Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session W14: Focus Session: Extreme Mechanics: Elasticity and Deformation III |
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Sponsoring Units: GSNP Chair: Pedro Reis, Massachusetts Institute of Technology Room: D227 |
Thursday, March 24, 2011 11:15AM - 11:27AM |
W14.00001: A general theory of mechanical instabilities in soft solids Evan Hohlfeld, L. Mahadevan Some instabilities in soft solids, e.g. buckling and wrinkling, can be detected in linearized analysis. Surprisingly, linearly stable configurations can still have nonlinear instabilities with strictly zero energy barrier. Two examples are cavitation (formation of voids) and sulcification (formation of sharply creased free surface folds), wherein singularities nucleate and grow when a critical strain is achieved. Here we present the first general theory of stability in nonlinearly elastic materials. The theory predicts when singularities spontaneously form, irrespective of linearized analysis, and how these can be controlled with geometry. Such ``hidden'' instabilities arise from the scale-free geometric and constitutive nonlinearities common in soft materials, and can be understood as scale symmetry breaking processes in simple cases. More deeply, even buckling and wrinkling can be traced back to scale-free linear instabilities (loss of ellipticity at an interface) as was first explained by M. A. Biot. We illustrate the theory with simulations and experiments on sulcification. Time allowing we will also discuss fracture and delamination. [Preview Abstract] |
Thursday, March 24, 2011 11:27AM - 11:39AM |
W14.00002: Elastocapillary imbibition Camille Duprat, Jeffrey Aristoff, Howard Stone The deformation of elastic structures under capillary forces (elastocapillarity), and their interaction with fluid flow (elastohyrodynamics), are relevant to many biological, geophysical and engineering processes. Here, we present the dynamics of surface-tension-driven flow into a gap between flexible boundaries (i.e. elastocapillary imbibition). We examine two model systems of elastocapillary imbibition, with and without gravitational effects, using a combination of experiment, theory, and numerical simulation. We identify the characteristic length and time scales, and demonstrate how the prescence of flexible boundaries leads to a departure from classical imbibition. The time to reach equilibrium (if one exists) is determined, and a criterion for the coalescence of the boundaries is established. Good agreement between experiment and theory is obtained. [Preview Abstract] |
Thursday, March 24, 2011 11:39AM - 11:51AM |
W14.00003: Buckling of swelling gels under constraints Howon Lee, Jiaping Zhang, Yonghao An, Hanqing Jiang, Nicholas Fang Buckling is a traditional topic in mechanics and has been thought to be well studied for the last hundred years. Recently, buckling has drawn new attention in a different perspective; a novel scheme for pattern transformation. Here we present an experimental study on buckling using swelling of gels under constraints. Under critical conditions combined with proper mechanical constraints, non-homogenous stress develops as gel swells, which gives rise to buckling instability. We developed a fabrication technique to make a 3D cylinder-shaped microgel, the bottom end of which is tightly fixed on a rigid substrate to impose constraints. Equilibrium swelling study of such gel structure allowed us to determine a critical geometrical condition for buckling. Furthermore, exploiting slow gel swelling process, we recorded time evolution of buckling as gel swells to study post-buckling morphologies. Numerical simulation also showed close relationship between geometric parameters and resulting buckling pattern. We believe our study on buckling of swelling gels will not only help us better understand the mechanics of soft materials, but it will also contribute to increasing the breadth of possible application of soft materials in many emerging fields such as photonic crystals. [Preview Abstract] |
Thursday, March 24, 2011 11:51AM - 12:03PM |
W14.00004: Optimal control of growing sheets Gareth Jones, L. Mahadevan There has been much recent interest in plates and sheets that have the ability to actively swell, grow and bend. In this presentation an inhomogeneously growing plate is modeled by prescribing the in-plane growth strain and the active change-of-curvature function. The plate will then change shape to accommodate the induced strains. For applications of this phenomenon, an important problem is how best to choose these functions in order for the plate to deform to a given target shape. In seeking an answer to this question, we have developed a computational approach, where the growth strains will be found as solutions to a numerical optimization procedure. Example results will be presented which will provide some insight into the mechanical behavior of growing thin structures. [Preview Abstract] |
