Ken Ahn, Associate Professor of Physics and Director of Materials Science and Engineering – Materials Science Option, New Jersey Institute of Technology
Flat Frequency Bands and Majorana-like Bound States in Topological Mechanical Metamaterials
Mechanical metamaterials have become a very useful tool to demonstrate phenomena of topological origins. In this presentation, I will discuss our recent theoretical and experimental studies on two such systems. The first is a two-dimensional chiral extension of the Su-Schrieffer-Heeger chain, which reveals flat frequency bands on open edges and antiphase boundaries. The second is the metamaterial-based Kitaev chain analog, which possesses the Majorana-like bound states. For both, we choose arrays of magnetically coupled spinners as the mechanical system, and demonstrate phenomena such as the control of flatness of the edge bands, the analog of fractional charge state, a topological phase transition, and the analog of parity switching in Majorana zero mode, a candidate for qubits. The experiment results are compared with the theoretical analyses based on the tight-binding Hamiltonians, which shows strong agreements.
Erhard Buchmann, Graduate Student, Institute of Lightweight Engineering, University of the Bundeswehr Munich
Control-Structure Integrated Design of Thermoelastic Structures using Mechanical Metamaterials: Application to Optical Benches on Satellites
Thermoelastic metamaterials are a class of metamaterials that allow architecting a specific thermal expansion behaviour of components. This designates at first the design of the passive behaviour, so the expansion when heated homogenously. Then, the reactive behaviour on certain perturbations (e.g. heating sources) and external stimuli can be designed. In particular, however, functional thermoelastic metamaterial structures with feedback-control can also be architectured. This allows the control-structure integrated design of thermoelastic structures, which is addressed rarely in previous works. Nevertheless, this would pave the way to very promising applications in various fields ranging from MEMS to satellite-borne optical systems. While the activation of thermoelastic metamaterials can be done with simple joule heating, the manufacturing of those materials is challenging: At least two materials with different coefficients of thermal expansion (CTE) have to be arranged in complex lattice structures. However, they become available for highly stressed structural parts due to the recent advances in metallic multi-material L-PBF. Thermoelastic metamaterials would be particularly suitable for building optical benches for space applications, which is not considered in research until now. Satellites undergo wide temperature variations when orbiting the earth which would result in large dimensional variations of integrated optical benches. Traditionally, the dimensional stability of optical benches is established by using materials with low CTE or by mitigating these temperature variations. In contrast, in this work truss structures with thermoelastic metamaterial elements and feedback-control for optical benches are considered. The dimensional stability is reached as a closed-loop system. This design has many advantages, including the higher structural efficiency, the lower precision requirements in manufacturing and the possibility for in-orbit re-adjustments. After reviewing the requirements for optical benches, a parametrized FEM-model with an LQ-regulator for control-structure integrated design is presented. Then, the impact of the truss layout and the way of integrating thermoelastic metamaterials on the control performance is investigated. Finally, an exemplary optical bench for the SeRANIS-Mission [1] is designed and the closed-loop dimensional stability is shown by a transient simulation with orbital thermal loads. [1] Project SeRANIS | Seamless Radio Access Networks in the Internet of Space, Digitalization and Technology Research Center of the Bundeswehr (dtec.bw). dtec.bw is funded by the European Union – NextGenerationEU. www.seranis.de
Mohammad Charara, Graduate Student, Engineering, University of Minnesota
Cell Augmentation Framework for Topological Lattices
Maxwell lattices are characterized by a number of degrees of freedom that match the number of constraints. A subset of these systems, dubbed topological lattices, have been shown to localize stress and deformation to opposing edges, displaying a polarized mechanical response protected by the reciprocal-space topology of their band structure. This behavior has been documented for structures with one-, two-, and three-dimensional periodicity. In two dimensions, opportunities for topological polarization have, thus far, been largely restricted to the kagome and square lattice benchmark configurations due to the non-triviality of generating arbitrary geometries that abide by Maxwell conditions. Here, we introduce a family of augmented topological lattices that display full in-plane topological polarization, as validated through analytical calculations, computational simulations, and table-top experiments on a 3D-printed prototype. We showcase the versatility of such augmentation via a generalized lattice generation framework. This work serves to push the paradigm in topological mechanical metamaterials to explore a larger subset of topological lattices that will enrich the design landscape.
