Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials.

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

Controlled pathways and sequential information processing in serially coupled mechanical hysterons.

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.

Model-free characterization of topological edge and corner states in mechanical networks.

Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust responses in wave guiding, sensing, computation, and filtering. However, determining whether a mechanical structure is topologically nontrivial and features topologically protected modes has hitherto relied on theoretical models. This strong requirement has limited the experimental and practical significance of topological mechanics to laboratory demonstrations. Here, we introduce and validate an experimental method to detect the topologically protected zero modes of mechanical structures without resorting to any modeling step. Our practical method is based on a simple electrostatic analogy: Topological zero modes are akin to electric charges. To detect them, we 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. Our method readily applies to any mechanical structure and effectively detects the edge and corner states of regular and higher-order topological insulators. Our findings extend the reach of chiral topological phases beyond designer materials and allow their direct experimental investigation.

Elasticity and rheology of auxetic granular metamaterials.

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials.

Bloch oscillations, Landau-Zener transition, and topological phase evolution in an array of coupled pendula.

We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su-Schrieffer-Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wave-packet in the bulk of the lattice, we observe Bloch oscillations, Landau-Zener transitions, and coupling between the isospin (i.e., the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the nontrivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 [Formula: see text] 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of [Formula: see text]. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure and shed light on the similarities and the differences between quantum and classical topological effects.

SonoTransformers: Transformable acoustically activated wireless microscale machines.

Shape transformation, a key mechanism for organismal survival and adaptation, has gained importance in developing synthetic shape-shifting systems with diverse applications ranging from robotics to bioengineering. However, designing and controlling microscale shape-shifting materials remains a fundamental challenge in various actuation modalities. As materials and structures are scaled down to the microscale, they often exhibit size-dependent characteristics, and the underlying physical mechanisms can be significantly affected or rendered ineffective. Additionally, surface forces such as van der Waals forces and electrostatic forces become dominant at the microscale, resulting in stiction and adhesion between small structures, making them fracture and more difficult to deform. Furthermore, despite various actuation approaches, acoustics have received limited attention despite their potential advantages. Here, we introduce "SonoTransformer," the acoustically activated micromachine that delivers shape transformability using preprogrammed soft hinges with different stiffnesses. When exposed to an acoustic field, these hinges concentrate sound energy through intensified oscillation and provide the necessary force and torque for the transformation of the entire micromachine within milliseconds. We have created machine designs to predetermine the folding state, enabling precise programming and customization of the acoustic transformation. Additionally, we have shown selective shape transformable microrobots by adjusting acoustic power, realizing high degrees of control and functional versatility. Our findings open new research avenues in acoustics, physics, and soft matter, offering new design paradigms and development opportunities in robotics, metamaterials, adaptive optics, flexible electronics, and microtechnology.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial.

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

Tunable liquid-solid hybrid thermal metamaterials with a topology transition.

Thermal metamaterials provide rich control of heat transport which is becoming the foundation of cutting-edge applications ranging from chip cooling to biomedical. However, due to the fundamental laws of physics, the manipulation of heat is much more constrained in conventional thermal metamaterials where effective heat conduction with Onsager reciprocity dominates. Here, through the inclusion of thermal convection and breaking the Onsager reciprocity, we unveil a regime in thermal metamaterials and transformation thermotics that goes beyond effective heat conduction. By designing a liquid-solid hybrid thermal metamaterial, we demonstrate a continuous switch from thermal cloaking to thermal concentration in one device with external tuning. Underlying such a switch is a topology transition in the virtual space of the thermotic transformation which is achieved by tuning the liquid flow via external control. These findings illustrate the extraordinary heat transport in complex multicomponent thermal metamaterials and pave the way toward an unprecedented regime of heat manipulation.

Programmable mechanical devices through magnetically tunable bistable elements.

Mechanical instabilities, especially in the form of bistable and multistable mechanisms, have recently garnered a lot of interest as a mode of improving the capabilities and increasing the functionalities of soft robots, structures, and soft mechanical systems in general. Although bistable mechanisms have shown high tunability through the variation of their material and design variables, they lack the option of modifying their attributes dynamically during operation. Here, we propose a facile approach to overcome this limitation by dispersing magnetically active microparticles throughout the structure of bistable elements and using an external magnetic field to tune their responses. We experimentally demonstrate and numerically verify the predictable and deterministic control of the response of different types of bistable elements under varying magnetic fields. Additionally, we show how this approach can be used to induce bistability in intrinsically monostable structures simply by placing them in a controlled magnetic field. Furthermore, we show the application of this strategy in precisely controlling the features (e.g., velocity and direction) of transition waves propagating in a multistable lattice created by cascading a chain of individual bistable elements. Moreover, we can implement active elements like a transistor (gate controlled by magnetic fields) or magnetically reconfigurable functional elements like binary logic gates for processing mechanical signals. This strategy serves to provide programming and tuning capabilities required to allow more extensive utilization of mechanical instabilities in soft systems with potential functions such as soft robotic locomotion, sensing and triggering elements, mechanical computation, and reconfigurable devices.

