Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session T14: Focus Session: Extreme Mechanics: Elasticity and Deformation II |
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Sponsoring Units: GSNP Chair: Benny Davidovitch, University of Massachusetts, Amherst Room: D227 |
Wednesday, March 23, 2011 2:30PM - 3:06PM |
T14.00001: Elasto-capillarity: The role of stretching Invited Speaker: Elasto-capillarity, the interaction between elasticity and surface tension or surface energies, has been much studied in recent years. However, to date the focus has been almost exclusively on situations where the bending stiffness of an object resists deformation by the surface tension of a liquid. In this talk I will consider some situations in which it is instead the stretching stiffness of an elastic object that resists its deformation by surface tension. I will focus on explaining recent experiments that demonstrate the wrinkling of floating elastic membranes [J. Huang \emph{et al.}, \emph{Science} \textbf{317}, 650 (2007)] but will also discuss related fundamental problems in wrinkling as well as other situations that involve an interaction between the stretching of an elastic object and capillarity. [Preview Abstract] |
Wednesday, March 23, 2011 3:06PM - 3:18PM |
T14.00002: Building blocks for the shapes of confined elastic sheets Robert Schroll, Eleni Katifori, Benny Davidovitch Several configurations, such as d-cones, minimal ridges, and developable patches, occur regularly in the configuration of elastic sheets. We dub such features ``building blocks.'' Here, we study elastic sheets confined in a manner that prohibits the sheet from taking on a single-buckle shape. We find not only building blocks where stress focuses, reminiscent of d-cones, but also ``diffuse-stress'' regions. The former is characterized by a geometrical constraint (inextensibility) while the latter is governed by a mechanical constraint: the dominance of a single component of the stress tensor. We characterize how boundary conditions and applied tension select which building blocks appear and discuss implications for the curtain problem. [Preview Abstract] |
Wednesday, March 23, 2011 3:18PM - 3:30PM |
T14.00003: Droplet Formation and Scaling in Dense Suspensions Marc Miskin, Heinrich Jaeger A drop detaching from a nozzle is a prototypical example of scaling behavior. For a pure fluid, this scaling is contingent on the fact that the material parameters remain invariant throughout the detachment. However, for a dense suspension, this assumption is invalid. We use high-speed photography to examine the formation of suspension droplets. We find that the minimum neck radius, $R_{m}$, near breakup can be described by a power law $(t_{b}- t)^{2/3}$, with a material independent exponent. By considering how particles deform the surface and appealing to topological constraints, we develop a modified version of the Laplace-Young equation relating the surface pressure to the macroscopic Gaussian curvature. This model, combined with a scaling argument, allows us to collapse all of our data for $R_{m}$ near breakup. These results open a new territory for modeling suspensions by asserting that a major stress resides at the boundary, and that it can be calculated using strictly macroscopic parameters. [Preview Abstract] |
Wednesday, March 23, 2011 3:30PM - 3:42PM |
T14.00004: Surface patterns in thermally responsive elastomeric gels Shawn Chester, Lallit Anand Many stimulus responsive elastomeric gels operate in non-isothermal, chemically saturated environments in a variety of applications. We have recently developed a three dimensional continuum level theory to describe the coupled fluid permeation and large deformation response of thermally responsive elastomeric materials. In this work, we apply our theory and numerical simulation capability to the specific case of surface wrinkles induced via swelling of a thermally responsive gel bonded on top of a compliant impermeable elastic substrate. We show that we can numerically model the swelling behavior and subsequent surface pattern formation. Also, we examine the effect of substrate thickness by varying the ratio of gel to substrate thickness. Further, we show that it is possible to modulate the amplitude of the surface wrinkles by taking advantage of the thermally responsive nature of this class of materials. [Preview Abstract] |
Wednesday, March 23, 2011 3:42PM - 3:54PM |
