Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session M17: Mechanical Metamaterials III - Vibrations and NonlinearityLive
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Sponsoring Units: GSNP DSOFT DMP Chair: Sung Kang, Johns Hopkins University |
Wednesday, March 17, 2021 11:30AM - 11:42AM Live |
M17.00001: Multifunctional disordered elastic networks: Designed response of mechanical metamaterials Danilo Liarte, Olaf Stenull, Stephen Thornton, James Patarasp Sethna, Tom Carl Lubensky We design intelligent protocols to tune the elastic response of metamaterials with flexible mechanical properties. We discuss phonon and elastic properties of randomly diluted twisted-Kagome lattices with tunable structures that include auxetics with negative Poisson ratios. We introduce two periodic lattice models that access negative values of the Poisson ratio, one of which accesses the full range from -1 to +1. These models exhibit rich critical phenomena that include rigidity percolation, jamming, shear-jamming, and double-jamming. We also discuss extensions of our models to include anisotropy, spatial dependence and generalizations to three dimensions. |
Wednesday, March 17, 2021 11:42AM - 11:54AM Live |
M17.00002: Programming impulsive deformation with mechanical metamaterials Xudong Liang, Alfred Crosby Impulsive deformation is widely observed in biological systems to generate movement with high acceleration and velocity. By storing elastic energy in a quasi-static loading and releasing it through an impulsive elastic recoil, organisms circumvent the intrinsic trade-off between force and velocity and achieve power amplified motion. However, such asymmetry in strain rate in loading and unloading often results in reduced efficiency in converting elastic energy to kinetic energy for homogeneous materials. Here, we demonstrate that specific internal structural designs can offer the ability to tune quasi-static and high-speed recoil independently to control energy storage and conversion processes. Experimental demonstrations with mechanical metamaterials reveal that certain internal structures optimize energy conversion far beyond unstructured materials under the same conditions. Our results provide the first quantitative model and experimental demonstration for tuning energy conversion processes through internal structures of metamaterials. |
Wednesday, March 17, 2021 11:54AM - 12:06PM Live |
M17.00003: Non-Hermitian topological metamaterials with odd elasticity Junyi Zhang, Di Zhou We establish non-Hermitian topological mechanics in one-dimensional (1D) and 2D lattices consisting of mass points connected by metabeams that lead to odd elasticity. Extended from the “non-Hermitian skin effect” in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of PT symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems. |
Wednesday, March 17, 2021 12:06PM - 12:18PM Live |
M17.00004: Input-independent frequency conversion through transition waves in bistable metabeams Myungwon Hwang, Andres Arrieta In this study, the input-independence characteristics of bistable lattices are extended to architectures exhibiting dynamics in two different size scales: the microscale excitation in the unit cell level and the macroscale response in the structural level. To that end, a metabeam is designed to allow vertical deflections augmenting a one-dimensional spring-joined bistable lattice. The metabeam is harmonically excited in the in-plane direction on the unit cell, and the out-of-plane motion is measured on the macroscopic structure. We construct a nonlinear frequency response diagram showing the contribution of available output frequencies for each input excitation. As long as transition waves propagate within the metastructure, the most dominant output frequency occurs near the natural frequency of the macroscale structure, which is independent of the input frequency. The studied metabeam shows a strong potential for energy transfer between two different size scales and uncorrelated frequencies (both low-to-high and high-to-low). Furthermore, we show that the triggering frequency range and the output frequency can be easily tuned by manipulating the unit cell and macroscopic frame designs, respectively. |
Wednesday, March 17, 2021 12:18PM - 12:30PM Live |