Thursday, March 24, 2011 12:03PM - 12:15PM |
W14.00005: Decoupling thermal, chemical, and mechanical strain components in thin films Meredith Silberstein, Ethan Crumlin, Yang Shao-Horn, Mary Boyce Many electrochemical systems have performance which is affected by internal strains due to thermal and/or chemical stimuli. The bi-material curvature method is a means to quantify these thermal and chemical strains and their coupling with mechanical stress. In this method, a thin layer of the material of interest is deposited on a substrate of intermediate thickness. The composite assumes a curvature that depends on the mismatch strains between the substrate and film. The Stoney formula provides an explicit expression for the film stress as a function of the elastic substrate properties, film and substrate thickness, and curvature. Here we study two distinct materials systems: Nafion used as the polymer electrolyte in low temperature fuel cells, and epitaxial perovskite thin films used as a catalyst for the oxygen reduction reaction in solid oxide fuel cells. The thermal, chemical, and mechanical strains are quantitatively determined as functions of temperature and atmospheric conditions by monitoring the curvature evolution with changes in these parameters. The extent of coupling of the thermal and chemical strains with mechanical stress is evaluated by conducting the experiment at multiple substrate thicknesses. [Preview Abstract] |
Thursday, March 24, 2011 12:15PM - 12:27PM |
W14.00006: Plane deformations generating a prescribed finite rotation field Gregory Rizza, Janet Blume Compatibility conditions for various strain measures are well known in both small and finite strain kinematics. For many problems, such conditions enable boundary value problems to be formulated using strains, stresses, or a generating potential function, as the fundamental dependent variable(s). These methods are effective, as most strain fields fully determine the generating deformations up to an arbitrary rigid deformation. Our research is concerned with the compatibility issue for the rotation field. Although it is not a direct measure of the distortion in a deformation, the rotation associated with a deformation and its variation from point to point within a body turns out to carry quite a bit of information about the actual deformation. For the case of plane deformation, we have been able to show that any suitably smooth plane proper orthogonal tensor field may serve as a finite rotation tensor for a generating deformation. We have developed several examples demonstrating this relationship between material deformation and rotation fields. Our results demonstrate in the case of plane deformation, any skew-symmetric two-dimensional tensor field can serve as a plane rotation field. The relation between the position-dependence of a rotation field and generating deformation information has implications in both mechanical twinning and shear banding. [Preview Abstract] |
Thursday, March 24, 2011 12:27PM - 12:39PM |
W14.00007: Mechanics of Suture Joints Yaning Li, Juha Song, Christine Ortiz, Mary Boyce Biological sutures are joints which connect two stiff skeletal or skeletal-like components. These joints possess a wavy geometry with a thin organic layer providing adhesion. Examples of biological sutures include mammalian skulls, the pelvic assembly of the armored fish Gasterosteus aculeatus (the three-spined stickleback), and the suture joints in the shell of the red-eared slider turtle. Biological sutures allow for movement and compliance, control stress concentrations, transmit loads, reduce fatigue stress and absorb energy. In this investigation, the mechanics of the role of suture geometry in providing a naturally optimized joint is explored. In particular, analytical and numerical micromechanical models of the suture joint are constructed. The anisotropic mechanical stiffness and strength are studied as a function of suture wavelength, amplitude and the material properties of the skeletal and organic components, revealing key insights into the optimized nature of these ubiquitous natural joints. [Preview Abstract] |
Thursday, March 24, 2011 12:39PM - 12:51PM |