Nan Cheng, Graduate Student, Physics, University of Michigan
Bloch’s Theorem on Hyperbolic Lattice
Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological metamaterials. One important feature of hyperbolic lattices is that their translation group is nonabelian, permitting high-dimensional irreducible representations (irreps), in contrast to abelian translation groups in Euclidean lattices. Here we introduce a general framework to construct wave eigenstates of high-dimensional irreps of infinite hyperbolic lattices, thereby generalizing Bloch’s theorem, and discuss its implications on unusual mode-counting and degeneracy, as well as bulk-edge correspondence in hyperbolic lattices. Our framework is not limited to hyperbolic lattices but all other lattices in curved space. As an example, we apply this method to a tight binding modelon icosahedron and characterize its spectrum and degeneracy of high dimensional irreps.
Wenting Cheng, Physics GSRA, University of Michigan
One-way edge states in two-dimensional auxetic Maxwell lattices and continua
Unidirectional propagation of sound waves is of fundamental interest in physics, and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps, or complex mechanisms involving active constituents or nonlinearity. Here we propose a new class of passive linear one-way edge states based on spin-momentum locking of Rayleigh waves, which provides 100% unidirectional edge propagation at a broad range of frequencies below the acoustic bands. These waves are back-scattering free for arbitrary geometries in the limit of vanishing bulk modulus, and are characterized by a topological winding number that plays the role of orbital angular momentum. These passive and back-scattering free edge waves enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.
Kshiteej Deshmukh, Assistant Professor, Mathematics, University of Utah
Energy conservation at space-time interfaces in mechanical metamaterials
Changing the microstructure properties of a space-time metamaterial while a wave is propagating through it, in general requires addition or removal of energy, which can be of exponential form depending on the type of modulation. This limits the realization and application of space-time metamaterials. We resolve this issue by introducing a novel mechanism of conserving energy in non-linear space-time media. The idea is first demonstrated by considering a wave-packet propagating in a discrete medium of 1-d chain of springs and masses, where using our energy conserving mechanism we show that the spring stiffness can be incremented at several time interfaces and the energy will still be conserved. We then consider an interesting application of time-reversed imaging in 1-d and 2-d spring-mass systems with a wave packet traveling in the homogenized limit. Our numerical simulations show that, in 1-d, when the wave packet hits the time-interface two sets of waves are generated, one traveling forward in time and the other traveling backward. The time-reversed waves re-converge at the location of the source and we observe its regeneration. In 2-d, we use more complicated initial shapes and even then, we observe regeneration of the original image or source. The energy conserving mechanism can be easily extended to continuum media.
Evgueni Filipov, Assistant Professor, Civil and Environmental Engineering, University of Michigan
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Michael Frazier, Assistant Professor, Mechanical and Aerospace Engineering, University of California San Diego
Phase Patterning in Mechanical Metamaterials
Phase transformations are an apparent manifestation of equilibration in materials whose microstructure exhibits more than one energetically stable configuration. Within a given material sample, regions of differing configuration (i.e., domains) may coexist, delimited by an interpolating interface (i.e., domain wall) whose motion constitutes a transition wave effectuating the transformation from one phase to another. The physical properties can vary drastically between domains of differing phase and even within the domain walls, affecting the macroscopic material behavior. Managing the occurrence and distribution of the disparate phases within the material sample (i.e., phase patterning) is essential to many current and emerging nanotechnologies and, thus, receives significant attention in the solid-state literature. Intriguingly, analogous transformation phenomena have been elicited at the structural level from mechanical metamaterials comprising multi-stable elements; however, in this context, domain wall control facilitating phase patterning is much less developed: most architectures are one-dimensional systems capable of transforming between uniform phases (i.e., demonstrating no patterning ability) and the few that support patterning are energetically restricted to only two rather than any number of phases. Yet, the ability to realize multi-phase patterns in mechanical metamaterials, e.g., might, if each phase is mechanically distinct, expand the space of tunable acoustic/mechanical performance or, if each phase is tied to the displacement of membrane, realize morphable surfaces for optical devices and fluid flow control. In this presentation, we discuss methods of domain wall control to achieve structural phase patterns in multi-stable metamaterials, which involves their immobilization, redirection, and conversion from one mode into another.
