Snapping mechanical metamaterials under tension

Unravelling Size-Dependent and Coupled Properties in Mechanical Metamaterials: A Couple-Stress Theory Perspective

The lack of material characteristic length scale prevents classical continuum theory (CCT) from recognizing size effect. Additionally, the even-order material property tensors associated with CCT only characterize the materials' centrosymmetric behavior and overlook their intrinsic chirality and polarity. Moreover, CCT is not reducible to 2D and 1D space without adding couples and higher-order deformation gradients. Despite several generalized continuum theories proposed over the past century to overcome the limitations of CCT, the broad application of these theories in the field of mechanical metamaterials has encountered significant challenges. These obstacles primarily arise from a limited understanding of the material coefficients associated with these theories, impeding their widespread adoption. Implementing a bottom-up approach based on augmented asymptotic homogenization, a consistent and self-sufficient effective couple-stress theory for materials with microstructures in 3D, 2D, and 1D spaces is presented. Utilizing the developed models, material properties associated with axial-twist, shear-bending, bending-twist, and double curvature bending couplings in mechanical metamaterials are characterized. The accuracy of these homogenized models is investigated by comparing them with the detailed finite element models and experiments performed on 3D-printed samples. The proposed models provide a benchmark for the rational design, classification, and manufacturing of mechanical metamaterials with programmable coupled deformation modes.

Mechanical Metamaterials for Handwritten Digits Recognition

The increasing needs for new types of computing lie in the requirements in harsh environments. In this study, the successful development of a non-electrical neural network is presented that functions based on mechanical computing. By overcoming the challenges of low mechanical signal transmission efficiency and intricate layout design methodologies, a mechanical neural network based on bistable kirigami-based mechanical metamaterials have designed. In preliminary tests, the system exhibits high reliability in recognizing handwritten digits and proves operable in low-temperature environments. This work paves the way for a new, alternative computing system with broad applications in areas where electricity is not accessible. By integrating with the traditional electronic computers, the present system lays the foundation for a more diversified form of computing.

Tunable sequential pathways through spatial partitioning and frustration tuning in soft metamaterials

Elastic instabilities have been leveraged in soft metamaterials to attain novel functionalities such as mechanical memory and sequential pathways. Pathways have been realized in complex media or within a collection of hysteretic elements. However, much less has been explored in frustrated and partitioned soft metamaterials. In this work, we introduce spatial partitioning as a method to localize deformation in sub-regions of a large and soft metamaterial. The partitioning is achieved through the strategic arrangement of soft inclusions in a soft lattice, which form distinct regions behaving as mechanical units. We examine two partitions: an equally spaced layer partition with mechanical units connected in series, and a cross partition, represented by interconnected series of mechanical units in parallel. Sequential pathways are obtained by frustrating the partitioned metamaterial post-manufacture and are characterized by tracking the polarization change in each partition region. Through a combination of experiments and simulations, we demonstrate that partitioning enables tuning the pathway from longitudinal with weak interactions to a pathway exhibiting strong interactions rising from geometric incompatibility and central domain rotation. We show that tuning the level of uniform lateral pre-strain provides a wide range of tunability from disabling to modifying the sequential pathway. We also show that imposing a nonuniform confinement and altering the tilting of one or two of the domain edges enables to program the pathway, access a larger set of states, and tune the level of interaction between the regions.

A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties

The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study.

Suture Interface Inspired Self-Recovery Architected Structures for Reusable Energy Absorption

Designing materials and structures with high energy absorption and self-recoverability remains a challenge for reusable energy absorption, particularly in aerospace engineering applications (i.e., planetary landers). While the prevalent design methods of reusable energy absorbers mainly use the mechanical instability of tilted and curved beams, the limited energy absorption capabilities and low strength of tilted or curved beams limit performance improvement. In nature, Phlorodes diabolicus has evolved extreme impact resistance, in which the suture interface structure plays a key role. Herein, we propose a convex interface slide design strategy for reusability and energy absorption through friction interface, geometry, and bending elasticity, inspired by the elytra of Phlorodes diabolicus. Convex interfaces slide to achieve a more than 270% higher energy absorption capacity per unit volume than the curved beams. The convex interface slide design can be easily integrated with other structures to achieve multiple functions, such as various shapes and self-recoverability. Furthermore, we developed a theoretical model to predict the mechanical behavior and energy absorption performance. Our strategy opens up a new design space for creating reusable energy-absorbing structures.

