Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session B48: Extreme Mechanical Instabilities, Defects, and Large Deformations I |
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Sponsoring Units: GSNP GSOFT Chair: Efi Efrati, Weizmann Institute of Science Room: LACC 510 |
Monday, March 5, 2018 11:15AM - 11:27AM |
B48.00001: Abstract Withdrawn A force free elastic filament living on a flat surface remains straight as this configuration minimises bending energy. This straight line is a geodesic for the simple planar metric. We ask if a filament minimises bending energy on other, more general surfaces by following a geodesic. We probe this question using both experiments and theoretical analysis. For special classes of surfaces such as developable surfaces, hyperboloids and spheres we show that geodesics are the energy minimised states. Using soap films as a venue to explore filament behaviour on spherical and hyperbolic surfaces, we examine different configurations of a thin elastic filament. For a spherical bubble the filament shape is determined by the ratio of the length L of the filament to sphere radius R and elasto-gravitational bendability ε_{g}, a non-dimensional number quantifying the relative importance of bending energy to gravitational potential energy. In the regime where gravity can be neglected, we find the filament lies along geodesics in these simple geometries. Transitions to configurations other than geodesics occur when the gravitational energy becomes significant. |
Monday, March 5, 2018 11:27AM - 11:39AM |
B48.00002: A chain falling onto a table, revisited James Hanna, Nicholas Corbin, Wesley Royston, Harmeet Singh, Rick Warner We confirm and explore a counterintuitive effect in which an anomalous extra acceleration is induced during impact of a ball-and-link chain with a surface, such that the chain’s trailing end descends faster than that of a chain in free fall. The extra distance traveled by the impacting chain exhibits a complicated non-monotonic dependence on the orientation of the impact surface, reflecting the presence of more than one mechanism. We employ high-speed imaging and particle tracking to examine this process in detail, compare with theoretical predictions, and comment on the roles of discreteness and compressibility of the chain. |
Monday, March 5, 2018 11:39AM - 11:51AM |
B48.00003: Material Symmetry and Conservation Laws Harmeet Singh, James Hanna The balance of material momentum, also known as impulse or pseudomomentum, is an important concept in continuum mechanics whose significance and utility is not always apparent. For certain simple systems, this balance can also be derived as the projection of the linear momentum balance onto the material manifold. We will discuss this balance law and its association with the material symmetry of purely mechanical systems governed by an action. We will explore the implications of this concept in various areas, including the classification of planar rods, solution of partial constraint problems, and derivation of conserved quantities in ideal fluids. |
Monday, March 5, 2018 11:51AM - 12:03PM |
B48.00004: The Role of Weak Forces in the Self-Similar Buckling of Non-Euclidean Elastic Sheets Kenneth Yamamoto, Shankar Venkataramani, Toby Shearman The mechanics of thin elastic sheets can exhibit extreme properties, from crumpled paper to lettuce leaves. The former are quite rigid; whereas the latter are floppy. In fact, we argue that non-Euclidean elastic sheets (like lettuce) are easily manipulated by weak forces, which play a role in their intricate wrinkling shapes, e.g, along edges of torn plastic sheets and growing leaves. I will discuss a quantitative measure for the “floppiness” of non-Euclidean sheets. Our investigations suggest that these complex morphologies result from the selection of potentially non-smooth configurations with vanishing in-plane strain (i.e., no stretching) that contain defects influenced by weak forces, i.e., effects other than stretching or bending. |
Monday, March 5, 2018 12:03PM - 12:15PM |
B48.00005: Elastic instabilities in floating shells Eleni Katifori, Desislava Todorova, Octavio Albarran, Lucas Goehring Pattern formation in thin elastic shells has attracted increasing interest in both fundamental studies and practical applications. Examples include biological systems and engineering applications, such as the fabrication of flexible microelectronics. In this talk we explore the mechanical instabilities of an intrinsically curved thin shell deposited on a liquid surface. Here, the pattern formation is not a direct result of externally imposed strain, but is due to the geometric incompatibility between a curved, stiff membrane and an (initially flat) liquid substrate. We observe several types of instabilities, including a wrinkle-to-fold transition from periodic sinusoidal solutions to morphologies that combine sinusoidal wrinkles and folds; a transition from dimples (geometric inversions) to periodic sinusoidal solutions; and a transition from flat bands with zero Gaussian curvature, to dimpled periodic patterns. We investigate how the global geometry of the curved shells and their elastic properties control these transitions. Further, we discuss various new strategies for creating and controlling patterns in thin elastic shells with natural curvature. |