Stefano Gonella, Professor, Civil, Environmental, and Geo- Engineering, University of Minnesota
The fate of topological edge and interface mechanics under increased geometric and material complexity
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Itay Griniasty, Postdoc, Physics, Cornell University Engineering
Bifurcation instructed design of multistate machines
(This abstract has been updated) Systems composed of many interacting elements that collaboratively generate a function, such as meta-material robots, proteins and neural-networks are often not amenable to compartmentalized design: where individual modules each perform a distinct sub-function, and are then composed to create the desired complex function. I will propose an alternative design paradigm where the function of machines arises from interactions of all the machine components, and the operation of the machine is organized by a bifurcation of multiple equilibria. These special points allow for robustly cycling between multiple distinct states by a small change of only a few control parameters. I will illustrate this approach on a simple magneto elastic machine, and discuss its implications for the design of microscopic robots and protein based machines.
Piyush Grover, Assistant Professor – Mechanical and Materials Engineering, University of Nebraska-Lincoln
Defect engineering by exploiting the nonlinear dynamics of solitary wave-defect interactions in acoustic metamaterials
We study the dynamics of solitary waves traveling in a chain of bistable elements in the presence of a local inhomogeneity (defect). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured or reflected upon interaction with the defect. The dynamics are dominated by energy exchange between the wave and a breather mode localized at the defect. We derive a reduced-order two degree of freedom Hamiltonian model for wave-breather interaction, and analyze it using dynamical systems techniques. Lobe dynamics analysis reveals the fine structure of phase space that leads to the complicated dynamics in this system. This work is a step towards developing a rational approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials.
Marcelo Guzmán, Postdoc, Physics, University of Pennsylvania & École Normale Supérieure de Lyon, France
Model-free characterization of topological states in mechanical networks
Topological materials possess unique properties, such as the ability to harbor protected edge and corner states, impervious to disorder and material imperfections. These materials offer unparalleled prospects for robust wave guiding, sensing, computation, and filtering. However, determining the topological character and the existence of topologically-protected modes in mechanical structures has traditionally relied solely on theoretical models. Consequently, the practical application and experimental relevance of topological mechanics have been largely confined to laboratory demonstrations. In this presentation, I propose an experimental technique for detecting topologically protected zero modes in mechanical structures, eliminating the need for any modeling procedure. This practical method draws upon a straightforward electrostatic analogy, equating topological zero modes to electric charges. I identify elementary mechanical molecules and measure their chiral polarization, a recently introduced marker of topology in chiral phases. Topological zero modes are then identified as singularities of the polarization field. Finally, through experiments and simulations, I validate and highlight the robustness of our predictions, even in the presence of uncontrolled dissipation processes, nonlinearities, and material imperfections.
