Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session A15: Geometry and Topology in MechanicsFocus

Hide Abstracts 
Sponsoring Units: GSNP Chair: Vincenzo Vitelli, University of Leiden Room: 274 
Monday, March 13, 2017 8:00AM  8:36AM 
A15.00001: Topological sound in activeliquid metamaterials Invited Speaker: Anton Souslov Active liquids can flow spontaneously even in the absence of an external drive. Recently, such liquids have been experimentally realized using molecular, colloidal, or macroscopic selfpropelled constituents. Using active liquids as a building material, we lay out design principles for artificial structures termed topological active metamaterials. Such metamaterials break timereversal symmetry and can be designed using periodic lattices composed of annular channels filled with a spontaneously flowing active liquid. We show that these active metamaterials support topologically protected sound modes that propagate unidirectionally (without backscattering) along either sample edges or domain walls, and despite overdamped particle dynamics. Our work illustrates how paritysymmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials. [Preview Abstract] 
Monday, March 13, 2017 8:36AM  8:48AM 
A15.00002: Pseudomagnetic fields for sound at the nanoscale Christian Brendel, Vittorio Peano, Oskar Painter, Florian Marquardt There is a growing effort in creating chiral transport of sound waves. However, most approaches so far are confined to the macroscopic scale. Here, we propose a new approach suitable to the nanoscale which is based on pseudomagnetic fields. These fields are the analogue for sound of the pseudomagnetic field for electrons in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and wellsuited for a variety of excitation and readout mechanisms, among them optomechanical approaches. [Preview Abstract] 
Monday, March 13, 2017 8:48AM  9:00AM 
A15.00003: Sonic Landaulevel lasing and synthetic gauge fields in mechanical metamaterials Hamed Abbaszadeh, Anoton Souslov, Jayson Paulose, Henning Schomerus, Vincenzo Vitelli Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also use the gauge field to design waveguides in which sound propagates robustly, as a consequence of the change in topological polarization that occurs along a domain wall in the bulk of the metamaterial. By introducing dissipation, we can selectively enhance the domainwallbound topological sound mode, a feature that may be exploited for the design of sound amplification by stimulated emission of radiation  SASERs, the mechanical analogs of lasers. [Preview Abstract] 
Monday, March 13, 2017 9:00AM  9:12AM 
A15.00004: Amorphous Gyroscopic Topological Metamaterials Noah P. Mitchell, Lisa M. Nash, Daniel Hexner, Ari M. Turner, William T. M. Irvine Mechanical topological metamaterials display striking mechanical responses, such as unidirectional surface modes that are impervious to disorder. This behavior arises from the topology of their vibrational spectra. All examples of topological metamaterials to date are finelytuned structures such as crystalline lattices or jammed packings. Here, we present robust recipes for building amorphous topological metamaterials with arbitrary underlying structure and no longrange order. Using interacting gyroscopes as a model system, we demonstrate through experiment, simulation, and theoretical methods that the local geometry and interactions are sufficient to generate topological mobility gaps, allowing for spatiallyresolved, realspace calculations of the Chern number. The robustness of our approach enables the design and selfassembly of noncrystalline materials with protected, unidirectional waveguides on the micro and macro scale. [Preview Abstract] 
Monday, March 13, 2017 9:12AM  9:24AM 
A15.00005: Topological mechanical metamaterials have perfectly directional bulk response D. Zeb Rocklin The elastic response of typical materials to a local load is stress and strain in all directions. Here, we show contrariwise that mechanical frames with balanced numbers of constraints and degrees of freedom (the "Maxwell" condition) can experience stress and/or strain on only one side of a load. Kane and Lubensky showed, in a recent, seminal work, that such systems possess a topologically nontrivial phonon band structure corresponding to the electronic modes of topological insulators. Applying bulkboundary correspondence, they demonstrated a signature physical consequence: the shifting of zero modes resultant from missing bonds from one edge to another. We now show that the same topological invariant governs such a system's bulk response: when bonds are swollen at one point the lattice does not distort evenly around it but instead only on one side dictated by the topological polarization. Similarly, when general forces are applied to a polarized lattice tension is induced in bonds only on one side of the applied force. Hence, topological polarization represents a sharp and robust way to direct force and motion and the response (Green's) function is a fundamental bulk signature of topological polarization. [Preview Abstract] 
