Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session F48: Mechanical Metamaterials II 
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Sponsoring Units: GSNP GSOFT DBIO DPOLY Chair: Sung Kang, Johns Hopkins Univ Room: LACC 510 
Tuesday, March 6, 2018 11:15AM  11:27AM 
F48.00001: Localizing softness and stress along loops in threedimensional topological metamaterials Anton Souslov , Guido Baardink , Jayson Paulose , Vincenzo Vitelli Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The rigidity of elastic networks is characterized by a topological invariant called the polarization; materials with a uniform polarization display a dramatic range of edge softnesses depending on the orientation of the polarization relative to the terminating surface. However, in all threedimensional mechanical metamaterials proposed to date, topological modes are mixed with bulk soft modes that organize themselves in Weyl loops. Here, we report the design of a 3D topological metamaterial without Weyl lines and with a uniform polarization that leads to an asymmetry between the number of soft modes on opposing surfaces. We use this construction to localize topological soft modes in interior regions via dislocation lines, which are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of selfstress localized along the dislocation to the handedness of the vector triad formed by lattice polarization, Burgers vector, and dislocationline direction. Our findings suggest a novel strategy for programming failure and softness localized along lines in 3D, while avoiding extended soft Weyl modes. 
Tuesday, March 6, 2018 11:27AM  11:39AM 
F48.00002: Amorphous topological insulators constructed from random point sets Noah Mitchell , Lisa Nash , Daniel Hexner , Ari Turner , William Irvine Mechanical lattices have recently been found to exhibit topological structure in their phononic excitations, giving rise to protected unidirectional edge modes. In these cases, however, as well as in other topological metamaterials, the underlying structure was finely tuned, be it through periodicity, quasiperiodicity or isostaticity. Here we show that amorphous Chern insulators can be readily constructed from arbitrary underlying structures, including hyperuniform, jammed, quasicrystalline, and uniformly random point sets. While our findings apply to mechanical and electronic systems alike, we focus on networks of interacting gyroscopes as a model system. Local decorations control the topology of the vibrational spectrum, endowing amorphous structures with protected edge modeswith a chirality of choice. Using a realspace generalization of the Chern number, we investigate the topology of our structures numerically, analytically and experimentally. The robustness of our approach enables the topological design and selfassembly of noncrystalline topological metamaterials on the micro and macro scale. 
Tuesday, March 6, 2018 11:39AM  11:51AM 
F48.00003: Quasistatic, Dynamic and Acoustic Characteristics of Microlattice Metamaterials Chang Quan Lai , Chiara Daraio The quasistatic, dynamic (strain rate~1000/s) and acoustic characteristics of ultrathin and highly porous microlattice metamaterials were investigated. The 3D microlattice architectures were systematically varied in such a way that bending deformation increasingly dominated, so that the Poisson’s ratio of the microlattices transitioned from positive to negative. Under quasistatic testing, this auxetic behaviour was found to improve the energy absorption properties of the microlattices, but played a much lesser role during dynamic compression tests, due to the onset of a secondary buckling mode which nullified the auxetic behaviour. In addition, it was also found that auxetic microlattices were able to significantly reduce the transmission of ultrasonic waves over an extended frequency range when compared to nonauxetic designs. Numerical computations suggest that the bending deformation of the auxetic microlattices introduced different mode shapes for the propagation of elastoacoustic waves. The insights derived from these studies are expected to contribute to the design of microlattice metamaterials with novel properties, such as ultrahigh impact/ acoustic energy absorption efficiency. 
Tuesday, March 6, 2018 11:51AM  12:03PM 
F48.00004: Buckling of TensegrityBased Metamaterials for Dynamic Applications Kirsti Pajunen , Paul Johanns , Chiara Daraio Tensegrity structures are promising building blocks for metamaterials, due to their tolerance to deformation and strength at low density. Recent theoretical studies show that a truncated octahedron tensegrity cell can be used to tessellate multidimensional lattices. These studies suggest that buckling of the struts greatly improves energy absorption, showing potential for impact mitigation and wave management. Here, finite element models and experiments are used to design and characterize tunable, 3D printed unit cells, with equivalent strain energy capacity as a pinjointed, “ideal” tensegrity structure. A drop weight setup is employed to characterize individual cells and 1D lattices under dynamic impacts. Experiments on individual cells show resilience to increasing impact speed and deformation, exhibiting load limitation and high energy absorption. The structure’s effective wave speed ranges from 2540 m/s, an order of magnitude lower than speeds in common foams. We model the dynamics of arrays of these unit cells with discrete numerical simulations. Results show dispersive and asymmetric wave propagation in 1D lattices. This study expands the fundamental understanding of energy absorption in buckling tensegrity metamaterials and provides design tools for applications. 
