Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session F25: Mechanical Metamaterials II |
Hide Abstracts |
Sponsoring Units: GSNP Chair: Johannes Overvelde, FOM Inst - Amsterdam Room: 402 |
Tuesday, March 3, 2020 8:00AM - 8:12AM |
F25.00001: On the design of multi-stable metastructures with rotational degrees of freedom Yong Zhang, Marcel Tichem, Fred Van Keulen Buckling-induced multi-stable metastructures are rationally designed structures whose unit cells exhibit bi-stable or multi-stable configurations. Apart from achieving transitions between two stable states at the unit cell level, metastructures composed of bi-stable beams are also able to realize rotations due to the spatial arrangement of beams. In this work, the design space of the geometric parameters for metastructures exhibiting both rotational and translational motions is explored on the basis of both theoretical and experimental studies. First, numerical results demonstrate that beam thickness, height and length play key roles in determining the rotational snapping. To quantify the effects of these structural parameters, we analytically model the rotational snapping behavior of a representative element that consists of two beam units. Furthermore, we conduct a comprehensive parametric survey based on the proposed model. This study reveals that the rotational stability is highly dependent on the ratio between beam thickness and height. In order to allow for rotational stable states, this ratio should be constrained within a specific range. Finally, we validate these effects by measuring the mechanical response of 3D-printed specimens with different geometric parameters. |
Tuesday, March 3, 2020 8:12AM - 8:24AM |
F25.00002: Prediction of Elastic Wave Propagation Characteristics of Composites via Strong-Contrast Expansions Jaeuk Kim, Salvatore Torquato The preponderance of previous treatments to predict the effective elastic properties of composites assume the purely static limit. Here we derive exact expressions for effective elastodynamic properties of two-phase composites at intermediate wavelengths by extending the "strong-contrast" expansion approach previously applied to the static problem. The resulting series expansion explicitly incorporates complete microstructural information about the composite via $n$-point correlation functions and is endowed with excellent convergence properties, even for high contrast ratios of phase moduli. The fast convergence of this series enables us to extract an accurate approximation that depends on the microstructure via the two-point correlation function or its Fourier counterpart, which we call the "spectral density." Our formula thus extends previous "mean-field" treatments that typically do not account for nontrivial microstructural information and/or are limited to small phase contrasts. We apply our spectral-density formula to a variety of models of disordered composites and discuss how to engineer composites with prescribed attenuation properties for elastic waves. |
Tuesday, March 3, 2020 8:24AM - 8:36AM |
F25.00003: What is the bending rigidity of a book? Stacked plates as a dissipative structured beam Samuel Poincloux, Tian Chen, Basile Audoly, Pedro Reis Multi-layered structures have long been exploited in engineering to design stiff and lightweight structural elements. For example, sandwich-structured composites involve an interplay between the mechanical properties of the individual layers and the inter-layer interactions through the matrix. In the absence of a matrix, when the layers are free to slide with respect to one another, energy is dissipated by frictional interactions. Here, in the context of designing high-performing metamaterial dampers, we focus on providing a quantitative description of the mechanical response of stacks composed of a large number (n~50) of elastic plates interacting through friction. In essence, we ask: “What is the bending rigidity of a book?” The mechanical response of our stacks is assessed experimentally through precision nonlinear bending tests. Naturally, our findings deviate from the purely linear elastic case, exhibiting surprising stiffening effects and hysteretic behavior. Taking friction as a perturbation, we develop a predictive model involving the coupling between the geometric nonlinearities, elasticity and friction that is in excellent agreement with experiments. |
Tuesday, March 3, 2020 8:36AM - 8:48AM |
F25.00004: The effect of dualities on elastic moduli Michel Fruchart, Vincenzo Vitelli Elasticity describes how a rigid object like a rubber duck goes back to its original form when slightly deformed. Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. For instance, the elasticity of a 2D crystal with triangular symmetry is isotropic, and hence has only two independent elastic moduli (instead of six without any symmetry). This is because the elastic tensor relating stress and deformation transforms as a tensor under spatial transformations. |
Tuesday, March 3, 2020 8:48AM - 9:00AM |
