Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session Q14: Focus Session: Extreme Mechanics: Elasticity and Deformation I |
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Sponsoring Units: GSNP Chair: Katia Bertoldi, Harvard University Room: D227 |
Wednesday, March 23, 2011 11:15AM - 11:51AM |
Q14.00001: Geometric Nonlinear Computation of Thin Rods and Shells Invited Speaker: We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. [Preview Abstract] |
Wednesday, March 23, 2011 11:51AM - 12:03PM |
Q14.00002: Wrinkling of an Annulus Kamil Toga, Benoit Roman, Jose Bico, Thomas Russell, Narayanan Menon We report on an experiment in which we study the wrinkling of an annular elastic film subject to different radial tensions at the inner and outer diameter. The annuli were made from polystyrene films of thickness ranging from 62 to 180 nm, and floated on water. They were then transferred onto a Langmuir-Blodgett trough filled with acidic aqueous subphase. The surface tension on the inside of the annulus is held fixed, while the surface tension outside the annulus is continuously varied by compressing an insoluble surfactant. When the differential tension is increased beyond a threshold value, radial wrinkles form in the interior of the annulus and extend outwards. We studied the length of wrinkles formed as a function of the differential tension produced by the surfactant, and for a range of film thickness. [Preview Abstract] |
Wednesday, March 23, 2011 12:03PM - 12:15PM |
Q14.00003: Dancing Discs: Bending and Twisting of Soft Materials by Anisotropic Swelling Douglas Holmes, Matthieu Roch\'e, Tarun Sinha, Howard Stone Soft materials, e.g. biological tissues and gels, undergo morphological changes, motion, and instabilities when subjected to external stimuli. Tissues can exhibit residual internal stresses induced by growth, and generate elastic deformations to move in response to light or touch, curl articular cartilage, aid in seed dispersal, and actuate hygromorphs, such as pine cones. Understanding the dynamics of such osmotically driven movements, in the influence of geometry and boundary conditions, is crucial to the controlled deformation of soft materials. We examine how thin elastic plates undergo rapid bending and buckling instabilities after anisotropic exposure to a favorable solvent that swells the network. An unconstrained beam bends along its length, while a circular disc bends and buckles with multiple curvatures. In the case of a disc, a large-amplitude transverse travelling wave rotates azimuthally around the disc. Theoretical interpretations inspired by the complementary thermal expansion problem of transient shape changes triggered by time-dependent heating are presented and allow collapse of time-dependent data on universal curves. Understanding the dynamics of strain-driven shape changes provides new insight into natural systems and control of advanced functional materials. [Preview Abstract] |
Wednesday, March 23, 2011 12:15PM - 12:27PM |
Q14.00004: Sinusoidal to helical buckling of a thin rod under a cylindrical constraint James Miller, Arnaud Lazarus, Nathan Wicks, Jahir Pabon, Pedro Reis We investigate the buckling and post-buckling behavior of a thin, elastic rod loaded under cylindrical constraint. Our desktop experiments consist of compressing a hyper-elastic rod inside a transparent acrylic pipe with a motorized linear actuator. Under imposed displacement, the initially straight rod first buckles into a sinusoidal mode and eventually undergoes a secondary instability into helical buckling. This buckling and post-buckling behavior is found to be highly dependent on the systems' geometry, namely the rod length and the aspect ratio of the rod to pipe diameter. We quantify the wavelength and pitch of the period patterns through direct digital imaging and record the reaction forces at both end of the pipe. The observed behavior is rationalized through scaling arguments. [Preview Abstract] |
Wednesday, March 23, 2011 12:27PM - 12:39PM |
Q14.00005: Shape evolution of a thin loop sedimenting in a viscous fluid James Hanna, Christian Santangelo We consider the non-local elastic problem of a closed thin filament settling under gravity in a fluid at zero Reynolds number. The filament is modeled as an inextensible chain, with no bending or twist rigidity. Although the equations admit rigid motions of the chain, there are no stable trajectories. We explore whether a stable envelope may exist around a recirculating blob and tail arrangement. [Preview Abstract] |