M17.00005: Deformation controlled negative group velocity state in soft composites Nitesh Arora, Yao Qi, Viacheslav Slesarenko, Jian Li, Pavel Galich, Stephan Rudykh Acoustic metamaterials allow us to access unusual properties that can be tailored through their microstructure design. Moreover, soft microstructured materials open the possibility to control and tune these properties through deformation. Here, we reveal the existence of a state in soft composites – layered and 3D fiber composites, characterized by negative group velocity. Interestingly, the transition in the state from positive to negative group velocity is not accompanied by significant geometrical changes and can be reversibly controlled via applied deformation. We further discuss how this unusual state of negative group velocity can be induced and further tuned by variations in the material and geometric parameters. |
Wednesday, March 17, 2021 12:30PM - 12:42PM Live |
M17.00006: Dynamics of rotationally symmetric elastic quasicrystals: numerical and experimental investigations Matheus Nora Rosa, Danilo Beli, Carlos De Marqui, Massimo Ruzzene Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterials structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry buy are unrestricted in rotational symmetries, which lead to largely unexplored mechanical and dynamic properties. In this talk, we investigate a family of continuous elastic quasicrystals with different rotational symmetry orders that are directly enforced through a design procedure in reciprocal space. Numerical results illustrate that higher order symmetries, such as 8, 10 and 14-fold, allow for nearly isotropic wave motion when compared to periodic counterparts, such as 4- and 6-fold symmetric crystals. Spectral contents are investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of band gaps that are also confirmed in frequency response computations. Finally, a series of experiments are conducted on 3D-printed quasicrystal plates to validate the behavior, wave propagation, and band gaps, predicted by the simulations. |
Wednesday, March 17, 2021 12:42PM - 12:54PM Live |
M17.00007: Closed-form existence conditions for band-gap resonances in a 1D linear elastic diatomic lattice with general boundary conditions Mary V. Bastawrous, Mahmoud I. Hussein The elastic band structure of an infinite periodic lattice may feature band gaps where waves experience destructive interferences and do not propagate. However, upon lattice truncation, resonances may appear within the band gaps depending on the nature of the finite boundaries. In this work, closed-form existence conditions are derived for band-gap resonances in discrete diatomic chains with general boundary conditions and arbitrary chain parity. Our approach is based on setting up the model in the form of a perturbed 2-Teoplitz matrix, from which a characteristic equation is obtained in closed form. The approach is general in that it could accommodate different compositions in the unit cell. A selected case of a free-free even chain with an arbitrary additional mass at one end is presented as an example. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions depending on the type of the chain boundaries and parity. This analysis is in principle applicable to the characterization of band-gap resonances in other physical systems beyond elastic chains. |
Wednesday, March 17, 2021 12:54PM - 1:06PM Live |
M17.00008: Topological gaps in 2D locally resonant meta-structures via twisting Yuning Guo, Matheus Rosa, Massimo Ruzzene, Emil Vasile Prodan Quasi-periodic structures are known to support topological gaps forming a fractal spectrum that resemble the Hofstadter butterfly. While most studies dwell on a variety of 1D quasi-periodic structures, research in 2D quasiperiodic domains and their topologies has been scarce. It was recently shown that twisted bilayered lattices are quasi-periodic systems that host higher dimensional topological phases akin to the 4D Quantum Hall effect, which are characterized by a second Chern number. Herein, we present a reconfigurable 2D elastic plate featuring arrays of resonators with tunable on-site frequency. The resonators are arranged according to a fixed square lattice, while their frequencies are modulated by a second twisted lattice. We demonstrate that the procedure opens topological gaps characterized by second Chern numbers, whose higher dimensional topological states are controlled by the phason of the modulation. Experiments are conducted on elastic plates whose tunable resonators allows for agile reconfiguration, and preliminary results are discussed. The existence of non-trivial gaps and localized modes in 2D non-periodic systems open new avenues for wave localization and transport exploring higher dimensional topologies. |
Wednesday, March 17, 2021 1:06PM - 1:18PM Live |
