Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session D09: Mechanical Metamaterials |
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Sponsoring Units: DSOFT Chair: Nidhi Pashine, Yale University Room: Room 132 |
Monday, March 6, 2023 3:00PM - 3:12PM |
D09.00001: Design ideal shock-absorbing metamaterials with sequential plastic buckling Wenfeng Liu, Corentin Coulais, Shahram Janbaz An ideal shock-absorbing material should be lightweight, stiff before impact, and maximum dissipative upon impact. To date, shock-absorbing structures are either stiff and strong before impact or energy-absorbing upon impact, and normally can be only used once for the stiffness loose after the first impact. Metamaterials have emerged as a promising avenue for shock absorption since their programmable deformation. Here we strategically use plastic buckling to create metamaterials that can buckle sequentially in an arbitrary large number of steps, behaving as ideal and reusable shock absorbers. We demonstrate this approach in 2D, 2D axisymmetric, and 3D metamaterials and show how they perform as ideal and reusable shock absorbers. Our work expands the metamaterial toolbox of using plasticity and opens the door for their use in automotive and aerospace fields |
Monday, March 6, 2023 3:12PM - 3:24PM |
D09.00002: Robust one-way transport in Maxwell-lattice mechanical metamaterials Wenting Cheng, Kai Sun, Xiaoming Mao In this talk, we introduce a 2D mechanical system based on Maxwell lattices with low-frequency topological edge waves and demonstrate direction-selecting energy transfer through phase control. In particular, these edge states are at acoustic frequency, in direct contrast to existing devices based on quantum Hall and valley Hall physics, where edge/interface modes exist only at high frequencies in the gaps between bulk phonon bands. Although this system is achiral and the edge modes contain both left- and right- moving components, we demonstrate that directed energy transfer can be achieved via using multiple sources, where the energy distribution between the left and right moving modes are dictated by the relative phase between the sources. This new design opens the opportunity for directional transport of mechanical waves at previously inaccessible frequencies. |
Monday, March 6, 2023 3:24PM - 3:36PM |
D09.00003: Architectured Floppy Modes in Combinatorial Metamaterials Tomer A Sigalov, Corentin Coulais, Yair Shokef Much of the functionality of mechanical metamaterials has to do with soft or floppy modes, which allow deformations with very small or even zero energetic cost. We combine two different anisotropic triangular building blocks – one with a single floppy mode and another with two floppy modes. The spatial distribution and mutual alignment of these blocks enable us to design the multiplicity and precise spatial structure of the cooperative floppy modes in the resulting metamaterial. We develop a theoretical framework for exactly constructing all the floppy modes of any such metamaterial. Our strategy allows us to design metamaterials with any number of floppy modes, ranging from zero, one or a few, up to an extensive number that scales linearly with system size. Most interestingly, we can design metamaterials that have an intermediate number of floppy modes that scales with the system surface, namely that their degeneracy scales sub-extensively with system size. Such modes are useful for instance for designing metamaterials with multiple textured functionalities or for concentrating stresses and deformations in multiple chosen regions within the metamaterial. |
Monday, March 6, 2023 3:36PM - 3:48PM |
D09.00004: Self-Dual 2D Elastic Lattices with Finite Frequency Topological Maxwell Modes Hrishikesh G Danawe, Heqiu Li, Kai Sun, Serife Tol This work presents our recent discovery of a new class of topological modes intrinsic to elastic self-dual lattices localized near pinned (i.e., restricted to move) lattice sites. This new topological phenomenon lies at the intersection of the two existing major topological classes: first, the finite frequency in-gap modes of topological insulators, and second, the zero-frequency dispersionless modes in Maxwell lattices. The new Maxwell-like topological modes in self-dual lattices appear at finite frequencies similar to the topological modes of topological insulators. In contrast, they follow the same topological structure as observed for the dispersionless zero-frequency flat bands in Maxwell lattices. Thus, the topological winding number defined for zero frequency modes of Maxwell lattices is utilized with a modified basis (displacement field) to explain the existence and topological origin of the finite frequency Maxwell-like topological modes in self-dual lattices. Unlike the existing topological phenomena, these modes are topologically protected against hybridization; thus, they offer avenues for seamless wave transport along the waveguides of pinned lattice sites. Further, the waveguides are reconfigurable by simply pinning and unpinning the lattice sites in a homogeneous lattice, unlike the fixed heterogeneous interfaces in topological insulators. Hence, we envision this new topological phenomenon to benefit many wave applications. |
Monday, March 6, 2023 3:48PM - 4:00PM |
D09.00005: Designing Ground States and Degeneracies of Complex Triangular Mechanical Metamaterials Chaviva E Sirote, Robin L Selinger, Yair Shokef Mechanical metamaterials are artificial structures exhibiting unusual mechanical properties that stem mainly from their geometrical structure rather than from the materials they are made of. We design complex responses by utilizing geometric frustration - the inability of all mechanical elements to simultaneously deform in harmony. We consider a metamaterial made of a triangular lattice of elastic beams of different widths. The three beams constituting each triangle cannot simultaneously bend to their first buckling mode and also maintain the angles at their contacts. For beams of a single width, this frustration is relieved by long-range elastic interactions, resulting in two possible ordered deformation patterns. We extend an existing mapping to an Ising spin model to theoretically show that varying the different beam widths leads to four possible deformation patterns, which we verify experimentally. Two of these phases exhibit extensively degenerate energy-minimizing states, which implies that the metamaterial deforms in a non-periodic manner, with multiple independent degrees of freedom. |