Wednesday, March 23, 2011 12:39PM - 12:51PM |
Q14.00006: 3D micro-modeling of wrinkling phenomena Damien Eggenspieler, Gozde Ince, Karen Gleason, Mary Boyce Wrinkles, formed by the buckling of stiff layers adhering to soft substrates, are commonplace in nature. From wrinkles on smiling or aging faces to the wrinkled shape of pumpkins or the wrinkled electrospun nano-fibers due to the radial evaporation of the solvent used in the processing of these fibers, wrinkles have been found ranging from the nano- to the macroscopic scales. More recently, studies have shown that this buckling phenomenon can be directed via a selective stiffening of either ones of the layers composing this composite system. We are introducing a 3D numerical model for the buckling of a shell on a soft layer. The selective stiffening of the shell can reproduce the ``stiffness patterning'' obtained experimentally by UV-Ozone treatment of a soft PDMS substrate through a photomask. This model can predict the final shape of the surface of this composite system for periodic photomasks and might be used in the design of specific micro-topographies. [Preview Abstract] |
Wednesday, March 23, 2011 12:51PM - 1:03PM |
Q14.00007: Coiling Spaghetti: Deposition of a Thin Rod onto a Moving Substrate Pedro Reis, Jungseock Joo, Josephine Mannent, Joel Marthelot, Danny Kaufman, Eitan Grinspun We investigate the oscillatory coiling patterns obtained when a thin elastic rod is deposited onto a moving solid boundary (conveyor belt). Through a combination of well controlled desktop experiments and numerics, we explore the phase diagram of this coiling process and identify the underlying physical ingredients. Our novel numerical method implements a discrete notion of bending and twist based on ideas ported from differential geometry, and exhibits excellent performance and robustness. This enables us to carry out predictive direct simulations of the large deformations of the thin elastic rod interacting with the moving substrate, that are in excellent agreement with our experiments. Applications of this coiling process range from the coiling of nanotubes to the laying down of transoceanic cable and pipelines in the ocean bed. [Preview Abstract] |
Wednesday, March 23, 2011 1:03PM - 1:15PM |
Q14.00008: Geometry-ruled deformation of thin elastic shells Arnaud Lazarus, Pedro Miguel Reis We study the mechanical response of thin elastic shells subject to point or plate load and in different mechanical environments (with or without an in-out pressure difference). The geometry and material properties of the ellipsoidal shells used in our experiments can be accurately controlled using digital fabrication techniques. The linear and nonlinear mechanical response of the shells is quantified through load-displacement compression tests and the post-buckling patterns are analyzed using digital imaging. In the linear regime, we explore the geometry-induced rigidity of shells with different shapes. In the nonlinear regime, we focus on the formation of structures with localized curvature, which we denote by s-cones (shell-cones) and examine their mechanical and morphological properties. [Preview Abstract] |
Wednesday, March 23, 2011 1:15PM - 1:27PM |
Q14.00009: The Buckliball: Pressure Induced Pattern Transformation of a Structured Elastic Shell Jongmin Shim, Claude Perdigou, Elizabeth R. Chen, Katia Bertoldi, Pedro Reis We report an experimental and computational study of a patterned elastic shell which, under pressure loading, undergoes a transformation in its structural configuration. The geometry of the ball comprises of an elastomeric spherical shell patterned with a regular array of circular holes. These voids are covered with a thin membrane, thereby making the ball air tight. Upon reduction of the internal pressure, the thin membranes first invert their curvatures inward. Consequently, beyond the critical pressure, the thin ligaments between the holes buckle leading to a cooperative buckling cascade of the skeleton of the ball. During this process, the initially circular holes evolve into an elliptical shape, and eventually become fully closed. This pattern transformation is induced by mechanical instability that opens the possibility for reversible encapsulation, over a wide range of length scales. [Preview Abstract] |
Wednesday, March 23, 2011 1:27PM - 1:39PM |