F25.00005: Emergent plasticity and hysteresis in disordered packings of filaments. Nichalas Weiner, Hunter King, Yashraj R Bhosale, Mattia Gazzola A bird's cup-nest can be viewed as a disordered packing of slender grains, defined by average quantities -- coordination number and packing fraction; and dependent on grain properties -- flexibility, friction, and aspect ratio. Experimental data from packings of varying aspect ratio grains, subject to cyclic, quasi-static, oedometric compression reveal two distinctly meta- mechanical responses: plasticity associated with rearrangement without damage; and hysteresis associated with static friction rather than viscoelasticity. These qualitative behaviors appear to be common across systems of round grains to extremely fine fibers. One-to-one numerical simulations allow us to relate otherwise inaccessible micromechanical quantities such as contact distributions to bulk behaviors, confirming underlying assumptions regarding their origin. |
Tuesday, March 3, 2020 9:00AM - 9:12AM |
F25.00006: Viscoelasticity and plasticity in the formation of creases in thin sheets Buwaneth Dharmadasa, Chinthaka H.M.Y. Mallikarachchi, Francisco Lopez Jimenez Origami inspired folding, which enables the transformation of a flat sheet into different geometries, has recently become a topic of interest among the engineering community as it helps solving problems ranging from deployable structures for space engineering to micro scale grippers for bio-medical applications. However, the mechanics of a folded sheet are not only governed by the sheet properties and the folding pattern, but also by the properties of the creases. We study them by performing experiments exploring the influence of different control parameters, such as the applied force and the time the film was pressed. We rationalize the experimental results with numerical simulations: a 1D elastica beam model and a high-fidelity finite element analysis, both accounting for elasto-plastic behavior and non-linear geometry. By considering the curvature localization, we can define a crease length that depends on the properties of the film and the fold control parameters. We found that non-dimensionalized results provide a robust scaling that enables to extend the results to other geometries and material properties. We also explore the effect of viscoelasticity of the sheet material. |
Tuesday, March 3, 2020 9:12AM - 9:24AM |
F25.00007: Viscoelastic Metamaterials David Dykstra, Joris Busink, Aleksi Bossart, Jop van der Laan, Bernard Ennis, Corentin Coulais We show how viscoelasticity can be harnessed to increase functionality in mechanical metamaterials. First, we explore experimentally the mechanical snap-through response of metamaterials that are made of constituents that exhibit large viscoelastic relaxation effects, encountered in the majority of rubbers [1]. Second, we demonstrate that we can rationally design multimode mechanical metamaterials, featuring viscoelastic and elastic elements. By altering the loading rate, we can switch between the two modes of deformation. Our findings bring a novel understanding of metamaterials in the dynamical regime and opens up avenues for the rational design of multifunctional viscoelastic metamaterials. |
Tuesday, March 3, 2020 9:24AM - 9:36AM |
F25.00008: Memory of a mechanical metamaterial hadrien bense, Martin Van Hecke Many disordered systems – granular suspensions, spin-glasses, crumpled paper – present history dependent features. |
Tuesday, March 3, 2020 9:36AM - 9:48AM |
F25.00009: Amplitude-dependent input to reprogram static and dynamic properties of multistable structures Hiromi Yasuda, Lucia Korpas, Jordan R. Raney Phase transformations can be observed from the nanometer scale of crystalline order to macroscale mechanical structures. These transformations are often associated with dramatic reconfigurations and changes to properties. Here, we study a tunable mechanical structure composed of a 1D chain of rotating squares and embedded magnets, with each cell along the chain capable of being in any of three possible stable phases, defined by the angular orientation of the square. We demonstrate the ability to change the static and dynamic responses, particularly linear/nonlinear wave dynamics, by reversibly reconfiguring the structure via controlled use of transition waves. We numerically and experimentally demonstrate the propagation of transition waves in a 1D chain. We then analyze the dynamic properties of the chain, including the opening/closing of a frequency band gap, and the coupling behavior between rotational and translational motion as a function of the phase. We demonstrate that transition waves with opposite rotational directions can be generated, and that a collision between such waves results in the formation of a phase boundary. |
Tuesday, March 3, 2020 9:48AM - 10:00AM |
F25.00010: Porous Inclined Auxetic Structural Material Matheus C Fernandes, Saurabh Mhatre, Olga Mesa, Katia Bertoldi, Martin Bechthold Porous structural materials with well-defined periodicity are ubiquitous not only in nature but also in synthetic structures and devices. These types of materials have been proven to offer various types of auxetic behavior, ranging from negative Poisson's ratio to high energy absorption and excellent acoustic damping. Yet, here we present a novel auxetic behavior harnessed by introducing angled cuts into a periodic porous material. Using this approach, we utilize out-of-plane behavior with the potential to control friction, light emission and reflection, as well as fluid flow properties. Using a combination of physical experiments and non-linear finite element analysis, we study the effects of geometry on creating and propagating this out-of-plane auxetic behavior. |
Tuesday, March 3, 2020 10:00AM - 10:12AM |