Robert Kohn, Professor Emeritus of Mathematics, The Courant Institute, New York University
The Mechanisms and Macroscopic Behavior of the Kagome Metamaterial
The design and analysis of mechanism-based mechanical metamaterials is a relatively new and rapidly growing research area. It studies artificial “materials” that take advantage of “mechanisms” (that is, nontrivial energy-free deformations) to achieve interesting macroscopic behavior. The relevant mechanics is nonlinear, since mechanisms involve large rotations. While there have been many insightful studies of interesting examples, some fundamental issues remain poorly understood. This talk will address two of them, namely (a) how to analyze a metamaterial’s macroscopic behavior, and (b) whether linear elastic calculations might still be of some use in the study of such systems, despite the fact that their mechanisms involve large rotations. I will discuss joint work with Xuenan Li, which focuses on a particular (very rich) example: the Kagome metamaterial. It is interesting because there are infinitely many mechanisms, and yet it behaves macroscopically as a nonlinear elastic material whose stress-free states are compressive conformal maps.
Albert Liu, Assistant Professor, Chemical Engineering, University of Michigan
Dynamic Self-Assembly in Anisotropic Colloidal Systems for Emergent and Synchronized Oscillation
Recent advances in electronic materials and colloidal science have led to the development of colloidal electronics. The colloidal electronic particles, comprised of polymers and low dimensional materials, integrate simultaneously the modularity of state-of-the-art electronics and the characteristic mobility of the colloidal particles in a dispersed phase. These mobile colloidal particles can have multiple functionalities including energy harvesting, chemical species sensing, and memory updating. While the fabrication of these artificial cell-sized systems represents a significant step forward, real biological cells exhibit complex and emergent behaviors in a synchronized and controlled oscillatory manner. Recent advances in electronic materials and colloidal science have led to the development of colloidal electronics. The colloidal electronic particles, comprised of polymers and low dimensional materials, integrate simultaneously the modularity of state-of-the-art electronics and the characteristic mobility of the colloidal particles in a dispersed phase. These mobile colloidal particles can have multiple functionalities including energy harvesting, chemical species sensing, and memory updating. While the fabrication of these artificial cell-sized systems represents a significant step forward, real biological cells exhibit complex and emergent behaviors in a synchronized and controlled oscillatory manner. To realize the complex functions exhibited in natural systems, programmed dynamic self-assembly is explored in symmetry-broken colloidal electronic cells to achieve synchronized oscillations found previously only in their biological counterparts. Recently, we have reported on the development of Pt-patched microdiscs that can generate autonomous oscillatory beating behavior at the air-hydrogen peroxide interface. These Janus particles, which are fueled by the well-studied platinum-based catalytic reaction, exhibit a 4-step beating cycle that consists of (1) mutual approach, (2) oxygen bubble contact, (3) bubble merger, and (4) bubble rupture. Despite the observed beating phenomena, the underlying kinetics require further analysis and elucidation both experimentally and in silico. In this study, we examine the physical parameters that affect the oscillatory behavior of the beating particle system and compare experimental observations with simulation models. Understanding the effects of these parameters will enable the design and engineering of Janus microparticles with more complex oscillatory beating behavior with improved frequency tunability and programmability.
Jihong Ma, Assistant Professor, Mechanical Engineering, The University of Vermont
Topologically Protected Edge States in Phononic Crystals with Beyond Nearest Neighbors
Topological indices, such as winding numbers, have been conventionally used to predict the number of topologically protected edge states (TPES) in topological insulators, a signature of the topological phenomenon called bulk-edge correspondence. In this work, we experimentally observe its breakdown in Su-Schrieffer-Heeger (SSH) lattices with beyond-nearest-neighbor interactions. We hereby propose a generalized methodology to accurately count the number of TPES in an SSH system with a domain boundary and validate it using the Jackiw-Rebbi zero-mode theory.
James McInerney, Postdoc, Physics, University of Michigan
Topological polarization of codimensional Maxwell lattices
Thin sheets and slender rods have intrinsic length scales that characterize the relative cost of bending modes to stretching modes and enable low-energy large-displacement deformations that may be utilized for shape-morphing mechanical metamaterials. In this presentation, I discuss the ability to tailor such low-energy modes through the topological polarization of critically-coordinated (Maxwell) lattices composed of point masses connected by harmonic springs. First, I discuss how the the dispersion relations in three-dimensional solids, two-dimensional sheets, and one-dimensional rods have distinct consequences for the persistence of topological edge modes in experimental realizations of the analogous Maxwell lattice. Then, I summarize design principles for novel classes of thin-walled structures and trusses with tailored modal properties and stress distributions.