Tuesday, March 6, 2018 12:03PM  12:15PM 
F48.00005: Realization of a Topological Phase Transition in a Gyroscopic Lattice Noah Mitchell , Lisa Nash , William Irvine Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological phase transition in real time could enable the use of protected waves for information storage and readout. Here we dynamically tune through a topological phase transition by breaking inversion symmetry in a metamaterial composed of interacting gyroscopes. Through the transition, we track the divergence of the edge modes' localization length and the change in Chern number characterizing the topology of the material's band structure. This work provides a new axis with which to tune the response of mechanical topological metamaterials. 
Tuesday, March 6, 2018 12:15PM  12:27PM 
F48.00006: Phononic and Topological Characteristics of Kagome Lattices in The Limit of Continuum Elasticity Jihong AlGhalith , Di Zhou , Kai Sun , Xiaoming Mao , Stefano Gonella Topological floppy edge phonon modes have been discovered in families of Kagome lattices. While rigorous theory has been developed to characterize these modes with ballspring models, little has been studied with continuum elasticity. Here we elucidate the inplane phononic characteristics of 2D regular and topological Kagome structures in the limit of continuum elasticity. The singlepoint connection between triangular plates are hereby replaced by continuous ligaments to mimic structures that can be fabricated via waterjet (or laser) cutting or printing techniques. Through a combination of finite element analyses and experimental wave reconstruction techniques with a 3D Scanning Laser Doppler Vibrometer, we provide a full map of phononic characteristics of these lattices and a mechanistic rationale to interpret the observed wave features. Specifically, we uncover the emergence of floppy edge modes in topological Kagome configurations, which localize the lattice deformation at domain boundaries at low frequency. Our results have implications for the design of acoustic metamaterials for wave control and smart sensing applications, and can provide general guidelines for the dynamic experimental characterization of architected materials. 
Tuesday, March 6, 2018 12:27PM  12:39PM 
F48.00007: Phonon diode and waveguide using topological Kagome lattice Di Zhou , Stefano Gonella , Xiaoming Mao Recent progress in topological mechanics revealed a series of lattice structures that exhibit topologically protected edge floppy modes. These edge modes, while being zero frequency and not propagating in the ideallattice limit, can gain finite frequency and propagate with positive velocity when additional interactions such as nextnearestneighbor bonds are added. In this talk, we present our recent designs of phonon diode and waveguide based on the topological kagome lattice. It is well known that systems with timereversal symmetry in the linear regime exhibit “reciprocity”, namely equal wave transmission rate from point A to B and B to A in space, making phonon diode challenging to realize. Our design takes advantage of topological edge modes and geometric nonlinearity in topological kagome lattices, and demonstrate nonreciprocal transport of sound waves in these lattices. We also show results on phonon waveguiding via these topological modes at interfaces between different types of topological kagome lattice. Our results open the door to realizing novel acoustic metamaterials that exhibit topologically protected nonreciprocal wave transport. 
Tuesday, March 6, 2018 12:39PM  12:51PM 
F48.00008: Geometric Frustration in NonPeriodic Mechanical Metamaterials Erdal Oğuz , Anne Meeussen , Martin Van Hecke , Yair Shokef We study geometric frustration in twodimensional latticebased mechanical metamaterials comprised of anisotropic triangular building blocks T, where each one possesses a nontrivial floppy mode of deformation. When each triangle is oriented randomly neighboring triangles typically cannot deform selfconsistently. On one hand, we analyze the conditions under which a nonperiodic packing of these blocks form compatible, frustrationfree largescale structures, i.e., structures that exhibit a global floppy mode that is compatible with the local deformations of each T. By mapping to an antiferromagnetic Ising model, we find an extensive number of possibilities to construct a compatible structure: Ω_{0}~exp(T). On the other hand, we study incompatible metamaterials in detail and we reveal two distinct types of source of frustration (defects) which either highly localize the frustrated region to a small and finite domain (local defects) or cause delocalized and longranged multistable conflicts (topological defects) whose multistability scales as Ω~exp(T^{1/2}). We further investigate the mechanical consequences of topological defects by identifying the corresponding states of self stresses and relating these to the mechanical response of the metamaterial to an external boundary load. 
