Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for wave filtering, cloaking, and sensing applications. This work studies the band topology and scattering behaviors near EPs, using discrete models of metamaterial (MM) systems. The questions of existence of EPs and their physical manifestations will be addressed with particular focus on symmetry considerations and scattering behavior. Discrete mass-spring models with adjustable parameters are used here to elucidate the EP-related phenomena in a fundamental form. The transfer and scattering matrices are analyzed to provide practical insights on the restrictions associated with reciprocity and fundamental symmetries. By including complex stiffness in frequency domain as a representation of non-conservative mechanical loss or gain, the MM arrays can be tuned to achieve bi-directional transparency or one-way reflection when operating at the EPs. This analytical study will contribute to the understandings of EPs in mechanical context and the design of micro-structured media for novel applications.
Wave-based reading of mechanical memory in multistable mass-in-mass metamaterials
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Laboratoire d’Acoustique de l’Université du Mans, UMR 6613, Institut d’Acoustique – Graduate School, CNRS, Le Mans Université（勒芒大学声学实验室，UMR 6613，声学研究所-研究生院，法国国家科学研究中心，勒芒大学）
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic properties is still at an early stage, especially in the nonlinear regime induced by their high deformability. Nevertheless, recent studies show that these systems provide new opportunities for the control of large amplitude elastic waves. Here, we summarize the recent results on the propagation of nonlinear waves in flexible elastic metamaterials, and highlight pos…
Shanghai Jiao Tong University（上海交通大学）；University of Toronto（多伦多大学）；Nanyang Technological University（南洋理工大学）；Imperial College London（伦敦帝国理工学院）；Zhejiang Lab（浙江实验室）；Huaibei Normal University（淮北师范大学）；University of Hong Kong（香港大学）
Nonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversability can be independently programmed and are not mutually exclusive. By conn…
We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits a frequency spectrum with unfolding (fractal) symmetries. Our study reveals a scale-free formation of exceptional points (EP) whose density is dictated by the fractal dimension of their Hermitian spectra. Demonstrated in a quasi-periodic Aubry-Harper, a geometric H-tree-fractal, and an aperiodic Fibonacci Ed-MetaMater, the universal route for EP-formation is established via a coupled mode theory model with controllable fractal spectrum. This universality will enable the…
Mechanical metamaterials are architected manmade materials that allow for unique behaviors not observed in nature, making them promising candidates for a wide range of applications. Existing metamaterials lack tunability as their properties can only be changed to a limited extent after the fabrication. In this paper, we present a new magneto-mechanical metamaterial that allows great tunability through a novel concept of deformation mode branching. The architecture of this new metamaterial employs an asymmetric joint design using hard-magnetic soft active materials that permits two distinct act…
We demonstrate a general route to making active, odd elastic solids from passive chiral elements that can act as sources of mechanical work by violating static equilibrium without internal sources of energy or momentum. We further demonstrate that by starting from a discrete, Newtonian mechanics viewpoint of the chiral unit cell, we can develop the continuum field equations for isotropic 2D chiral metamaterials that reveal odd elasticity, while elucidating the structure-property relationships underpinning the chiral, elastic moduli that enable the mechanical activity of the chiral metamaterial…
EMetaNode: Electromechanical Metamaterial Node for Broadband Vibration Attenuation and Self-powered Sensing
Hong Kong Polytechnic University（香港理工大学）；Politecnico di Milano（米兰理工大学）；ETH Zürich（苏黎世联邦理工学院）；Zürich University of Applied Sciences (ZHAW)（苏黎世应用科学与艺术大学）
Transition Waves in Mechanical Metamaterials with Neighbor-Programmable Energy Landscapes
Le Mans Université（勒芒大学）；CNRS（法国国家科学研究中心）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Department of Mechanical & Industrial Engineering, University of Toronto（多伦多大学机械与工业工程系）
Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening unprecedented opportunities to program mechanic…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose mechanical properties rely on deformation-induced transitions in nodal-topology by formation of internal self-contact. The universal nature of the principle presented, is demonstrated for tension, compression, shear and torsion. In particular, it is shown that by frustration of soft deformation modes, large highly non-linear stiffening effects can be generated. …
In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second gradient, classical Mindlin-Eringen micromorphic etc.), the relaxed micromorphic model is endowed to capture the main microscopic and macroscopic characteristics of the targeted metamaterial, namely, stiffness, anisotropy, dispersion and band-gaps. The simple structure of our material model, which simultaneously lives on a micro-, a meso- and a macroscopic scale, r…
Mechanical metamaterials owe their extraordinary properties and functionalities to their micro-/nanoscale design of which shape, including both geometry and topology, is perhaps the most important aspect. 4D printing enables programmed, predictable, and precise change in the shape of mechanical metamaterials to achieve multi-functionality, adaptive properties, and the other types of desired behaviors that cannot be achieved using simple 3D printing. This paper presents an overview of 4D printing as applied to mechanical metamaterials. It starts by presenting a systematic definition of what 4D …
Mechanical metamaterials are designed to enable unique functionalities, but are typically limited by an initial energy state and require an independent energy input to function repeatedly. Our study introduces a theoretical active mechanical metamaterial that incorporates a biological reaction mechanism to overcome this key limitation of passive metamaterials. Our material allows for reversible mechanical signal transmission, where energy is reintroduced by the biologically motivated reaction mechanism. By analysing a coarse grained continuous analogue of the discrete model, we find that signa…