In Situ Activation of Snap-Through Instability in Multi-Response Metamaterials through Multistable Topological Transformation

Snap-through instability has been widely leveraged in metamaterials to attain non-monotonic responses for a specific subset of applications where conventional monotonic materials fail to perform. In the remaining more plentiful set of ordinary applications, snap-through instability is harmful, and current snapping metamaterials become inadequate because their capacity to snap cannot be suppressed post-fabrication. Here, a class of topology-transformable metamaterials is introduced to enable in situ activation and deactivation of the snapping capacity, providing a remarkable level of versatility in switching between responses from monotonic to monostable and bistable snap-through. Theoretical analysis, numerical simulations, and experiments are combined to unveil the role played by contact in the topological transformation capable of increasing the geometry incompatibility and confinement stiffness of selected architectural members. The strategy here presented for post-fabrication reprogrammability of matter and on-the-fly response switching paves the way to multifunctionality for application in multiple sectors from mechanical logic gates, and adjustable energy dissipators, to in situ adaptable sport equipment.

Electromagnetic Reconfiguration Using Stretchable Mechanical Metamaterials

Response to environmental thermomechanical inputs in applications that range from wearable electronics to aerospace structures necessitates agile communication systems driven by reconfigurable electromagnetic structures. Antennas in these systems must dynamically preserve acceptable radiation characteristics while enabling on-demand performance reconfiguration. However, existing reconfiguration mechanisms through stretchable conductors rely on high-strain behavior in soft substrates, which limits their applicability. Herein, this work demonstrates the use of mechanical metamaterials for stretchable conductors and dielectrics in antennas. Metamaterials allow conductor stretching up to 30% with substrate base material tensile moduli ranging from 26 MPa to 44 GPa. It is shown, through several antenna designs, that mechanical metamaterials enable similar frequency reduction upon stretching as monolithic conductors, while simultaneously providing a miniaturization effect. The conductor patterning, furthermore, provides control over coupling between mechanical stretching and electromagnetic reconfiguration. This approach enables designing reconfigurable antenna functionality through metamaterial geometry in response to arising needs in applications ranging from body-adapted electronics to space vehicles.

A hydrogel-based mechanical metamaterial for the interferometric profiling of extracellular vesicles in patient samples

The utility of mechanical metamaterials for biomedical applications has seldom been explored. Here we show that a metamaterial that is mechanically responsive to antibody-mediated biorecognition can serve as an optical interferometric mask to molecularly profile extracellular vesicles in ascites fluid from patients with cancer. The metamaterial consists of a hydrogel responsive to temperature and redox activity functionalized with antibodies to surface biomarkers on extracellular vesicles, and is patterned into micrometric squares on a gold-coated glass substrate. Through plasmonic heating, the metamaterial is maintained in a transition state between a relaxed form and a buckled state. Binding of extracellular vesicles from the patient samples to the antibodies on the hydrogel causes it to undergo crosslinking, induced by free radicals generated via the activity of horseradish peroxidase conjugated to the antibodies. Hydrogel crosslinking causes the metamaterial to undergo fast chiral re-organization, inducing amplified changes in its mechanical deformation and diffraction patterns, which are detectable by a smartphone camera. The mechanical metamaterial may find broad utility in the sensitive optical immunodetection of biomolecules.