Arvind Murugan, Assistant Professor, Physics, University of Chicago
Learning through non-equilibrium memory
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Sidney Nagel, Stein-Freiler Distinguished Service Professor, Dept. of Physics, James Franck Institute, University of Chicago
Memory formation in disordered matter
Preamble: The recollection of events from childhood is part of what makes each of us unique. Manipulation of memories allows us to think and reason. Repetition allows precision performance in music and sports. When our faculties fail and no reason is left, we may still recall the names of our closest relatives – a memory that lasts when our brains can no longer retrieve newer information. Our muscular aches and pains remind us of recent activities. Yes! Our experience of memory is an indelible imprint of being alive. Non-biological materials can mimic the biological memories mentioned above: There are materials that perform functions only because of how they were initially manipulated – a form of rote memory. There are others that, akin to muscle memory, learn pathways between initial and final states. Some physical systems store many memories initially and then forget all but one – losing the ability to learn anything new. Many materials accumulate the dings and scratches caused by everyday use.
Memory for training: Memory connotes the ability to encode, access, and erase signatures of past history. Once a system has reached thermal equilibrium, it can no longer recall aspects of its evolution. Out-of-equilibrium systems preserve memories of their formation in a variety of ways allowing for an innovative classification of material and dynamics. While memories are interesting in themselves, they are also useful for creating function in a material via training protocols. After all, a system could not be trained unless it was capable of retaining a memory of how it was manipulated. Materials can even learn how to learn – that is, they can be trained to be adaptable.
Memories in sheared jammed packings: An example of a system with a physical memory is a cyclically sheared jammed packing that can fall into a periodic orbit where each particle returns to its identical position in subsequent cycles. The packing encodes a memory of the shear amplitude at which it was trained. Simple models, based on collections of bistable objects (called hysterons), treat clusters of rearranging particles as isolated two-state systems. Such models offer insight but fail to account for other behavior. Adding interactions between hysterons overcomes some of these deficiencies, and of particular interest, allow simultaneous encoding of a second, novel form of memory. Hysterons are typically treated quasistatically but can be generalized to include dynamics to study how the system chooses a minimum. Changing the timescale of forcing allows a transition between a situation where the fate is determined by the local energy minimum to one determined by the path taken through configuration space
Vishal Patil, Postdoc, Bioengineering, Stanford University
Self-learning mechanical circuits
Dynamical self-adaptivity and embodied computation are ubiquitous in biological systems, from cytoplasm and biofilms to animal flocks. Despite recent progress in such material computation, the problem of designing mechanical systems which self-learn remains poorly understood. Here we introduce the concept of self-learning mechanical circuits, which take mechanical inputs from changing environments and constantly update their internal state in response, thus representing an entirely mechanical information processing unit. Our circuits are composed of a new mechanical construct: an adaptive directed spring (ADS), which changes its stiffness in a directional manner, enabling neural network-like computations. We provide both a theoretical foundation and experimental realization of these elastic learning units and demonstrate their ability to autonomously uncover patterns hidden in environmental inputs. Our results pave the way towards the construction of energy-harvesting, adaptive materials which can autonomously and continuously sense and self-optimize to gain function in different environment
Jayson Paulose, Assistant Professor, Department of Physics, University of Oregon
Space-time control of parametric amplification in active mechanical metamaterials
Active mechanical metamaterials harbor acoustic signal processing functionalities that are impossible to achieve in passive structures. Amplifying an elastic wave as it passes through the material is a prominent example, with potential applications in acoustic signal processing and loss mitigation. The fundamental mechanism of wave amplification is the parametric amplifier–an oscillator whose stiffness is periodically modulated in time, which can inject energy into mechanical oscillations. Typically, parametric amplification occurs at special modulation frequencies that are trivially related to the resonance frequencies of the unmodulated system, which hinders its utility for amplifying spectrally complex signals such as wave packets. In this talk, I’ll show how spatial control of the parametric modulation phase in active metamaterials enables amplification phenomena that are far richer than those achievable by uncoupled and uncoordinated parametric amplifiers. Examples include turning off amplification at specific parametric resonance frequencies in small assemblies, achieving nonreciprocal broadband amplification in periodic lattices, and realizing amplified bands with nontrivial non-Hermitian topology.