W14.00008: Mechanical and thermal stability of adhesive membranes with nonzero bending rigidity Tuomas Tallinen, Jan Astrom, Pekka Kekalainen, Jussi Timonen Membranes at a microscopic scale are affected by thermal fluctuations and self-adhesion due to Van der Waals forces. Methods to prepare membranes of even molecular scale, e.g. graphene, have been recently developed, and the question of their mechanical and thermal stability is of crucial importance. To this end we modeled microscopic membranes with a short-range attractive interaction and applied Langevin dynamics. Their behavior was also analyzed under external loading. Even though these membranes folded during isotropic compression as a result of energy minimization, the process at high confinement did not differ much from crumpling of macroscopic thin sheets. The main difference appeared when the external load was released. In such cases, for membranes of sufficiently large size $L$, folded or scrolled conformations emerged. At high enough temperature $T$ entropic effects made such conformations unfavorable, however. Possible conformations of free-standing membranes (``phase diagrams'') were determined in the $TL$-plane. [Preview Abstract] |
Thursday, March 24, 2011 12:51PM - 1:03PM |
W14.00009: Universal Shapes formed by Interacting Cracks Melissa Fender, Frederic Lechenault, Karen Daniels Brittle failure through multiple cracks occurs in a wide variety of contexts, from microscopic failures in dental enamel and cleaved silicon to geological faults and planetary ice crusts. In each of these situations, with complicated curvature and stress geometries, pairwise interactions between approaching cracks nonetheless produce characteristically curved fracture paths known in the geologic literature as en passant cracks. While the fragmentation of solids via many interacting cracks has seen wide investigation, less attention has been paid to the details of individual crack-crack interactions. We investigate the origins of this widely observed crack pattern using a rectangular elastic plate which is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until the pass each other, after which they curve and release a lenticular fragment. We find that, for materials with diverse mechanical properties, the shape of this fragment has an aspect ratio of 2:1, with the length scale set by the initial cracks offset $s$ and the time scale set by the ratio of $s$ to the pulling velocity. The cracks have a universal square root shape, which we understand by using a simple geometric model and the crack-crack interaction. [Preview Abstract] |
Thursday, March 24, 2011 1:03PM - 1:15PM |
W14.00010: Pericyte Actomyosin-Mediated Contraction at the Cell-Material Interface can Modulate the Microvascular Niche Adam Zeiger, Maciej Kotecki, John Maloney, Ira Herman, Krystyn Van Vliet Here we employ the experimental finding that pericytes can wrinkle a freestanding, underlying membrane via actin-mediated contraction. Pericytes were cultured on deformable silicone substrata. Local stiffness of subcellular domains was investigated by using AFM-enabled nanoindentation. Substratum contraction was quantified by normalized change in wrinkle contour lengths, and a model was used to relate local strain energies to pericyte contractile forces. The nature of pericyte-generated wrinkling and contractile protein-generated force transduction was further explored by the addition of pharmacological cytoskeletal inhibitors that affected contractile forces and the effective elastic moduli of pericyte domains. Actin-mediated forces are sufficient for pericytes to exert an average contraction of 38{\%} on the substrata employed in these in vitro studies. Pericyte generated contractile forces thus serve as a direct mechanical stimulus to adjacent vascular endothelial cells, potentially altering the effective mechanical stiffness of nonlinear-elastic extracellular matrices, to modulate pericyte-endothelial cell interactions that directly influences physiologic angiogenesis. [Preview Abstract] |
Thursday, March 24, 2011 1:15PM - 1:27PM |