F25.00011: Engineering auxetic geometry design for flexible and stretchable devices Yu-Ki Lee, Young-Joo Lee, Young-Chang Joo, In-Suk Choi In this talk, we present how the auxetic design can be used to flexible and stretchable electronic devices. An auxetic structure called ‘fractal cut’, which means that the basic rotating units can be subdivided into a self-similar hierarchy, enables us to develop extremely and omni-directionally deformable batteries. During stretching or crumpling, deformation occurs only at hinges between two adjacent units while the units did not undergo distortion. In addition, a re-entrant auxetic elastomer used for capacitive-type stretchable strain sensor can overcome the theoretical limit of the conventional capacitive-type strain sensor. We believe that our auxetic geometry design can provide a strategy to apply mechanical metamaterials for fabricating flexible and stretchable electronic devices. |
Tuesday, March 3, 2020 10:12AM - 10:24AM |
F25.00012: Auxetic foam revisited: understanding the origin of negative Poisson's ratio using micro-CT and pore structure analysis Lamei Du, Sida Luo, Ye Xu Porous foam with negative Poisson’s ratio, namely auxetic foam, is a typical mechanical metamaterial. One of the commonly used approach in producing auxetic foam is the thermomechanical compression of porous thermoplastic materials such as Polyurethane (PU) foams. While qualitatively it is well understood that the negative Poisson’s ratio arises from the reentrant cell shape, quantitative relation between the auxetic behavior and pore structure is still lacking. Using micro-CT, we systematically quantify the pore structures of a series of auxetic PU foams prepared with various degrees of thermomechanical compression, and correlate with their mechanical behaviors measured from tensile tests. We find that the fraction of bucked ribs of the pore structure is related to the initial value of Poisson’s ratio upon stretching while the extent of buckling is related to the maximum tensile strain for negative Poisson’s ratio. Our findings can shed light in designing mechanical metamaterials with targeted auxetic behaviors. |
Tuesday, March 3, 2020 10:24AM - 10:36AM |
F25.00013: Dynamics and Topology of Non-Hermitian Elastic Lattices with Non-Local Feedback Interactions Matheus Nora Rosa, Massimo Ruzzene We investigate a family of non-Hermitian 1D elastic lattices whereby feedback control is used to establish non-local, non-reciprocal strain based interactions. We demonstrate that wave propagation is largely non-reciprocal for all frequencies within the dispersion bands, manifesting as either gain or loss for opposite propagation directions. The non-reciprocal bands are tunable based on the non-local interactions, which can define multiple frequency bands with opposite non-reciprocal behavior. The large non-reciprocity also manifests in finite lattices whereby all the bulk eigenmodes are localized at a boundary, which is known as the non-Hermitian skin effect. In analogy to recent work in quantum lattices, we show that the winding numbers of the dispersion bands on the complex plane predict the localization edge of the skin modes of finite lattices, which can be interpreted as a bulk-bulk correspondence principle. Finally, we investigate wave propagation in 2D lattices where directional non-reciprocity is demonstrated, and show preliminary results that suggest a 2D manifestation of the non-Hermitian skin effect in the form of corner modes for finite lattices. |
Tuesday, March 3, 2020 10:36AM - 10:48AM |
F25.00014: Non-Commuting Mechanical Metamaterials Amitesh Singh, Matthieu Labousse, Martin Van Hecke Strategies for programmable metamaterial design need to be sensitive to the order of input signals. Here, we introduce a non-commuting mechanical metamaterial that consists of a quasi-1D chain of weakly symmetry-broken beams. We demonstrate, via simulations and experiments, that its response depends on the order of external actuation. Our work opens a new route to mechanical memory and reprogrammable metamaterials. |
Tuesday, March 3, 2020 10:48AM - 11:00AM |
F25.00015: Bounds on resonant bandgap limits in a branched 1D lattice modeled by Bloch’s theorem Mary Bastawrous, Mahmoud I. Hussein Elastic metamaterials exhibit unique properties associated with local resonance band gaps. A 1D lattice unit cell comprising a monatomic chain connected to a branch is examined leading to mathematical relations relating the vibration behavior of the independent branch to the dispersion of the entire unit cell. This perspective is distinct from studying the resonances of the full system and relating them to the local-resonance band gaps. The closed-form relation, based on Bloch’s theorem, determines the dependence of the upper and lower band-gap limits on the resonances and antiresonances of the frequency response of the separate branch. This offers a formal approach for identifying bounds for the location of band-gap edges. Moreover, it demonstrates that local resonance band gaps form as a result of a balance between the inertia and restoring forces of the main chain and the branch effective restoring force. This framework is further employed to study a special case where the branch is constructed out of a finite number of repeating diatomic units where the periodic branch’s Bragg band gaps are exploited. Conditions are derived for a global unit-cell dispersion exhibiting super-wide local resonance band gaps or pass bands, super narrow pass bands, and tailored fano-resonances. |
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