Jerry Qi, Professor, Mechanical Engineering, Georgia Institute of Technology
Multimaterial 3D Printing of Active Mechanical Metamaterials with Tunable Properties
Mechanical metamaterials derive their properties or behaviors from the geometrical design of their internal structures. As a result, the behaviors of mechanical metamaterials usually are fixed, i.e. one geometrical design only corresponds to one set of mechanical behaviors. However, in future applications, it is highly desirable that a metamaterial can exhibit different behaviors when the environmental conditions change. In this talk, we will present some of our recent efforts in using active polymers and multimaterials 3D printing to create mechanical metamaterials that can change its periodic structures and behaviors when a stimulus is applied. These efforts reply on two multimaterials 3D printing methods recently developed in our group. In the first method, we integrate two 3D printing methods, direct-ink-write (DIW) and digit light processing (DLP) into one system. In this system, the DLP can be used to print complex bulk parts while DIW can print functional inks. In the second approach, we recently developed a grayscale DLP (g-DLP) 3D printing method where we can print a monolithic part with gradient material properties. We further explore on how to use these multimaterial 3D printing capabilities to fabricate mechanical metamaterials and demonstrate their advantage, including direct 3D/4D printing of 2D lattice structures, lattice structures with changing shape driven by liquid crystal elastomers, and 3D lattice structures by gradient materials. These new capabilities can be utilized for further exploring broader applications of mechanical metamaterials.
Sourav Roy, Graduate Student, Physics, Syracuse University
A generalized continuum elasticity theory for mechanical metamaterials
Mechanical metamaterials have been studied extensively to explore the unusual mechanical properties owing to instabilities arising from their microstructures, yet challenges still remain in studying their complex deformations. We explore a simple continuum framework for the mechanics of a thin, metamaterial sheet in which a scalar field, coupled to the reference metric, captures the soft in-plane deformation of the material. In the Föppl–von Kármán limit, we show how the unusual elasticity of the sheet screens curvature-induced stress in the bulk for metamaterials with soft conformal and soft simple shear modes. We further use this framework to study the buckling of geometrically-frustrated metamaterial sheets.
Massimo Ruzzene, Vice Chancellor for Research & Innovation, Dean of the Institutes, and Slade Professor of Mechanical Engineering, University of Colorado Boulder
Elastic Hyperbolic Lattices
Hyperbolic lattices tessellate the hyperbolic space, which affords the opportunity for an infinite number of regular tessellations. Thus, hyperbolic lattices significantly extend the design space typically associated with lattices in Euclidean space, and potentially provide access to unexplored wave phenomena. We illustrate the dynamic behavior of hyperbolic tessellations governed by interactions whose strength depends upon the distance of neighboring nodes. The exploration of their spectral characteristics unveils a rich dynamic behavior, which is characterized by eigenstates that are primarily localized either at the center, or towards the boundary of the Poincare circle. We also show how conformal mapping can be performed to obtain a variety of lattice geometries of engineering relevance. Specifically, elastic hyperbolic strips are obtained that leverage the high density of localized modes which characterize circular elastic hyperbolic lattices, while presenting themselves as useful engineering structures. The conformal mapping provides the versatility to accommodate any direction or path, as well as produce an infinite extension in bulk geometry designs through simple rotations and translations of the generating space. The result is a practical engineering structure which not only inherits a high density of boundary modes, but also a notable number of center-localized modes, which could be of interest for a variety of engineering applications. As such, elastic hyperbolic strips open the door to a new class of elastic hyperbolic metamaterials with waveguiding capabilities that rely on the ability to localize vibrations at edges or to the interior of structural assemblies.
