Programmable and robust static topological solitons in mechanical metamaterials

Modular design of curved beam-based recyclable architected materials

Advances in manufacturing technologies have enabled architected materials with unprecedented properties. These materials are typically irreversibly designed and fabricated with characteristic geometries and specific mechanical properties, thus rendering them suitable for pre-specified requests. However, these materials cannot be recycled or reconstructed into different shapes and functionalities to economically adapt to various environments. Hence, we present a modular design strategy to create a category of recyclable architected materials comprising elastic initially curved beams and rigid cylindrical magnets. Based on numerical analyses and physical prototypes, we introduce an arc-serpentine curved beam (ASCB) and systematically investigate its mechanical properties. Subsequently, we develop two sets of hierarchical modules for the ASCB, thus expanding the constructable shape of architected materials from regular cuboids to complex curved surfaces. Furthermore, we demonstrate that the magnets attached to the centers of specific serpentine patterns of the modules allows the effective in-situ recycling of the designed materials, including sheet materials for non-damage storage, bulk materials for tunable stiffness, and protective package boxes for reshaping into decorative lampshades. We expect our approach to improve the flexibility of architected materials for multifunctional implementation in resource-limited scenarios.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Mechanical metamaterials and beyond

Mechanical metamaterials enable the creation of structural materials with unprecedented mechanical properties. However, thus far, research on mechanical metamaterials has focused on passive mechanical metamaterials and the tunability of their mechanical properties. Deep integration of multifunctionality, sensing, electrical actuation, information processing, and advancing data-driven designs are grand challenges in the mechanical metamaterials community that could lead to truly intelligent mechanical metamaterials. In this perspective, we provide an overview of mechanical metamaterials within and beyond their classical mechanical functionalities. We discuss various aspects of data-driven approaches for inverse design and optimization of multifunctional mechanical metamaterials. Our aim is to provide new roadmaps for design and discovery of next-generation active and responsive mechanical metamaterials that can interact with the surrounding environment and adapt to various conditions while inheriting all outstanding mechanical features of classical mechanical metamaterials. Next, we deliberate the emerging mechanical metamaterials with specific functionalities to design informative and scientific intelligent devices. We highlight open challenges ahead of mechanical metamaterial systems at the component and integration levels and their transition into the domain of application beyond their mechanical capabilities.

Water nanolayer facilitated solitary-wave-like blisters in MoS2 thin films

Solitary waves are unique in nonlinear systems, but their formation and propagation in the nonlinear fluid-structure interactions have yet to be further explored. As a typical nonlinear system, the buckling of solid thin films is fundamentally related to the film-substrate interface that is further vulnerable to environments, especially when fluids exist. In this work, we report an anomalous, solitary-wave-like blister (SWLB) mode of MoS₂ thin films in a humid environment. Unlike the most common telephone-cord and web buckling deformation, the SWLB propagates forward like solitary waves that usually appear in fluids and exhibits three-dimensional expansions of the profiles during propagation. In situ mechanical, optical, and topology measurements verify the existence of an interfacial water nanolayer, which facilitates a delamination of films at the front side of the SWLB and a readhesion at the tail side owing to the water nanolayer-induced fluid-structure interaction. Furthermore, the expansion morphologies and process of the SWLB are predicted by our theoretical model based on the energy change of buckle propagation. Our work not only demonstrates the emerging SWLB mode in a solid material but also sheds light on the significance of interfacial water nanolayers to structural deformation and functional applications of thin films.

Non-Hermitian topology in static mechanical metamaterials

The combination of broken Hermiticity and band topology in physical systems unveils a novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that breaks reciprocity is usually used to achieve NHSE, and gain and loss in energy are inevitably involved. Here, we demonstrate non-Hermitian topology in a mechanical metamaterial system by exploring its static deformation. Nonreciprocity is introduced via passive modulation of the lattice configuration without resorting to active control and energy gain/loss. Intriguing physics such as the reciprocal and higher-order skin effects can be tailored in the passive system. Our study provides an easy-to-implement platform for the exploration of non-Hermitian and nonreciprocal phenomena beyond conventional wave dynamics.