Monday, March 13, 2017 9:24AM  9:36AM 
A15.00006: Intrinsically polarized elastic metamaterial Osama Bilal, Roman Suesstrunk, Sebastian Huber, Chiara Daraio Mechanical metamaterials, with periodically repeating basic building blocks in space, expand the envelope of possible properties of matter. Metamaterials harness their effective properties through structure rather than chemical composition. Successful implementations of such materials enabled the realization of ultrastiffutralight materials, negative Poisson ratio materials, and fluidlike solids. In this work, we theoretically analyze and experimentally implement a new design principle for mechanical metamaterials. By combining states of selfstress, topological invariants and additive manufacturing techniques, we realize a new class of threedimensional mechanical metamaterials with polar elasticity. The fabricated specimens show, at two of its opposing faces along the same axis, an asymmetric elastic response (i.e., soft on one face and harder on the other). We design our lattice to retain angular dependency to a perpendicular load, providing a direct experimental observation of nodal Weyl lines. [Preview Abstract] 
Monday, March 13, 2017 9:36AM  9:48AM 
A15.00007: A Design Method for Topologically Insulating Metamaterials Kathryn Matlack, Marc SerraGarcia, Antonio Palermo, Sebastian Huber, Chiara Daraio Topological insulators are a unique class of electronic materials that exhibit protected edge states that are insulating in the bulk, and immune to backscattering and defects. Discrete models, such as massspring systems, provide a means to translate these properties, based on the quantum hall spin effect, to the mechanical domain. This talk will present how to engineer a 2D mechanical metamaterial that supports topologicallyprotected and defectimmune edge states, directly from the massspring model of a topological insulator. The design method uses combinatorial searches plus gradientbased optimizations to determine the configuration of the metamaterialâ€™s building blocks that leads to the global behavior specified by the target massspring model. We use metamaterials with weakly coupled unit cells to isolate the dynamics within our frequency range of interest and to enable a systematic design process. This approach can generally be applied to implement behaviors of a discrete model directly in mechanical, acoustic, or photonic metamaterials within the weakcoupling regime. [Preview Abstract] 
Monday, March 13, 2017 9:48AM  10:00AM 
A15.00008: Topology and symmetries in gyroscopic lattices Lisa M. Nash, Noah P. Mitchell, Ari M. Turner, William T.M. Irvine Mechanical metamaterials  including static frames, coupled pendula, and gyroscopic lattices  can support topologically protected vibrational behavior. In particular, fastspinning gyroscopes pinned on a honeycomb lattice break timereversal symmetry and exhibit topologically protected, oneway edge modes. As in electronic systems, symmetries play an important role in determining the topological properties of the material. Here we present the roles of inversion symmetry, local coordination number, and time reversal symmetry on the band topology of gyroscopic metamaterials with several lattice geometries. [Preview Abstract] 
Monday, March 13, 2017 10:00AM  10:12AM 
A15.00009: Connecting the Chern number to polarization singularities Thomas F\"osel, Vittorio Peano, Florian Marquardt Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an important quantity in this field. Another example of topology, in polarization physics, are polarization singularities, called L lines and C points. By establishing a connection between these two theories, we develop a novel technique to visualize and potentially measure the Chern number: it can be expressed either as the winding of the polarization azimuth along L lines in reciprocal space, or in terms of the handedness and the index of the associated C points. For mechanical systems, it is directly connected to the visible motion patterns. [Preview Abstract] 
Monday, March 13, 2017 10:12AM  10:24AM 