Q14.00010: Polymer Thin Film Buckling: Wrinkling and Strain Localizations Yuri Ebata, Andrew B. Croll, Alfred J. Crosby Out of plane deformations of thin films are observed in everyday life, e.g. wrinkled aging human skin or folded fabrics. Recently, these deformations are being pursued for fabricating unique patterned surfaces. In this study, the transition from wrinkling, a low-strain buckling behavior, to localized deformations such as fold and delamination, is investigated for polystyrene films with thickness ranging from 5nm to 180nm. The thin films are attached to a uniaxially strained polydimethysiloxane substrate and the strain is released incrementally to apply increasing compressive strain to the attached film. The wavelength and the amplitude of local out-of-plane deformation are measured as global compression is increased to distinguish between wrinkling, folding, and delamination. The transition from wrinkling to strain localizing events is observed by tracking the statistics of amplitude distribution sampled across a large lateral area. A critical strain map is constructed to denote the strain regimes at which wrinkle, fold, and delamination occur. [Preview Abstract] |
Wednesday, March 23, 2011 1:39PM - 1:51PM |
Q14.00011: Statistical Mechanics of Pressurized Shells Jayson Paulose, Gerrit Vliegenthart, Gerhard Gompper, David Nelson It is well known that thermal fluctuations strongly modify the large length scale elastic behavior of flat solid membranes. A thin spherical shell may be considered a solid membrane with a uniform nonzero curvature. This curvature couples the in-plane stretching modes with the out-of-plane undulation modes, giving rise to qualitative differences in the fluctuations of spherical shells compared to flat membranes. In addition, a shell can support a pressure difference between its interior and exterior. We study the statistical mechanics of deformations of a spherical shell using perturbation theory and Monte Carlo simulations, explicitly including the effects of curvature and pressure. Thermal corrections to the predictions of classical shell theory for point indentation and pressure-induced buckling experiments on microscale shells diverge as the ratio of shell radius to thickness tends to infinity. [Preview Abstract] |
Wednesday, March 23, 2011 1:51PM - 2:03PM |
Q14.00012: Complex Morphogenesis from Elastic Instability of Thin Sheets Pascal Damman Thin sheets are mechanically unstable to boundary or substrate-induced compressive loads. Moderate compression results in regular wrinkling while further confinement can lead to crumpling. In this communication, we will first show the emergence of a new morphological instability triggered by a period-doubling bifurcation observed for large compression ratio. A periodic self-organized focalization of the deformation energy is observed provided a symmetry breaking, induced by the elastic foundation, occurs. This effect will be explained by considering geometrical nonlinearities leading to a Euler-Lagrange equation similar to the equation of a parametric resonance in nonlinear oscillator. In the second part, we will show that thin sheets, from suspended graphene to ordinary hanging curtains, under boundary confinement spontaneously generate a universal self-similar cascade of wrinkled patterns. We develop a formalism based on \emph{wrinklons}, a localized transition zone in the merging of two wrinkles, as building-blocks to describe the cascade morphology. These physical models based on elasticity and geometry constitutes a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues. Moreover, it also opens the way to new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography via self-organization. [Preview Abstract] |
Wednesday, March 23, 2011 2:03PM - 2:15PM |
Q14.00013: Stability of a drop-strip system Marco Rivetti, S\'ebastien Neukirch, Arnaud Antkowiak When a flexible material is placed in contact with a liquid-air interface, capillary forces may cause deformations and large displacements in the structure. Such kind of elastocapillary interactions play a crucial role in many technological applications, like deflection of nanotubes carpets or microscale self-assembly. We study the problem of a drop deposited on a thin and narrow strip. Using a simplified 2D model including surface tension interactions, elastic and gravitational energies, we are able to predict the shape of the equilibrium solutions, as well as the appearance of instability in the system. Theoretical predictions are confronted to experiments and a good agreement is obtained. [Preview Abstract] |
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