Non-orientable order and non-commutative response in frustrated metamaterials

From atomic crystals to animal flocks, the emergence of order in nature is captured by the concept of spontaneous symmetry breaking^1-4. However, this cornerstone of physics is challenged when broken symmetry phases are frustrated by geometrical constraints. Such frustration dictates the behaviour of systems as diverse as spin ices^5-8, confined colloidal suspensions⁹ and crumpled paper sheets¹⁰. These systems typically exhibit strongly degenerated and heterogeneous ground states and hence escape the Ginzburg-Landau paradigm of phase ordering. Here, combining experiments, simulations and theory we uncover an unanticipated form of topological order in globally frustrated matter: non-orientable order. We demonstrate this concept by designing globally frustrated metamaterials that spontaneously break a discrete [Formula: see text] symmetry. We observe that their equilibria are necessarily heteregeneous and extensively degenerated. We explain our observations by generalizing the theory of elasticity to non-orientable order-parameter bundles. We show that non-orientable equilibria are extensively degenerated due to the arbitrary location of topologically protected nodes and lines where the order parameter must vanish. We further show that non-orientable order applies more broadly to objects that are non-orientable themselves, such as buckled Möbius strips and Klein bottles. Finally, by applying time-dependent local perturbations to metamaterials with non-orientable order, we engineer topologically protected mechanical memories^11-19, achieve non-commutative responses and show that they carry an imprint of the braiding of the loads' trajectories. Beyond mechanics, we envision non-orientability as a robust design principle for metamaterials that can effectively store information across scales, in fields as diverse as colloidal science⁸, photonics²⁰, magnetism⁷ and atomic physics²¹.

Influence of the internal degrees of freedom of coronene molecules on the nonlinear dynamics of a columnar chain

The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.

Robotic Materials Transformable Between Elasticity and Plasticity

Robotic materials, with coupled sensing, actuation, computation, and communication, have attracted increasing attention because they are able to not only tune their conventional passive mechanical property via geometrical transformation or material phase change but also become adaptive and even intelligent to suit varying environments. However, the mechanical behavior of most robotic materials is either reversible (elastic) or irreversible (plastic), but not transformable between them. Here, a robotic material whose behavior is transformable between elastic and plastic is developed, based upon an extended neutrally stable tensegrity structure. The transformation does not depend on conventional phase transition and is fast. By integrating with sensors, the elasticity-plasticity transformable (EPT) material is able to self-sense deformation and decides whether to undergo transformation or not. This work expands the capability of the mechanical property modulation of robotic materials.

Encoding and Storage of Information in Mechanical Metamaterials

Information processing using material's own properties has gained increasing interest. Mechanical metamaterials, due to their diversity of deformation modes and wide design space, can be used to realize information processing, such as computing and storage. Here a mechanical metamaterial system is demonstrated for material-based encoding and storage of data through programmed reconfigurations of the metamaterial's structured building blocks. Sequential encoding and decoding are achieved in the three-dimensional (3D) printed pixelated mechanical metamaterial via kirigami-based "pixels" with programmable, temperature-dependent bistability. The mechanical metamaterial is demonstrated via a multistep deformation of encoding messages of texts and surfaces with arrays of binary data, and then decoding them by applying a predetermined stretching and heating regimen to sequentially retrieve layers of stored information and display them on its surface. This approach serves as a general framework to enable the encoding and storage of data with mechanical metamaterials.