Magneto-Thermomechanically Reprogrammable Mechanical Metamaterials

Future active metamaterials for reconfigurable structural applications require fast, untethered, reversible, and reprogrammable (multimodal) transformability with shape locking. Magnetic control has a superior advantage for fast and remotely controlled deployment; however, a significant drawback is needed to maintain the magnetic force to hold the transformation, limiting its use in structural applications. The shape-locking property of shape-memory polymers (SMPs) can resolve this issue. However, the intrinsic irreversibility of SMPs may limit their reconfigurability as active metamaterials. Moreover, to date, reprogrammable methods have required high power with laser and arc welding proving to be energy-inefficient control methods. In this work, a magneto-thermomechanical tool is constructed and demonstrated, which enables a single material system to transform with untethered, reversible, low-powered reprogrammable deformations, and shape locking via the application of magneto-thermomechanically triggered prestress on the SMP and structural instability with asymmetric magnetic torque. The mutual assistance of two physics concepts-magnetic control combined with the thermomechanical behavior of SMPs is demonstrated, without requiring new materials synthesis and high-power energy for reprogramming. This approach can open a new path of active metamaterials, flexible yet stiff soft robots, multimodal morphing structures, and mechanical computing devices where it can be designed in reversible and reprogrammable ways.

Remodeling of Architected Mesenchymal Microtissues Generated on Mechanical Metamaterials

Mechanical metamaterials constitute a nascent category of architected structures comprising arranged periodic components with tailored geometrical features. These materials are now being employed as advanced medical implants due to their extraordinary mechanical properties over traditional devices. Nevertheless, to achieve desired tissue integration and regeneration, it is critical to study how the microarchitecture affects interactions between metamaterial scaffolds and living biological tissues. Based on human induced pluripotent stem cell technology and multiphoton lithography, we report the establishment of an in vitro microtissue model to study the integration and remodeling of human mesenchymal tissues on metamaterial scaffolds with different unit geometries. Microtissues showed distinct tissue morphologies and cellular behaviors between architected octet-truss and bowtie structures. Under the active force generated from mesenchymal tissues, the octet-truss and bowtie metamaterial scaffolds demonstrated unique instability phenomena, significantly different from uniform loading using conventional mechanical testing.

Design and Manufacturing of a Metal-Based Mechanical Metamaterial with Tunable Damping Properties

In the present work, a novel concept for metallic metamaterials is presented, motivated by the creation of next-generation reversible damping systems that can be exposed to various environmental conditions. For this purpose, a unit cell is designed that consists of a parallel arrangement of a spring and snap-fit mechanism. The combination of the two concepts enables damping properties one order of magnitude higher than those of the constituting metal material. The spring element stores elastic energy while the snap-fit allows to absorb and dissipate energy and to reach a second stable state. Different configurations of single unit cells and connected cell assemblies are manufactured by laser powder bed fusion using Ti6Al4V powder. The dimensioning is supported by finite element modelling and the characteristic properties of the unit cells are studied in cyclic compression experiments. The metamaterial exhibits damping properties in the range of polymeric foams while retaining its higher environmental resistance. By variation of selected geometrical parameters, either bistable or self-recovering characteristics are achieved. Therefore, a metamaterial as an assembly of the described unit cells could offer a high potential as a structural element in future damping or energy storage systems operating at elevated temperatures and extreme environmental conditions.

Vibration Analysis of a Finite Lightweight Locally Resonant Beam Suspended with Periodic Force-Moment-Type Resonators inside Using an Exact Wave-Based Approach

This paper employs and develops the exact wave-based vibration analysis approach to investigate the propagation properties of a designed finite lightweight locally resonant (LR) beam with two-degree-of-freedom (2-DOF) force-moment-type resonators attached periodically inside. By deriving the propagation, reflection, and transmission matrices of the structural discontinuities, the vibration of the LR beam can be described as structural waves. By assembling wave relations into the beam, the approach shows high efficiency because the forced vibration problem of the lightweight LR structure is turned to be the solution to a related set of matrix equations. The accuracy of the developed approach is validated with two examples carried out using the finite element method. In addition, the influence of the main parameters of the LR beam is studied and we found that the increase in the mass of the resonator and the stiffness of the spring are more sensitive in broadening the width and increasing the center frequency of the band gap of the designed lightweight LR beam. The proposed structure and analysis approach in this paper may provide an exact and efficient means for the design and analysis of structures in which damping and lightweight properties are required, such as space-arm and the framework of antennas in the field of aerospace.