Monday, March 5, 2018 12:15PM - 12:27PM |
B48.00006: Actuating shape change in hydrogels via "Extreme Thermodynamics" Alberto Fernandez-Nieves, Ya-Wen Chang, Michael Dimitriyev, Anton Souslov, Svetoslav Nikolov, Alexander Alexeev, Paul Goldbart “Extreme Mechanics” often refers to exploiting mechanical instabilities to achieve large shape deformations. An example is provided by the swelling of patterned hydrogels. Here, we consider an alternative mechanism in which a thermodynamic instability or phase transition plays the operative role, actuating similarly large shape changes in an unpatterned hydrogel. This example of “Extreme Thermodynamics” consists of rapidly heating a swollen hydrogel torus through a first-order phase transition to its de-swollen phase. The resulting phase coexistence is characterized by large internal stresses that deform the gel and induce buckling. We will present both our experimental results and a theory qualitatively accounting for our observations. |
Monday, March 5, 2018 12:27PM - 12:39PM |
B48.00007: Patterning origami in nematic elastomer sheets Paul Plucinsky, Benjamin Kowalski, Timothy White, Kaushik Bhattacharya Nematic elastomers dramatically change their shape in response to actuation by light or heat. In this work, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of nonisometric origami building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that: 1) the nonisometric origami building blocks actuate in the predicted manner, 2) the integration of multiple building blocks leads to complex multistable, yet predictable, shapes, 3) we can bias the actuation experimentally to obtain a desired complex shape amongst the multi-stable shapes. We then show that this experimentally realized functionality enables a rich possible design landscape for actuation using nematic elastomers. We highlight this landscape through theoretical examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which we hope will provide a template for the application of nematic elastomers to emerging technologies. |
Monday, March 5, 2018 12:39PM - 12:51PM |
B48.00008: Nascent deformations of slender elastic solids under applied tension and twist Arshad Kudrolli, Andreea Panaitescu We discuss experiments on the deformations of slender elastic solids held under tension at two ends and then twisted through a prescribed angle. While a rich phase set of buckled structures are observed in ribbons for large enough twist and tension [1,2], here we focus on the the regime before the onset of buckling instabilities. We measure the shape and deformation field observed as a function of applied tension and twist to understand the development of stress in the solid as a function of geometric aspect ratios. Thus, the competition of geometry and elasticity on the evolving structure is examined as a function of distance from the boundary. The shapes obtained will be discussed in terms of the strain relaxed shapes possible in the system. |
Monday, March 5, 2018 12:51PM - 1:03PM |
B48.00009: Thermalized Euler buckling in clamped ribbons with variable aspect ratio. Sourav Bhabesh, David Yllanes, Mark Bowick Micro structures such as cantilevers made by cutting graphene sheets have recently been studied experimentally in great detail with application in NEMS and MEMS [1]. To better design such mechanical resonators one needs to understand the dependence of thermal buckling on the aspect ratio of the mechanical resonator. It is well known that thermal fluctuations renormalize the bending rigidity of elastic membranes, leading to power-law stiffening as a function of system size. We explore ribbons clamped at both ends via Molecular Dynamics simulations [2]. We find that by changing the aspect ratio at a fixed temperature one can tune the onset of buckling in these ribbons. Ribbons with large aspect ratio feel stronger effects of clamping and are flat compared to low aspect ratio ribbons. We also study the compressive forces required to buckle ribbons of higher aspect ratio. |
Monday, March 5, 2018 1:03PM - 1:15PM |