Origami Tribo-Metamaterials with Mechanoelectrical Multistability

The emerging mechanical functional metamaterials reported with promising mechanoelectrical characteristics bring increasing attention to structurally functional materials. It is essential to deploy mechanical metamaterials in energy materials for effective triggering and controllable mechanoelectrical response. This study reports origami tribo-metamaterials (OTMs) that design triboelectric materials in the origami-enabled, tubular metamaterials. The octagonal, hexagonal, and conical origami units are deployed as the metamaterial substrates to trigger the triboelectric pairs for mechanoelectrical multistability. For the octagonal OTM configuration with the triboelectric pair of fluorinated ethylene propylene-paper, the peak open-circuit voltage, short-circuit current, and transferred charge are obtained as 206.4 V, 4.66 μA, and 0.38 μC, respectively, and the maximum instantaneous output power density is 0.96 μW/cm² with the load resistance of 20 MΩ. The OTM takes advantage of the origami metamaterials to obtain the multistable force-displacement response as effective stimuli for the triboelectric materials, which leads to tunable mechanoelectrical performance for speed and weight sensing and energy harvesting. The proposed OTM not only offers a strategy to structurally design energy materials to achieve desirable mechanoelectrical response, but also provides a guideline for the applications of mechanical functional metamaterials in practice.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Reprogrammable Metasurface Controlled by 2D Thermal Fields

The combination of thermal field sensing and microwave operation is an innovative topic in metamaterials. Although there exists research on modulating electromagnetic waves by controlling each column of the metasurface elements for programmable metasurfaces, the regulation is not flexible. In view of this, this paper proposes a metasurface based on distributed thermal sensing that can be independently modulated by each element. In this paper, the metasurface adopts a 1-bit coding metasurface, which is combined with PIN diodes to modulate the phase response. The voltage control circuit feeds back the change in the thermistors to the switching state of the PIN diode. Each metasurface unit contains thermistors, which are used to sense thermal stimulation and can be independently modulated. The metasurface composed of these elements can feel the field generated via heat energy. We can control electromagnetic waves by controlling this field. In order to prove the feasibility of this scheme, a metasurface sample of 8 × 8 elements was designed. Three patterns were used for the design, fabrication, and measurement of the samples. Meanwhile, printed circuit board (PCB) technology was applied. The results show that the simulated results are highly consistent with the experimental results, which verifies that this scheme is practicable.

Deployable mechanical metamaterials with multistep programmable transformation

Transformations in shape are critical to actuation in engineered metamaterials. Existing engineering metamaterials are typically limited to a small number of shape transformations that must be built-in during material synthesis. Here, inspired by the multistability and programmability of kirigami-based self-folding elements, a robust framework is introduced for the construction of sequentially programmable and reprogrammable mechanical metamaterials. The materials can be locked into multiple stable deployed configurations and then, using tunable bistability enabled by temperature-responsive constituent materials, return to their original reference configurations or undergo mode bifurcation. The framework provides a platform to design metamaterials with multiple deployable and reversible configurations in response to external stimuli.

Sequential snapping and pathways in a mechanical metamaterial

Materials that feature bistable elements, hysterons, exhibit memory effects. Often, these hysterons are difficult to observe or control directly. Here, we introduce a mechanical metamaterial in which slender elements, interacting with pushers, act as mechanical hysterons. We show how we can tune the hysteron properties and pathways under cyclic compression by the geometric design of these elements and how we can tune the pathways of a given sample by tilting one of the boundaries. Furthermore, we investigate the effect of the coupling of a global shear mode to the hysterons as an example of the interactions between hysteron and non-hysteron degrees of freedom. We hope our work will inspire further studies on designer matter with targeted pathways.

A mechanical metamaterial with reprogrammable logical functions

Embedding mechanical logic into soft robotics, microelectromechanical systems (MEMS), and robotic materials can greatly improve their functional capacity. However, such logical functions are usually pre-programmed and can hardly be altered during in-life service, limiting their applications under varying working conditions. Here, we propose a reprogrammable mechanological metamaterial (ReMM). Logical computing is achieved by imposing sequential excitations. The system can be initialized and reprogrammed via selectively imposing and releasing the excitations. Realization of universal combinatorial logic and sequential logic (memory) is demonstrated experimentally and numerically. The fabrication scalability of the system is also discussed. We expect the ReMM can serve as a platform for constructing reusable and multifunctional mechanical systems with strong computation and information processing capability.