W14.00011: Extraordinary Elasticity of the Distorted Kagome Lattice Anton Souslov, Kai Sun, Xiaoming Mao, Tom Lubensky J. C. Maxwell discovered that a system of particles in $d$-dimensions will be marginally rigid, or \emph{isostatic}, if each particle interacts on average with $2 d$ of its neighbors. Isostatic models have been used to describe such diverse soft phenomena as the jamming transition and the elasticity in networks of semi-flexible polymer gels. We develop models based on the isostatic kagome lattice, which has a subextensive number of floppy phonon modes. We show that these can be extended into soft deformations by changing the particle configurations while keeping the bond lengths fixed. Thus, we create families of novel isostatic lattices, which exhibit highly tunable elastic properties as a consequence of isotropic linear elasticity with a zero bulk modulus. They have a negative Poisson ratio, or auxetic (anti-rubber) behavior. Further, we find no bulk soft phonons at large length scales due to conformal symmetry. We discuss the intimate relationship between various symmetries and soft response in these models as well as the relation of these models to other marginally rigid systems. [Preview Abstract] |
Thursday, March 24, 2011 1:27PM - 1:39PM |
W14.00012: Suppression of Viscous Fingers in Miscible Hele-Shaw Flow Radha Ramachandran, Justin Burton, Sidney Nagel The flow of two immiscible fluids between closely-spaced parallel plates can be highly unstable and produce a series of complex fingering patterns when the less viscous injected fluid invades the more viscous one. Air displacing granular material in such a Hele-Shaw geometry shows similar patterns with sharp features consistent with the granular/air surface tension being virtually zero [1]. Here we investigate the flow of two $\textit{miscible}$ fluids in a radial Hele-Shaw cell, with an inner liquid displacing an outer one of higher viscosity. We use two glycerol- water mixtures so that the viscosity can be tuned by varying the glycerol concentration. We vary the plate spacing and flow rate as well as the fluid viscosites. The non-equilibrium interfacial tension between these two miscible fluids is expected to be nearly zero. However, extrapolating to zero surface tension in the linear theory for Hele-Shaw flow does not describe our results. Specifically, flow becomes \textit{stable} even when the inner liquid has a much lower viscosity than the outer one. At higher velocity, it is possible to see small amplitude fingering patterns develop. \\[4pt] [1] X. Cheng, L. Xu, A. Patterson, H. M. Jaeger and S. R. Nagel \textit{Nature Physics} 4, 234 (2008). [Preview Abstract] |
Thursday, March 24, 2011 1:39PM - 1:51PM |
W14.00013: Patterns on thin sheets: buckling, wrinkling, crumpling, folding Benny Davidovitch Recent experiments on thin sheets under various geometric confinements and distributions of exerted forces found a multitude of pattern types. I will discuss the possibility of classifying this diverse phenomenology by generalizing concepts of primary and secondary instabilities, and basic types of symmetry breaking. [Preview Abstract] |
Thursday, March 24, 2011 1:51PM - 2:03PM |
W14.00014: Mechanics and chemical thermodynamics of a temperature-sensitive hydrogel Shengqiang Cai, Zhigang Suo A temperature-sensitive hydrogel is a network of polymers containing monomers, whose interaction with water molecules can be tuned dramatically by changing temperature. In most cases, the swelling ratio of a temperature-sensitive hydrogel changes discontinuously upon heating above or cooling below a critical temperature, which is called volume phase transition. Interestingly, the coexistence of swollen phases and shrunk phases are frequently observed in the experiments for temperature-sensitive hydrogels and additionally, people have also discovered that a uniaxial force can induce phase transition in a temperature-sensitive gel bar .In order to understand these phenomena, we studied the mechanics and chemical thermodynamics of a temperature-sensitive hydrogel bar, by using the free-energy landscape of a bar made from PNIPAM gel. Following Gibbs, we plot the phase diagram of a temperature-sensitive hydrogel bar under uniaxial force. [Preview Abstract] |
Thursday, March 24, 2011 2:03PM - 2:15PM |
W14.00015: Mechanics of Curved Folds Marcelo A. Dias, Christian D. Santangelo Despite an almost two thousand year history, origami, the art of folding paper, remains a challenge both artistically and scientifically. Traditionally, origami is practiced by folding along straight creases. A whole new set of shapes can be explored, however, if, instead of straight creases, one folds along arbitrary curves. We present a mechanical model for curved fold origami in which the energy of a plastically-deformed crease is balanced by the bending energy of developable regions on either side of the crease. Though geometry requires that a sheet buckle when folded along a closed curve, its shape depends on the elasticity of the sheet. [Preview Abstract] |
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