A15.00010: Measurement of Berry's Phase in Microscopic Triaxial Cracking Excitations HAMED O.GHAFFARI, W. ASHLEY GRIFFITH, William Flynn, R.Paul Young Many intractable systems can be reduced to a system of interacting spins. Here, we introduce a system of artificial acoustic spins which are manipulated with ultrasound excitations from microcracking sources with three control parameters in a 3D inhomogeneous confined stress field. We evaluate the evolution of the order parameter visualized as dancing strings constructed from time series collected using multiarray ultrasound sensors. We study the adiabatic cyclic change of the order parameter of the system due to rotation of the pseudostress field. We show that the order parameter acquires a geometric phase factor in addition to the dynamic phase known as Berry's phase. We demonstrated the accumulation of a geometric phase in the ``kchains'' and show that the system can be manipulated geometrically by means of microscopic ultrasound radiation of cracking excitations and observed the realtime accumulated phase. We found that the observed geometric phase is an excellent agreement with Berry's predictions. The introduced acousticspin system opens new horizon to study other aspects of spinsystems including different time characteristics of relaxation phases, topological phases induced by driving and stressquenched induced defects. [Preview Abstract] 
Monday, March 13, 2017 10:24AM  10:36AM 
A15.00011: Discombinations in Nonlinear Elastic Solids Arash Yavari We consider the problem of \emph{discombinations}, that is a combined distribution of fields of dislocations, disclinations, and point defects. Given a discombination, we compute the geometric characteristics of the material manifold (curvature, torsion, nonmetricity), its Cartan's moving frames and structural equations. As an example, we calculate the residual stress field of a cylindricallysymmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid. [Preview Abstract] 
Monday, March 13, 2017 10:36AM  10:48AM 
A15.00012: Scar lines and topological singularities in the orientation field of fibers advected in fluid flows Greg Voth, Bardia Hejazi We examine the orientation fields of slender fibers advected by chaotic and turbulent fluid flows. The fibers show fascinating structures called scar lines, where their orientations rotate by $\pi$ over very short distances. When brownian motion is important, for example in liquid crystals, there are topological singularities, or disclinations in 3D, that are the dominant structures in the orientation field. Consideration of the fluid stretching using CauchyGreen strain tensors in a 2D chaotic flow allows us to identify similar topological singularities in the nonBrownian orientation field as well. We identify the mechanisms for formation of scar lines and topological singularities. The scar lines screen the topological singularities so that the dominant structures in the orientation field become asymptotically independent of the existence of the topological singularities. The rheology of fiber suspensions and the dynamics of turbulent flows are both strongly dependent on the orientation of the recent stretching, allowing these insights into the geometry of fiber orientation to provide insights into the mechanics of the fluid flow. [Preview Abstract] 
Monday, March 13, 2017 10:48AM  11:00AM 
A15.00013: Statistical Mechanics of Square Frames SOURAV BHABESH, DAVID YLLANES, MARK BOWICK, MICHAEL MOSHE Kirigami has opened a new avenue for manipulating mechanical properties of thin sheets to create metamaterials. It is well known that thermal fluctuations renormalize the bending rigidity of elastic membranes, leading to powerlaw stiffening as a function of system size. Kirigami structures, however, are expected to decrease the bending rigidity and it is of particular importance to explore how thermal fluctuations affect the mechanics of sheets with nontrivial topology. We explore sheets with single square holes (frames) via Monte Carlo simulations and a geometric formalism of elasticity theory. We find that thermal fluctuations lead to frame buckling from a flat (low temperature) to a buckled (high temperature) state. Further, we note that allowing frames to buckle requires a trade off between stretching and bending energy. We also find that buckling is accompanied by the formation of E cones and simple cones, giving rise to Gaussian curvature at the corners of the square hole. Buckling is also sensitive to the size of the hole, with larger holes buckling more readily. [Preview Abstract] 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2020 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
1 Research Road, Ridge, NY 119612701
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700