B48.00010: Brittle Hydraulic Fracture In Transparent Heterogeneous Hydrogel William Steinhardt, Shmuel Rubinstein Hydraulic fractures occur miles underground, below complex, layered, heterogeneous rocks, making direct measurements of their dynamics or structure extremely difficult. As such, these fractures are typically studied at the surface within blocks of glass, PMMA, or rocks that are hydraulically broken with air or fluid. We have developed a system to study hydraulic fractures within hydrogels, where we can take advantage of their highly tunable rheology, optical transparency, and 2-3 orders of magnitude lower fracture speeds and breakdown pressures compared to PMMA. Using a combination of fast camera photography and laser sheet microscopy, we can study the morphology and dynamics of hydraulic fractures at extremely high spatiotemporal fidelity. Furthermore, the hydrogels can be polymerized with transparent mechanical heterogeneities, whose distribution can be characterized through comparable experiments with silica beads. This allows the study of the effect of increasingly dense mechanical heterogeneity on fracture properties, where we observe the emergence of different fracture morphologies. |
Monday, March 5, 2018 1:15PM - 1:27PM |
B48.00011: Universal scaling of polygonal crack patterns in dried particulate suspensions Xiaolei Ma, Justin Burton, Janna Lowensohn Polygonal crack patterns exist in nature over a surprisingly wide array of length scales. Although many factors are known to influence the crack pattern, one well-known result is that the characteristic area of the polygons increases with material thickness. We have quantified this dependence in drying particulate suspensions of cornstarch and CaCO_{3} particles. By varying the thickness, boundary adhesion, packing fraction, and suspending liquid, we provide a universal picture of how polygonal crack patterns are formed. We find that all polygonal crack patterns follow the same power law dependence, A ∝ h^{4/3}, where A is the average area of a polygon and h is the thickness. This power law is due to a simple energy balance between stress and surface energy. In both cornstarch and CaCO_{3}, large polygons form during the initial drying stage, with prefactors which depend on the modulus of the film and the adhesion to the surface. In cornstarch, well-known columnar polygons form at a later stage during the drying process due to a deswelling of the hygroscopic particles. In this regime, the effective material thickness is determined by the diffusion of solvent from the material, leading to a boundary between "wet" and "dry" particles. |
Monday, March 5, 2018 1:27PM - 1:39PM |
B48.00012: Influence of liquid substrates on the mechanics of single-layer graphene Hervé Elettro, Francisco Melo Emerging 2D materials are excellent candidates for next generation technologies such as supercapacitors, filtration membranes and flexible solar cells. In particular, the price of production of high quality graphene, a 2D carbon honeycomb lattice, plummeted over the past decade. Only an atom thin, graphene does not obey the laws of continuum mechanics. A striking example is that electron-electron repulsion pilots the bending stiffness at zero temperature, not the elasticity of the atomic bonds. |
Monday, March 5, 2018 1:39PM - 1:51PM |
B48.00013: Quantum and Classical Ripples in Graphene Juraj Hasik, Roman Martonak, Erio Tosatti Flexural fluctuations and thermal ripples of suspended graphene are known to be gigantic at room temperature, but their quantum counterpart at ultralow temperatures, addressed so far mostly by asymptotic RG techniques, are still in need of a realistic and quantitative description and comparison on the same grounds. Here we present fully atomistic |
Monday, March 5, 2018 1:51PM - 2:03PM |
B48.00014: Poisson’s Ratio of Thermalized Sheets Mohamed El Hedi Bahri, Andrej Kosmrlj The technological revolution of nanostructures has revived the interest in mechanics of atomically thin sheets. In 1980s it was already demonstrated that for freely suspended sheets thermal fluctuations become important beyond the characteristic thermal lengthscale L_th, which is only a few nanometers for graphene at room temperature. It was found that in sheets larger than L_th, elastic constants become scale dependent with universal power law exponents. In many applications, it is important to understand how sheets respond to external forces. In this talk we will focus on the response of sheets to uniaxial tension and in particular to the Poisson’s ratio defined as the negative ratio between the lateral expansion and the expansion in direction of applied load. We employ renormalization group procedure to study the response of sheets in a broad range of applied tensions. For sheets that are much larger than L_th we observe three different regimes. In the linear regime, a universal negative Poisson’s ratio -1/3 is observed, while the intrinsic material constant is recovered for large loads. We find also an interesting intermediate regime, where sheets expand nonlinearly with the universal exponent of ~0.7, which is reminiscent of the critical phenomena in ferromagnetism. |
Monday, March 5, 2018 2:03PM - 2:15PM |
B48.00015: How the Hopper Pops: Unraveling Visco-elastic Instabilities Through a Metric Description |
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