PM 
C40.00013: Defectdriven shape instabilities in cohesive filament bundles Isaac Bruss, Gregory Grason When defects are incorporated into the lattice of a flexible 2D crystalline membrane, it buckles into a new configuration. Specifically, 5 and 7fold disclinations produce conical and saddlelike geometries respectively. For bundles composed of a crystalline array of cohesive flexible filaments, we propose a similar phenomena of defectinduced buckling. This revelation is fueled by a recently discovered mapping between the metric properties of a curved surface, and the interfilament spacing within a deformed bundle. Using a combination of continuum elasticity theory and numerical simulations, we investigate the effects of defects in the cross section on a bundle's global structure. We find that positive disclinations promote the twisting of filaments around a central axis within the bundle, while negative disclinations promote twisting around two parallel axes simultaneously. Both instabilities are interpreted by means of their equivalent Gaussian curvature, and map appropriately to the the corresponding membrane responses. Additionally, for 5fold disclinations we uncover a new equilibria structure, torsional wrinkling, with the intriguing ability to focus gradients in filament tilt much like curvaturefocusing for the analogous membrane. [Preview Abstract] 
Monday, March 14, 2016 5:06PM  5:18PM 
C40.00014: Ring Correlations in TwoDimensional (2D) Random Networks Mahdi Sadjadi, M. F. Thorpe Amorphous materials can be characterized by their ring structure. Recently, two experimental groups imaged bilayers of vitreous silica at atomic resolution which provides a direct access to the ring structure of a 2D glass \footnote{Lichtenstein L et al, \textit{Angew. Chem. Int. Ed.} 51 404 (2012) and Huang P Y et al, \textit{Nano Lett.} 12 1081 (2012)}. It has been shown that experimental samples have various ring statistics, obey AboavWeaire law and have a distinct area law \footnote{Kumar A et al, \textit{Journal of Physics: Condensed Matter} 26 39 (2014): 395401.}. In this work, we study correlations between rings as a function of their size and topological separation. We show that correlation is mediumrange and vanishes when the separation is about three rings apart. We also present a generalization of the AboavWeaire law. [Preview Abstract] 
Monday, March 14, 2016 5:18PM  5:30PM 
C40.00015: The Effect of Loops in Connectivity Percolation Varda F. Hagh, M. F. Thorpe We introduce a new method that employs the concepts of redundancy and stress from rigidity theory to study the effect of loops in connectivity percolation. In the rigidity percolation redundant bonds are not necessary to maintain the rigidity of a network. These redundant bonds cause internal stress in some regions and as a result those regions carry finite forces that characterize them as overconstrained. In connectivity percolation the bonds that cause a loop correspond to redundant bonds in rigidity and all the bonds that are part of a loop are equivalent to overconstrained bonds in rigidity. To illustrate this we start with a network in 2D where all the bonds are present and remove the bonds randomly. Then using renormalization groups and numerical simulations we study the behavior of loops near percolation transition in hierarchical networks and lattices. [Preview Abstract] 
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