Observation of Ultraslow Shock Waves in a Tunable Magnetic Lattice

The combination of fast propagation speeds and highly localized nature has hindered the direct observation of the evolution of shock waves at the molecular scale. To address this limitation, an experimental system is designed by tuning a one-dimensional magnetic lattice to evolve benign waveforms into shock waves at observable spatial and temporal scales, thus serving as a "magnifying glass" to illuminate shock processes. An accompanying analysis confirms that the formation of strong shocks is fully captured. The exhibited lack of a steady state induced by indefinite expansion of a disordered transition zone points to the absence of local thermodynamic equilibrium and resurfaces lingering questions on the validity of continuum assumptions in the presence of strong shocks.

Optimization of multiscale digital speckle patterns for multiscale deformation measurement using stereo-digital image correlation

Simultaneous monitoring of multiple fields of view (FOVs) by multiscale stereo-digital image correlation (stereo-DIC) can quantify the deformation of a material when localized phenomena occur within a larger FOV or moving object. In multiscale deformation measurement via stereo-DIC, optimization of the digital speckle patterns (DSPs) is essential to achieve high accuracy and efficiency. This work optimizes and fabricates multispectral DSPs used for multiple scales. First, an optimization of the DSP for two FOVs is achieved using both spatial modulation and specified spectra. A spatially modulated DSP is compared with two spectral DSPs achieved by visible and ultraviolet-excited blue light. Then, a spatially modulated visible DSP fabricated by an ultraviolet printer overlaid with an ultraviolet-excited blue DSP fabricated by a photosensitive seal is designed for multiscale stereo-DIC measurements of three FOVs. Experiments were performed to illustrate the functionality and utility of this multiscale DSP. Such experimental analyses can supply adequate full-field data to validate localized or kinetic mechanical behavior.

Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

The realization of the mechanical nonreciprocity requires breaking either the time-reversal symmetry or the material deformation symmetry. The time-reversal asymmetry was the commonly adopted approach to realize dynamic nonreciprocity. However, a static nonreciprocity requires—with no any other option—breaking the material deformation symmetry. By virtue of the Maxwell–Betti reciprocal theorem, the achievement of the static nonreciprocity seems to be conditional by the use of a nonlinear material. Here, we further investigate this and demonstrate a novel “nonreciprocal elasticity” concept. We investigated the conditions of the attainment of effective static nonreciprocity. We revealed that the realization of static nonreciprocity requires breaking the material deformation symmetry under the same kinematical and kinetical conditions, which can be achieved only and only if the material exhibits a nonreciprocal elasticity. By means of experimental and topological mechanics, we demonstrate that the realization of static nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear. We experimentally demonstrated linear and nonlinear metamaterials with nonreciprocal elasticities. The developed metamaterials were used to demonstrate that nonreciprocal elasticity is essential to realize static nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of metamaterials that can effectively break the material deformation symmetry and achieve, both, static and dynamic nonreciprocity.

Frictionless Motion of Lattice Defects

Energy dissipation by fast crystalline defects takes place mainly through the resonant interaction of their cores with periodic lattice. We show that the resultant effective friction can be reduced to zero by appropriately tuned acoustic sources located on the boundary of the body. To illustrate the general idea, we consider three prototypical models describing the main types of strongly discrete defects: dislocations, cracks, and domain walls. The obtained control protocols, ensuring dissipation-free mobility of topological defects, can also be used in the design of metamaterial systems aimed at transmitting mechanical information.

Active control on topological immunity of elastic wave metamaterials

The topology concept in the condensed physics and acoustics is introduced into the elastic wave metamaterial plate, which can show the topological property of the flexural wave. The elastic wave metamaterial plate consists of the hexagonal array which is connected by the piezoelectric shunting circuits. The Dirac point is found by adjusting the size of the unit cell and numerical simulations are illustrated to show the topological immunity. Then the closing and breaking of the Dirac point can be generated by the negative capacitance circuits. These investigations denote that the topological immunity can be achieved for flexural wave in mechanical metamaterial plate. The experiments with the active control action are finally carried out to support the numerical design.