Discrete symmetries control geometric mechanics in parallelogram-based origami.

Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson's ratio Miura-ori origami crease pattern. Here, we develop a formalism for linear compatibility that enables explicit investigation of the interplay between geometric symmetries and functionality in origami crease patterns. We apply this formalism to a particular class of periodic crease patterns with unit cells composed of four arbitrary parallelogram faces and establish that their mechanical response is characterized by an anticommuting symmetry. In particular, we show that the modes are eigenstates of this symmetry operator and that these modes are simultaneously diagonalizable with the symmetric strain operator and the antisymmetric curvature operator. This feature reveals that the anticommuting symmetry defines an equivalence class of crease pattern geometries that possess equal and opposite in-plane and out-of-plane Poisson's ratios. Finally, we show that such Poisson's ratios generically change sign as the crease pattern rigidly folds between degenerate ground states and we determine subfamilies that possess strictly negative in-plane or out-of-plane Poisson's ratios throughout all configurations.

Omnimodal topological polarization of bilayer networks: Analysis in the Maxwell limit and experiments on a 3D-printed prototype.

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as "omnimodal polarization." While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers, whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.

Memory from coupled instabilities in unfolded crumpled sheets.

Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these behaviors lies in understanding the contribution of the complex geometry of the sheet. Here we combine cyclic driving protocols and three-dimensional (3D) imaging to correlate the global mechanical response and the underlying geometric transformations in unfolded crumpled sheets. We find that their response to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. Using 3D imaging we show that these behaviors emerge due to an interplay between localized and interacting geometric instabilities in the sheet. A simple model confirms that these minimal ingredients are sufficient to explain the observed behaviors. Finally, we show that after training, multiple memories can be encoded, a phenomenon known as return point memory. Our study lays the foundation for understanding the complex mechanics of crumpled sheets and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities.

Transient learning degrees of freedom for introducing function in materials.

SignificanceMany protocols used in material design and training have a common theme: they introduce new degrees of freedom, often by relaxing away existing constraints, and then evolve these degrees of freedom based on a rule that leads the material to a desired state at which point these new degrees of freedom are frozen out. By creating a unifying framework for these protocols, we can now understand that some protocols work better than others because the choice of new degrees of freedom matters. For instance, introducing particle sizes as degrees of freedom to the minimization of a jammed particle packing can lead to a highly stable state, whereas particle stiffnesses do not have nearly the same impact.

Mechanical cloak via data-driven aperiodic metamaterial design.

SignificanceAn invisibility cloak to conceal objects from an outside observer has long been a subject of interest in metamaterial design. While cloaks have been manufactured for optical, thermal, and electric fields, limited progress has been made for mechanical cloaks. Most existing designs rely on mapping-based methods, which have so far been limited to special base cells and a narrow selection of voids with simple shapes. In this study, we develop a fundamentally different approach by exploiting data-driven designs to offer timely, customized solutions to mechanical cloaking that were previously difficult to obtain. Through simulations and experimental validations, we show that excellent cloaking performance can be achieved for various boundary conditions, shapes of voids, base cells, and even multiple voids.

Phase-transforming metamaterial with magnetic interactions.

Solid-solid phase transformations can affect energy transduction and change material properties (e.g., superelasticity in shape memory alloys and soft elasticity in liquid crystal elastomers). Traditionally, phase-transforming materials are based on atomic- or molecular-level thermodynamic and kinetic mechanisms. Here, we develop elasto-magnetic metamaterials that display phase transformation behaviors due to nonlinear interactions between internal elastic structures and embedded, macroscale magnetic domains. These phase transitions, similar to those in shape memory alloys and liquid crystal elastomers, have beneficial changes in strain state and mechanical properties that can drive actuations and manage overall energy transduction. The constitutive response of the elasto-magnetic metamaterial changes as the phase transitions occur, resulting in a nonmonotonic stress-strain relation that can be harnessed to enhance or mitigate energy storage and release under high-strain-rate events, such as impulsive recoil and impact. Using a Landau free energy-based predictive model, we develop a quantitative phase map that relates the geometry and magnetic interactions to the phase transformation. Our work demonstrates how controllable phase transitions in metamaterials offer performance capabilities in energy management and programmable material properties for high-rate applications.