Monday, March 6, 2023 4:00PM - 4:12PM |
D09.00006: A single input state switching building block harnessing internal instabilities Malte A ten Wolde, Davood Farhadi Mechanical metamaterials are a promising platform to alter mechanical properties post-fabrication. Recent efforts have shown this using a set of external stimuli that control an equivalent set of states, representing material properties, by changing the internal geometry and stresses of a metamaterial unit-cell. To decrease the number of external stimuli for a set of states, a building block is required that uses internal information as an extra input. Here, we present an elastic and contact-less state-changing building block that harnesses internal instabilities to switch between two distinct states as a response to a single stimulus. The building block consists of a buckling beam at its bifurcation, a nonlinear spring and a bistable element representing the internal information state. Upon applying a stimulus in the form of a displacement, the state is measured by the nonlinear spring which determines the desired deformation branch of the buckling beam at bifurcation; as a result the internal state will switch to the other stable state. Such a state-changing building block can be associated with geometric changes in the cellular structure, resulting in different material properties. |
Monday, March 6, 2023 4:12PM - 4:24PM |
D09.00007: Volterra Series as an Intermediate Representation for Designing Smart Mechanical Structures Finn T Bohte, Théophile Louvet, Vincent Maillou, Marc Serra-Garcia We have recently demonstrated speech recognition by linear passive elastic mechanical structures. However, the design of these structures requires computationally challenging non-convex optimization, which complicates inclusion of non-linear interactions in the design. Non-linear systems can be represented by Volterra series, which offer a generalization to impulse responses, under the assumption of fading memory. Since speech recognition is of fading memory, we propose to optimize mechanical systems for speech recognition through Volterra series representations. Here, we investigate how Volterra series representations can be realized through the dynamics of mechanical structures. We consider binary classification of spoken words by optimizing the Volterra kernels up to second order, and how these can be implemented by passive mechanical systems. |
Monday, March 6, 2023 4:24PM - 4:36PM |
D09.00008: Tetra-, Tri-, Di-, and Mono-mode Metamaterials with Cubic Symmetry Yunya Liu, Pai Wang, Christian Kern, Bolei Deng We report a comprehensive design guide for crystalline metamaterials with tetra-, tri-, di-, and mono-mode based on cubic elasticity - the simplest anisotropic case specified by 3 elastic constants only. To clarify some popular misconceptions, we first present a discussion about symmetry requirements. Next, we demonstrate a complete design protocol for periodic structures that are guaranteed to exhibit cubic elastic behaviors, with an emphasis on designs without any four-fold rotational symmetry or mirror symmetry. These extremal metamaterials can realize elastic tetra-, tri-, di-, and mono-mode in addition to the well-known penta-mode. Further, we show several examples with different extreme anisotropic cases as well as functionalities for wave manipulation. |
Monday, March 6, 2023 4:36PM - 4:48PM |
D09.00009: Towards Two Time Axes: Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial Ian Frankel, Haning Xiu, Xiaoming Mao, Zi Chen, Nicholas Boechler, Kai Qian, Siddhartha Sarkar, Harold Y Liu, Brianna MacNider The discovery of novel topological phases of matter has quickly become important in the study of condensed matter physics, photonics, and more recently mechanics. However, most research on topological mechanical metamaterials, such as Maxwell lattices, takes place in the linear regime. In this study, the large deformation quasi-static response of a topological Maxwell lattice is studied through geometric simulations and experiments. We further show a mapping between our linearized, homogenized system, and a non-Hermitian, non-recriprocal, one-dimensional wave equation demonstrating an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and a one dimensional nonlinear dynamical active system. The holographic nature of the Maxwell Lattice allows for a space dimension to act as a ‘synthetic time’ dimension. This mapping opens the door to new questions about what happens when dynamics are incorporated into a system with a ‘synthetic time’ dimension, creating a system with two ‘time’ dimensions. Our study shows new tools for controlling stress and strain in lattices, and expands the applications of such metamaterials to adaptive and smart materials, and mechanical logic. |
Monday, March 6, 2023 4:48PM - 5:00PM |