T14.00005: Morphologies of Equibiaxially Wrinkled Surfaces Derek Breid, Shengqiang Cai, Zhigang Suo, John Hutchinson, Alfred Crosby The morphological characteristics of a wrinkled film are largely determined by the state of stress at the onset of the instability. For surfaces compressed equibiaxially, it is well established that ridge-based structures, including herringbone or labyrinth patterns, provide the lowest energy state for stresses far exceeding critical buckling. For near-critical stresses, the equilibrium morphology is less understood. Using surface-oxidized poly(dimethylsiloxane) as a model wrinkling material, we control the applied stress by swelling the oxide film with a compatible vapor-phase solvent. The extent of swelling is controlled by the vapor pressure of the solvent and the thickness of the oxide layer, and the generated overstress in turn dictates the observed morphology. Analytical and numerical models are used to determine the deformation morphologies that provide the lowest energy state with increasing overstress. Comparison of experimental observations and theoretical predictions provides insight into the importance of substrate curvature in determining final equilibrium morphologies. [Preview Abstract] |
Wednesday, March 23, 2011 3:54PM - 4:06PM |
T14.00006: Revisiting the curvature cancellation in forced thin sheets Jin Wang, Thomas Witten We revisit the numerically observed spontaneous vanishing of mean curvature [1] on a developable cone or ``d-cone'' [2] made by pushing a thin elastic sheet into a circular container. The deflection of the d-cone is the distance by which the sheet is pushed into the container. We investigate the ratio of the two principal curvatures versus sheet thickness $h$ over a wider dynamic range than was used previously, holding the deflection and radius fixed. Instead of tending towards 1 as suggested by previous work, we find that the ratio scales as $h^{1/3}$. Scaling arguments and geometric variants support this $h^{1/3}$ finding. Thus the mean curvature does not vanish for very thin sheets as previously claimed. \\[4pt] [1] T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006). \newline [2] E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999). [Preview Abstract] |
Wednesday, March 23, 2011 4:06PM - 4:18PM |
T14.00007: Mechanics of Geometrically-Tuned pH-Responsive Polymers Lifeng Wang, Lin Han, Khek-Khiang Chia, Robert Cohen, Michael Rubner, Mary Boyce, Christine Ortiz Stimuli-responsive polymer materials have been extensively explored over the past two decades because of their promising applications. We consider the mechanics of mechanomutable polyelectrolyte multilayers (PEMs), which undergo reversible pH-responsive transition from a condensed, ionically crosslinked state (small pH) to a hydrated, ionized state (large pH). Instrumented indentation and micro-structurally-based finite element analysis are conducted on the PEM thin films and PEM tube forests to determine the effective elastic properties and further the mechanomutability as a result of the coupling between inherent responsive material properties and geometry. We demonstrate that geometry can be used to introduce and tailor different deformation mechanisms as a means to tune mechanomutabilibility of stiffness and dissipation in addition to the constitutive material properties. The rate-dependent stimulus-responsive mechanomutability can be finely controlled within a wide range from $\sim $ 2 -- 100 times by tailoring the tube geometrical factors at different indentation rates. These studies provide fundamental understanding and mechanics of indentation of PEM thin films and tube forests and show the tremendous potential for dynamically tuning surface and bulk properties of novel complex structured materials. [Preview Abstract] |
Wednesday, March 23, 2011 4:18PM - 4:30PM |
T14.00008: Stretch-induced compressive stresses and wrinkling in hyperelastic thin sheets Rui Huang, Vishal Nayyar, K. Ravichandar Wrinkles are commonly observed in stretched thin sheets. This paper presents a study on stretch-induced wrinkling of hyperelastic thin sheets using the finite element method. The model problem is set up for uniaxial stretching of a rectangular sheet with two clamped ends and two free edges. A two-dimensional stress analysis is performed first under the plane-stress condition to determine stretch-induced stress distributions in the elastic sheets, assuming no wrinkles. As a prerequisite for wrinkling, the development of compressive stresses in the transverse direction is found to depend on the length-to-width aspect ratio of the sheet and the applied stretch. A phase diagram is constructed with a set of different distribution patterns of the compressive stress spanning a wide range of aspect ratios and up to moderately large tensile strain ($\sim $150{\%}). Next, an eigenvalue analysis is performed to find the potential buckling modes of the elastic sheet under the prescribed boundary conditions. Finally, a nonlinear post-buckling analysis is performed to show evolution of the stretch-induced wrinkles. In addition to the aspect ratio and the applied stretch, it is found that the critical condition for wrinkling and the post-buckling behavior both depend sensitively on the sheet thickness. [Preview Abstract] |
Wednesday, March 23, 2011 4:30PM - 4:42PM |