Strong Optical Coupling of Lattice Resonances in a Top-down Fabricated Hybrid Metal-Dielectric Al/Si/Ge Metasurface.

Optical metasurfaces enable the manipulation of the light-matter interaction in ultrathin layers. Compared with their metal or dielectric counterparts, hybrid metasurfaces resulting from the combination of dielectric and metallic nanostructures can offer increased possibilities for interactions between modes present in the system. Here, we investigate the interaction between lattice resonances in a hybrid metal-dielectric metasurface obtained from a single-step nanofabrication process. Finite-difference time domain simulations show the avoided crossing of the modes appearing in the wavelength-dependent absorptance inside the Ge upon variations in a selected geometry parameter as evidence for strong optical coupling. We find good agreement between the measured and simulated absorptance and reflectance spectra. Our metasurface design can be easily incorporated into a top-down optoelectronic device fabrication process with possible applications ranging from on-chip spectroscopy to sensing.

Optical Spin Waves.

Chirality is inherent to a broad range of systems, including solid-state and wave physics. The precession (chiral motion) of the magnetic moments in magnetic materials, forming spin waves, has various properties and many applications in magnetism and spintronics. We show that an optical analogue of spin waves can be generated in arrays of plasmonic nanohelices. Such optical waves arise from the interaction between twisted helix eigenmodes carrying spin and orbital angular momenta. We demonstrate that these optical spin waves are reflected at the interface between successive domains of enantiomeric nanohelices, forming a heterochiral lattice regardless of the wave propagation direction within the lattice. Optical spin waves may be applied in techniques involving photon spin, ranging from data processing and storage to quantum optics.

Three-Dimensional Optical Imaging of Internal Deformations in Polymeric Microscale Mechanical Metamaterials.

Recent advances in two-photon polymerization fabrication processes are paving the way to creating macroscopic metamaterials with microscale architectures, which exhibit mechanical properties superior to their bulk material counterparts. These metamaterials typically feature lightweight, complex patterns such as lattice or minimal surface structures. Conventional tools for investigating these microscale structures, such as scanning electron microscopy, cannot easily probe the internal features of these structures, which are critical for a comprehensive assessment of their mechanical behavior. In turn, we demonstrate an optical confocal microscopy-based approach that allows for high-resolution optical imaging of internal deformations and fracture processes in microscale metamaterials under mechanical load. We validate this technique by investigating an exemplary metamaterial lattice structure of 80 × 80 × 80 µm3 in size. This technique can be extended to other metamaterial systems and holds significant promise to enhance our understanding of their real-world performance under loading conditions.

Homotopy, symmetry, and non-Hermitian band topology.

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time (PT) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases inPT-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneousPTsymmetry breaking is captured by Chern-Euler and Chern-Stiefel-Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.

Flexible Block Copolymer Metamaterials Featuring Hollow Ordered Nanonetworks with Ultra-High Porosity and Surface-To-Volume Ratio.

By utilizing bicontinuous and nanoporous ordered nanonetworks, such as double gyroid (DG) and double diamond (DD), metamaterials with exceptional optical and mechanical properties can be fabricated through the templating synthesis of functional materials. However, the volume fraction range of DG in block copolymers is significantly narrow, making it unable to vary its porosity and surface-to-volume ratio. Here, the theoretically limited structural volume of the DG phase in coil-coil copolymers is overcome by enlarging the conformational asymmetry through the association of mesogens, providing fast access to achieving flexible structured materials of ultra-high porosities. The new materials design, dual-extractable nanocomposite, is created by incorporating a photodegradable block with a solvent-extractable mesogen (m) into an accepting block, resulting in a new hollow gyroid (HG) with the largely increased surface-to-volume ratio and porosity of 77 vol%. The lightweight HG exhibits a low refractive index of 1.11 and a very high specific reduced modulus, almost two times that of the typical negative gyroid (porosity≈53%) and three times that of the positive gyroid (porosity≈24%). This novel concept can significantly extend the DG phase window of block copolymers and the corresponding surface-to-volume ratio, being applicable for nanotemplate-synthesized nanomaterials with a great gain of mechanical, catalytic, and optoelectronic properties.