In this work, we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we experimentally and numerically observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we observe that the…
Structures and/or materials with engineered functionality, capable of achieving targeted mechanical responses reacting to changes in external excitation, have various potential engineering applications, e.g. aerospace, oceanographic engineering, soft robot, and several others. Yet tunable mechanical performance is normally realized through carefully designing the architecture of structures, which is usually porous, leading to the complexity of the fabrication of the structures even using the recently emerged 3D printing technique. In this study we show that origami technique can provide an alt…
Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite structure comprising two types of materials without a cavity was optimized. Moreover, a mechanical metamaterial with a negative Poisson's ratio that can be fabricated using an additive manufacturing method was developed. First, a homogenization method that characterizes the properties of composite structures was briefly described. Then, an optimization problem…
The recent progress of non-Hermitian physics and the notion of exceptional point (EP) degeneracies in elastodynamics has led to the development of novel metamaterials for the control of elastic wave propagation, hypersensitive sensors, and actuators. The emergence of EPs in a Parity-Time symmetric system relies on judiciously engineered balanced gain and loss mechanisms. Creating gain requires complex circuits and amplification mechanisms, making engineering applications challenging. Here, we report strategies to achieve EPs in passive non-Hermitian elastodynamic systems with differential loss…
A reinforcement learning approach to design optimised graded metamaterials for mechanical energy confinement and amplification is described. Through the proximal policy optimisation algorithm, the reinforcement agent is trained to optimally set the lengths and the spacing of an array of resonators. The design optimisation problem is formalised in a Markov decision problem by splitting the optimisation procedure into a discrete number of decisions. Being the physics of graded metamaterials governed by the spatial distribution of local resonances, the space of possible configurations is constrai…
A lattice model is developed to describe the mechanical displacement of and current through each electrode of a surface acoustic wave (SAW) interdigitated tranducer (IDT). Each electrode of an IDT is treated as a mass connected mechanically to its neighbors with a spring and electrically with a capacitor. Simulations for the electrical admittance of a typical SAW IDT are performed and compared with the results of an accurate finite element method simulation. The utility of this lattice model is demonstrated by simulating the admittance of an IDT structure known as a hiccup resonator, which has…
Active matter is ubiquitous in biology and becomes increasingly more important in materials science. While numerous active systems have been investigated in detail both experimentally and theoretically, general design principles for functional active materials are still lacking. Building on a recently developed linear response optimization (LRO) framework, we here demonstrate that the spectra of nonlinear active mechanical and electric circuits can be designed similarly to those of linear passive networks.
Using an alternative mechanism to dissipation or scattering, bistable structures and mechanical metamaterials have shown promise for mitigating the detrimental effects of impact by reversibly locking energy into strained material. Herein, we extend prior works on impact absorption via bistable metamaterials to computationally explore the dependence of kinetic energy transmission on the velocity and mass of the impactor, with strain rates exceeding $10^2$ s$^{-1}$. We observe a large dependence on both impactor parameters, ranging from significantly better to worse performance than a comparativ…
The subject of mechanical metamaterials has been gaining significant attention, however, their widespread application is still halted. Such materials are usually considered as stand-alone, vis-à-vis all characteristic length scales being associated solely with geometry of material itself. In this work we propose novel application of mechanical metamaterials as interface regions joining two materials with potential of replacing bulk adhesives. This idea leads into paradigm shifts for both metamaterials and adhesive joints. In specific, we outline methodology for testing and evaluating confined …
A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective elastic moduli of such structures upon suitable aspect ratios, which characterize the geometry of the generic pentamode layer at the micro- and macro-scale, and the lamination scheme of the layered structure. The given numerical results highlight that the examined structures exhibit bending-dominated response, and are able to achieve low values of the effectiv…
This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice of the face cubic-centered unit cell typically analyzed in the current literature on pentamode materials. The studied systems exhibit only three soft deformation modes in the infinitesimal stretch-dominated regime, as opposed to the five zero-energy modes of unconfined pentamode lattices. We develop analytical formulae for the vertical and bending stiffness properties and study the dependence of s…
Morphogenetic mechanical metamaterials: Emerging tensor properties from self-organized structures
University of Limoges（利摩日大学）；CNRS（法国国家科学研究中心）；XLIM（XLIM研究所）；Institut universitaire de France (IUF)（法国高等研究院）；IRCER（陶瓷与复合材料研究与创新中心）；IUT du Limousin（利穆赞理工学院）
Delft University of Technology (TU Delft)（代尔夫特理工大学）；Leiden University Medical Center (LUMC)（莱顿大学医学中心）
Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive manufacturing techniques often requires solving such inverse problems for specific sizes. One should, therefore, find multiple microarchitectural designs that exhibit the desired properties for a specimen with given dimensions. Moreover, the candidate microarchitectures should be resistant to fatigue and fracture, meaning that peak stresses should be minimized as…