D09.00010: Computational Discovery of Microstructured Composites with Optimal Strength-Toughness Trade-Offs Bolei Deng The conflict between strength and toughness is a fundamental problem in engineering materials design. However, systematic discovery of microstructured composites with optimal strength-toughness trade-offs has never been demonstrated due to the discrepancies between simulation and reality and the lack of data-efficient exploration of the entire Pareto front. Here, we report a widely applicable pipeline harnessing physical experiments, numerical simulations and artificial neural networks to efficiently discover microstructured designs that are simultaneously tough and strong. Using a physics-based simulator with moderate complexity, our strategy runs a data-driven proposal-validation workflow in a nested-loop fashion to bridge the gap between simulation and reality in high sample efficiency. Without any prescribed expert knowledge of materials design, our approach automatically identifies existing toughness enhancement mechanisms that were traditionally discovered through trial-and-error or biomimicry. We provide a blueprint for the computational discovery of optimal designs, which inverts traditional scientific approaches, and is applicable to a wide range of research problems beyond composites, including polymer chemistry, fluid dynamics, meteorology, and robotics. |
Monday, March 6, 2023 5:00PM - 5:12PM |
D09.00011: Effects of Pore Shape Contour on Band Gaps of 2D Periodic Structures Sharat Chandra C Paul, Hongsup Oh, Jacob Hochhalter, Pai Wang We study contours of pore shape and investigate their effects on the band gaps of two-dimensional monolithic porous phononic metamaterials. As pore shape plays a significant role in the performance of metamaterials, previous studies considered up to 2nd coefficients of the Fourier series describing the pore shape. In our research, up to 6th shape coefficients are used to design the pore shapes to realize the changes in band gaps. We use both two-fold and four-fold symmetric unit cells in square lattices to capture the response and observe significant influences on the band gaps at different frequency levels due to the higher-order shape factors. These findings could lead us to new design of metamaterials with band gaps at desirable frequencies. |
Monday, March 6, 2023 5:12PM - 5:24PM |
D09.00012: Mirror-symmetry-protected higher-order topological zero-frequency edge and corner modes in Maxwell lattices Siddhartha Sarkar, Xiaoming Mao, Kai Sun Higher order topological phases in two dimensions are known to host protected corner modes. However, these corner modes are only robust in the presence of chiral symmetry. Here, we demonstrate mirror symmetry protected higher order topology in a Maxwell lattice consisting of point masses connected by springs where the number of degrees of freedom equals the number of constraints. We show that along mirror symmetric lines in the reciprocal space the compatibility matrix of the Maxwell lattice can be block-diagonalized into even and odd parity sectors, and a winding number can be defined within each sector (mirror graded winding number MGWN). We further show that two systems with the same topological polarization can have different MGWN. Using analytical theory and numerical diagonalization, we prove the existence of edge and corner modes localized at mirror invariant domain walls and corners between two systems with different MGWN. Interestingly, even and odd parity edge/corner modes appear at opposite edges/corners. Furthermore, due to an inherent chiral symmetry of Maxwell lattices, these edge and corner modes are pinned at zero frequency and cannot be removed as long as the bulk spectrum is gapped. |
Monday, March 6, 2023 5:24PM - 5:36PM |
D09.00013: Optimization of the small-amplitude dynamic triggering mechanism of bi-stable metamaterials Md Nahid Hasan, Taylor E Greenwood, Yong Lin Kong, Pai Wang We analyze and optimize a new class of multi-stable mechanical metamaterials with a high stretch ratio between the contracted state and the expanded state. The goal is to maintain mechanical stability in two or more configurations while achieving controlled reconfiguration. The designed architected materials can switch between different stable states under mechanical stimuli without the loss of structural integrity. Furthermore, we also optimize the small-amplitude dynamic triggering mechanism for state-switching to enable a broad range of applications. |
Monday, March 6, 2023 5:36PM - 5:48PM |
D09.00014: Observation of Frozen Mode of Stationary-Inflection-Point Dynamics in Nonlocal Phononic Metamaterials Fei Chen, Pai Wang We report a new type of phononic metamaterials with non-local interactions. Our designs demonstrate a unique and fundamental advantage in achieving any arbitrarily specified dispersion band, which governs the propagation of elastic waves. In particular, we fabricate a sample with a stationary inflection point (SIP a.k.a undulation point) where both the first and second derivatives of the dispersion curve vanish. We perform wave-propagation testing on the sample and observe the localized and non-spreading mode, which is distinctive from regular zero-group-velocity (ZGV) modes. This breaks the restriction on vibro-elastic energy localization and may open a new avenue to design metamaterials to manipulate non-propagating waves. |
Monday, March 6, 2023 5:48PM - 6:00PM |
D09.00015: Elastic Mimicry of Gravitational Waves zilong zhao We design a new mechanical metamaterial for a series of experiments to mimic the characteristics of gravitational waves. In a multi-layer lattice consisting of bars, sliders, and elastic springs, we observe tensor-polarized elastic waves, where the stable and harmonic propagation of the strain tensor resembles the spacetime metric tensor perturbed by gravitational waves. Experimental results show that this simple design is a fertile platform to realize the rich physics of novel elastic strain waves with spin-2 rotational symmetry. The phase difference between the "+" polarization and "x" polarization of the gravitational wave is simulated by controlling two coordinated components in our design. The frequency and amplitude of the gravitational wave are simulated by the slider motion. Our demonstrations may potentially lead to unprecedented capabilities to bridge the field of mechanical metamaterials to studies in general relativity and cosmology. |
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