T14.00009: Elastic Instabilities of Nematic Liquid Crystals in Spherical Geometries Vinzenz Koning, Teresa Lopez-Leon, K.B.S. Devaiah, Alberto Fernandez-Nieves, Vincenzo Vitelli We investigate elastic instabilities of nematic liquid crystals confined in spherical shells characterized by extreme thickness inhomogeneity. For shells with a uniform thickness there exists an equilibrium defects structure containing two pairs of boojums at the north and south poles. By minimizing the elastic free energy (subject to tangential boundary conditions on both bounding surfaces), we determine the locations of the defects as a function of thickness inhomogeneity. We find that the defects make an abrupt confinement transition to the thinnest hemisphere from the initial antipodal arrangement, when the thickness inhomogeneity exceeds a critical value. Our results agree well with recent experimental studies on nematic double emulsions and suggest design criteria to engineer micron scaled particles with directional binding capabilities. [Preview Abstract] |
Wednesday, March 23, 2011 4:42PM - 4:54PM |
T14.00010: Near critical phenomena in amorphous smart materials Eduard Oberaigner, Michael Fischlschweiger The importance of smart materials e.g. shape memory alloys (SMAs) for technological applications has been growing during the last 20 years. Especially modeling SMAs behavior has become of high interest in materials science for the prediction of macroscopic effects like pseudoelasticity. The key for their behavior is a displacive solid - solid phase transformation, called martensitic phase transformation. However, such a critical phenomenon requires investigations for deep relations between physical quantities nearby the region of phase transformation. The present study is focusing on a statistical mechanics approach for the description of relations between heat capacity, pseudoelasticity, volume fraction compressibility, alternatively fraction expansion coefficient, and a compressibility tensor, leading to the compliance tensor in the case of elasticity. Also a heat expansion tensor along the line of magnetic phase transitions and transformations has been formulated for shape memory alloys. The work discusses martensitic variants (which occur due to a subgroup relation between the austenitic and martensitic phase) and their asymmetry, which influences the above mentioned quantities as well and gives ideas and suggestions for model improvements. [Preview Abstract] |
Wednesday, March 23, 2011 4:54PM - 5:06PM |
T14.00011: The role of membrane viscosity in the relaxation dynamics of fluid membranes Marino Arroyo, Luca Heltai, Antonio DeSimone Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles driven by curvature elasticity. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. [Preview Abstract] |
Wednesday, March 23, 2011 5:06PM - 5:18PM |
T14.00012: The star shaped pattern on broken thin sheets Nicolas Vandenberghe, Romain Vermorel, Emmanuel Villermaux We study transverse impacts of rigid objects on a thin elastic sheet made of acrylic. After impact, a transverse wave propagates on the sheet and orthoradial stresses lead to the formation of radial cracks. The result of this fragmentation process is the star shaped pattern frequently observed on broken windows. We investigate the variation of the pattern and in particular the number of radial cracks with impact speed and material properties. The formation of rayed craters by meteorite impacts will be briefly discussed. [Preview Abstract] |
Wednesday, March 23, 2011 5:18PM - 5:30PM |
T14.00013: How to make sticky tapes stickier Laurent Ponson, Shuman Xia, Guruswami Ravichandran, Kaushik Bhattacharya Thin film adhesives have become increasingly important in various applications such as packaging and coating, and we benefit daily of their adhesion properties by using various kinds of tapes. Despite the apparent simplicity of these systems, a certain number of questions remain open. In particular, important efforts have been deployed recently to understand the effect of the complex tridimensional and highly heterogeneous structure at the interface of some adhesives, such as the one encountered in nature like the geckos toes. Although inspired by these natural adhesives, we studied a much simpler system, and however largely unexplored: a thin film with spatially varying adhesion energy and elastic properties. We will show how these heterogeneities introduced at the microscale can generate quite unexpected macroscopic behaviors, and that one can this way design stronger adhesives with new properties. Beyond their practical interests, these systems involve long range elastic interactions and heterogeneities resulting in a rich and complex physics that will be illustrated through experimental examples and their theoretical interpretation. [Preview Abstract] |
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