Chris Santangelo, Professor & Director of Graduate Studies, Physics Syracuse University, New York
Designing materials with tunable properties
I will discuss a new approach to designing mechanical metamaterials from spring networks that takes advantage of special configurations called critical points which are poised between two qualitatively different kinds of behavior. Because the behavior of mechanisms near critical points are universal, we have unprecedented control over material response. I will give examples of structures with bifurcations, structures whose behavior can be gated, and materials with highly tunable stiffnesses.
Siddhartha Sarkar, Physics GSRA, University of Michigan
Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
Maxwell lattices, where the number of degrees of freedom equals the number of constraints, are known to host topologically-protected zero-frequency modes and states of self stress, characterized by a topological index called topological polarization. In this letter, we show that in addition to these known topological modes, with the help of a mirror symmetry, the inherent chiral symmetry of Maxwell lattices creates another topological index, the mirror-graded winding number (MGWN). This MGWN is a higher order topological index, which gives rise to topological zero modes and states of self stress at mirror-invariant domain walls and corners between two systems with different MGWNs. We further show that two systems with same topological polarization can have different MGWNs, indicating that these two topological indices are fundamentally distinct.
Kai Sun, Professor of Physics, University of Michigan
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Serife Tol, Assistant Professor, Mechanical Engineering, Applied Physics, University of Michigan
Reconfigurable Elastic Metasurfaces for Tunable Wavefront Shaping
Metasurfaces have recently gained increasing research interest due to their ability to control elastic/acoustic wavefronts with a compact footprint which is especially desired for low-frequency applications. This talk covers reconfigurable elastic metasurfaces which can be tailored to the desired phase modulation and wavefront manipulation by tuning either the structural elements of the passive metasurface or the external electrical stimuli on the electromechanical metasurface. To this end, we present three approaches to tunable elastic wave control via (i) a reflective metasurface, (ii) an origami-inspired metasurface, and (iii) an electromechanical metasurface. The reflecting metasurface is formed by locally resonant elements based on threaded rods and nuts, and the phase properties of the metasurface are controlled by changing the amount of nuts’ screw distances. In addition to controlling antisymmetric (A0) mode Lamb wave propagation, mode conversion is also exploited to manipulate symmetric (S0) mode Lamb waves. In the second metasurface, an array of zigzag-based folded sheets with parallel corrugations is used to control the wavefront of the refracted A0 Lamb mode wave. Our results show that the origami-inspired metasurface can reconfigure the wavefront by changing its folding angle. Finally, in the last case, we present a piezoelectric-based metasurface that is connected to individual inductive electrical loads and tailor the phase modulation according to the desired wavefront, including wave focusing and deflection. We show that through single and multi-resonant electrical shunts, propagating A0 mode Lamb waves can be controlled in a tunable and broadband fashion achieving the desired dynamic function.
Martin Van Hecke, Professor, Mechanical Metamaterials, FOM Institute AMOLF, Leiden University, Netherlands
Emergent Computing in Metamaterials
Bistable elements, controlled by buckling and snapping, naturally act as mechanical bits. The central tenet of this talk is that interactions between such bits allow flexible (meta) materials to exhibit complex orbits and store and process information. I will discuss metamaterials that count how often they are compressed and that can select and process input strings composed of complex compression cycles. These materials can be mapped to finite state machines so that their computation power can precisely be characterized. This work shines new light on the nonlinear response of complex materials and opens the door to ‘intelligent matter’.