Tuesday, March 6, 2018 12:51PM  1:03PM 
F48.00009: Sequential Motion in Mechanical Metamaterials Martin Van Hecke The execution and interpretation of sequences of actions are 
Tuesday, March 6, 2018 1:03PM  1:15PM 
F48.00010: Highfrequency Homogenization of Periodic Elastic Structures Yurii Zubov , Bahram DjafariRouhani , Arkadii Krokhin

Tuesday, March 6, 2018 1:15PM  1:27PM 
F48.00011: Towards PseudoRigid Body Models for Mechanical Metamaterials: Analysis and Design of Tubular Structures Freek Broeren , Volkert van der Wijk , Just Herder Pseudorigid body (PRB) modeling is a wellknown technique from the field of compliant mechanisms. This technique approximates the behavior of compliant mechanisms, which rely on bending elements instead of hinges for their motion, by a classical rigid body mechanism where springs add stiffness to the hinges. This allows us to describe and design compliant mechanisms without having to use elaborate and computationally expensive continuum elastic models. 
Tuesday, March 6, 2018 1:27PM  1:39PM 
F48.00012: Experimental demonstration of elastic WannierStark Ladders and Bloch oscillations in 1D granular crystals Xiaotian Shi , Rajesh Chaunsali , ying wu , Jinkyu Yang We numerically investigate and experimentally demonstrate the existence of elastic WannierStark Ladders (WSLs) and Bloch oscillations (BOs) in a highly tunable 1D granular crystal consisting of cylindrical particles. These WSLs are obtained by introducing a gradient in contact stiffness along the chain so that it resembles the analogous physics of an electron under a uniform external electric field. We perform direct velocity measurements using Laser Doppler Vibrometer to detect the existence of timeresolved BOs, which are spatially localized elastic vibrations in the system. Experimental findings agree well with the numerical simulation results. We also show that this system can be easily tuned further to tailor the spatial and temporal properties of the Bloch oscillations, including localization length, position, and period. We envision that such tunable systems could be potentially used for vibration energy harvesting purposes as they promise a great degree of control over energy localization in a system. 
Tuesday, March 6, 2018 1:39PM  1:51PM 
F48.00013: Asymmetric Wave Propagation in a Modulated Magnetic Lattice Behrooz Yousefzadeh , Yifan Wang , Chiara Daraio We investigate, numerically and analytically, the breakdown of reciprocity in a onedimensional periodic system in which the elastic properties are modulated in time and space. The system is comprised of an array of repelling magnets, with the modulations caused by electromagnets that act on individual magnets in a controlled way. This provides an effective wavelike elastic foundation for the system. We show how directional wave propagation characteristics can be realized and tuned by dynamically modulating the elasticity of the foundation. Our theoretical findings complement the asymmetric wave propagation characteristics that are observed in experiments on this system. 
Tuesday, March 6, 2018 1:51PM  2:03PM 
F48.00014: Porous mechanical metamaterials as aggregates of elastic charges Gabriele Librandi , Michael Moshe , Yoav Lahini , Katia Bertoldi We present a new framework to describe the complex nonlinear response of twodimensional porous mechanical metamaterials. We adopt a geometric approach to elasticity in which pores are represented by elastic charges, and show that this method captures with high level of accuracy both the shape deformation of individual pores as well as collective deformation patterns resulting from interactions between neighboring pores. The response of the metamaterials, both in the linear and nonlinear regime, is obtained by minimizing the nonlinear energy of the system written in terms of interacting elastic charges located at each hole. In particular, we show that quadrupoles and hexadecapoles  the two lowest order multipoles available in elasticity  are capable of matching the experimentally observed evolution in shape and relative orientation of the holes in a variety of periodic porous mechanical metamaterials. Our work demonstrates the ability of elastic charges to capture the physics of highly deformable porous solids and paves the way to the development of new theoretical frameworks for the description and rational design of porous mechanical metamaterials. 
Tuesday, March 6, 2018 2:03PM  2:15PM 
F48.00015: Thermally responsive mechanical metamaterials Damiano Pasini We present mechanical metamaterials capable of shape transforming under a given change in temperature. Compliant unit cells are programmed in period architectures to achieve desired deformation of extension and compression, as well as capable of uniform scaling and shearing. A broad diversity of basic shape transformations is reproduced, each with adjustable level of thermal expansion. Others more complex feature traits of shape reversibility and trajectory tracking that can be functional for deployable satellites, morphing components, and actuation devices. 
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