M17.00009: Mechanical vibration and acoustic bandgaps in lattices and triply periodic bi-continuous composites Dong-Wook Lee, Alya Alhammadi, Mahra Almheiri, Fatima Alzaabi, Mohammed Al Teneiji In last decade, cellular materials which are based on triply periodic minimal surfaces have gotten a lot of attention due to their extraordinary properties and performances like low density with high stiffness and strength but their mechanical vibration and acoustic characteristics are not well investigated. In this work, phononic and acoustic bandgaps and phonon dispersion and sound attenuation curves in lattices and triply periodic bi-continuous composites, which are based on the Schwarz’ Primitive and Diamond and Schoen’s I-WP and Gyroid, are found and the widths of these bandgaps are depending on volume fraction and these bandgaps can be controlled by the choice of cell type, size and volume fraction and utilized to control vibration and noise. |
Wednesday, March 17, 2021 1:18PM - 1:30PM Live |
M17.00010: Klein-like tunneling in acoustic metamaterials Lea Sirota Quantum tunneling is the ability of relativistic particles to enter a classically forbidden region, and unimpededly cross an energy barrier of arbitrary height and width. Such tunneling is permitted by the uncertainty principle but becomes paradoxical when particles tunnel with certainty. This is known by the Klein paradox. A similar effect, known by the Klein tunneling of massless Dirac electrons, is associated with graphene. Based on pseudo-spin conservation, the tunneling occurs into a region augmented by lattice potential. |
Wednesday, March 17, 2021 1:30PM - 1:42PM Live |
M17.00011: Topological Mechanics and Nonlinearity Rajesh Chaunsali, Georgios Theocharis Due to the recent discovery of topological insulators in condensed matter physics, a new notion of topology has emerged in association with the intrinsic wave dispersion of a structure. It has led to a plethora of mechanical designs with nontrivial and robust localization of energy -- potentially offering novel applications in energy harvesting, vibration isolation, and structure health monitoring. |
Wednesday, March 17, 2021 1:42PM - 1:54PM Live |
M17.00012: Mechanical Metamaterials with Strain-Rate Adaptive Energy Absorption Sung Kang A metamaterial is a class of materials that provide new properties that are not observed in natural materials or from a bulk material that the “material” is made of. We report strain-rate adaptive mechanical metamaterials with a power-law relation between specific energy absorption and the strain rate based on liquid crystalline elastomer (LCE). Their power-law exponent can be modulated by changing the degree of mesogen alignment. We did experimental measurements and numerical simulations in a large range of strain rates (~10-4/s to ~104/s) to understand the strain rate-dependent energy absorption behaviors. Our metamaterials showed up to ~6 MJ/m3 specific energy absorption at ~700 /s strain rate, which is comparable to an irreversible plastic deformation-based dissipation of metals with up to two orders of magnitudes lower weight. Moreover, we can leverage the viscoelastic behaviors of LCE to significantly improve the specific energy absorption. We envision our study can contribute to lightweight extreme energy-dissipating materials with applications including personnel protection and automotive and aerospace parts. |
Wednesday, March 17, 2021 1:54PM - 2:06PM Live |
M17.00013: Effective wave transmission at interfaces between metamaterials. Kshiteej Deshmukh, Kaushik Dayal Generally, dynamic homogenization techniques are performed for infinite periodic composites and the results are applied to finite domains. This approximation is not always true. At an interface between 2 composites, the displacement and traction continuity need to be satisfied, and evanescent waves play an important role. Without the evanescent waves, the displacement and traction continuity conditions are not satisfied exactly. We consider the problem of transmission and reflection of waves from an interface between a bilayer composite and an homogenous medium. Our aim is to determine the scattering coefficients that satisfy the conservation of energy flux and find the appropriate jump conditions to be satisfied at the interface. We use a rational function approximation of the exact dispersion relation, and then invert it to the space-time domain to obtain a dynamic higher-order pde and interface jump conditions. The scattering coefficients are obtained by imposing the higher order jump conditions at the interface. Numerical calculations are performed to test performance of the higher order jump conditions, by comparing with the results obtained from solving the exact wave equation. We present results for both 1d and 2d cases. |
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