Kon-Well Wang, Stephen P. Timoshenko Collegiate Professor of Mechanical Engineering, University of Michigan
Reconfigurable Mechanical Metastructures – From Wave Controls to Mechano-Intelligence
In recent years, the concept of adaptive metastructures engineered based on nature-inspired modular architectures has been explored to create advanced engineering systems. For example, inspired by the observation that some of skeletal muscle’s intriguing macroscale functionalities result from the assembly of nanoscale cross-bridge constituents with metastability, the idea of synthesizing structures from the integration of mechanical metastable modules has been pursued. In another example, inspired by the physics behind the plant nastic movements and the rich designs of origami folding, a class of metastructures is created building on the innovation of fluidic-origami modular elements. Overall, the metastructure modules are designed to be reconfigurable in their shape, mechanical properties, and dynamic characteristics, so to produce synergistic and intriguing functionalities at the system level, such as adaptive phononic crystals for vibration/noise control and nontraditional wave steering. More recently, with the rapid advances in high-performance intelligent systems, we are witnessing a prominent demand for the next generation of mechanical metastructures to have much more built-in intelligence and autonomy. An emerging idea is therefore to pioneer and harness the metastructures’ high dimensionality and nonlinearity for physical computing to achieve mechano-intelligence. That is, we aim to embed and integrate some of the elements of intelligence, such as perception and decision-making, directly in the mechanical domain, advancing from conventional systems that solely rely on add-on electronics and digital computers. This presentation will highlight some of these recent advances in reconfigurable mechanical metastructures, from phononic wave controls to self-tuning structural intelligence.
Pai Wang, Assistant Professor, Mechanical Engineering, The University of Utah
How to achieve any band structure you want – Extreme Customization of Dispersion Relations
We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both single-band and double-band cases, we can achieve any valid dispersion curves with analytical precision. We further employ our method to design phononic crystals in 2D and 3D.
Martin Wegener, Director and Research Institute Chair – Nanophotonics, Karlsruhe Institute of Technology, Germany
Different routes towards roton-like dispersion relations in mechanical metamaterials
We review our recent theoretical and experimental work on mechanicla metamaterials exhibiting roton-like phonon dispersion relations. The used mechanisms include chirality (chiral micropolar elasticity), nonlocality (high-order gradient models), and monomode metamaterials (extreme Cauchy elasticity).
Shu Yang, Professor, Materials Science and Engineering, University of Pennsylvania
Programming shape morphing and chirality switching of metamaterials from liquid crystalline elastomers
Materials that can change shapes in a programmable fashion upon stimuli are of interests for applications such as soft robotistic, smart wearables, 3D displays, and topological materials. Among different responsive materials, liquid crystal elastomers (LCEs) with intrinsic anisotropy have been attractive. Here, we report spatially programming the out-of-plane and in-plane bending in elastomer films embedded with shape-changing LCE microparticles, leading to complex shape morphing. Further, by encoding such particles in a honeycomb lattice, their continuous shape change in response to temperature leads to lattice reconfiguration, from a right-handed chiral state to achiral one, then to a left-handed chiral state, without breaking the translational symmetry. Accordingly, the sign of rotation of the polarized light passing through the lattices changes as measured by time-domain terahertz (THz) spectroscopy. Further, we can locally alter the chirality in the adjacent domains using near-infrared (NIR) light illumination.
Robert Ziff, Professor Chemical Engineering, Complex Systems, University of Michigan
Riddles of Sphinx Tilings
We describe properties of “sphinx” tiles (composed of six triangles in the shape of the sphinx) in frames also of the same shape. These tiles allow a “rep-tile” quasicrystalline tiling, but here we focus on general tilings, including the entropy, chirality, dependence on temperature (when an interaction is included). To carry out a Monte Carlo simulation, we develop a method based upon “polyads” which are collections of tiles that can be re-tiled. We also develop algorithms to enumerate sphinx tilings, up to order 13, where the number of tilings is 1 257 159 787 425 487 037 702 548 758 466.