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.

Harnessing Friction in Intertwined Structures for High-Capacity Reusable Energy-Absorbing Architected Materials

Energy-absorbing materials with both high absorption capacity and high reusability are ideal candidates for impact protection. Despite great demands, the current designs either exhibit limited energy-absorption capacities or perform well only for one-time usage. Here a new kind of energy-absorbing architected materials is created with both high absorption capacity and superior reusability, reaching 10 kJ kg-1 per cycle for more than 200 cycles, that is, unprecedentedly 2000 kJ kg-1 per lifetime. The extraordinary performance is achieved by exploiting the rate-dependent frictional dissipation between prestressed stiff cores and a porous soft elastomer, which is reinforced by an intertwined stiff porous frame. The vast interfaces between the cores and elastomer enable high energy dissipation, while the magnitude of the friction force can adapt passively with the loading rate. The intertwined structure prevents stress concentration and ensures no damage and reusability of the constituents after hundreds of loading cycles. The behaviors of the architected materials, such as self-recoverability, force magnitude, and working stroke, are further tailored by tuning their structure and geometry. This design strategy opens an avenue for developing high-performance reusable energy-absorbing materials that enable novel designs of machines or structures.

Performance Evaluation of Sandwich Structures Printed by Vat Photopolymerization

Additive manufacturing such as vat photopolymerization allows to fabricate intricate geometric structures than conventional manufacturing techniques. However, the manufacturing of lightweight sandwich structures with integrated core and facesheet is rarely fabricated using this process. In this study, photoactivatable liquid resin was used to fabricate sandwich structures with various intricate core topologies including the honeycomb, re-entrant honeycomb, diamond, and square by a vat photopolymerization technique. Uniaxial compression tests were performed to investigate the compressive modulus and strength of these lightweight structures. Sandwich cores with the diamond structure exhibited superior compressive and weight-saving properties whereas the re-entrant structures showed high energy absorption capacity. The fractured regions of the cellular cores were visualized by scanning electron microscopy. Elastoplastic finite element analyses showed the stress distribution of the sandwich structures under compressive loading, which are found to be in good agreement with the experimental results. Dynamic mechanical analysis was performed to compare the behavior of these structures under varying temperatures. All the sandwich structures exhibited more stable thermomechanical properties than the solid materials at elevated temperatures. The findings of this study offer insights into the superior structural and thermal properties of sandwich structures printed by a vat photopolymerization technique, which can benefit a wide range of engineering applications.

A metafluid with multistable density and internal energy states

Investigating and tailoring the thermodynamic properties of different fluids is crucial to many fields. For example, the efficiency, operation range, and environmental safety of applications in energy and refrigeration cycles are highly affected by the properties of the respective available fluids. Here, we suggest combining gas, liquid and multistable elastic capsules to create an artificial fluid with a multitude of stable states. We study, theoretically and experimentally, the suspension’s internal energy, equilibrium pressure-density relations, and their stability for both adiabatic and isothermal processes. We show that the elastic multistability of the capsules endows the fluid with multistable thermodynamic properties, including the ability of capturing and storing energy at standard atmospheric conditions, not found in naturally available fluids.

Investigating and tailoring the thermodynamic properties of different fluids is crucial to many applied fields such as energy and refrigeration cycles. Here, authors use multistable, gas filled, particles suspension to enhance the macro-properties of thermodynamic fluids.

Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses

SignificanceCreating structures to realize function-oriented mechanical responses is desired for many applications. Yet, the use of a single material phase and heuristics-based designs may fail to attain specific target behaviors. Here, through a deterministic algorithmic procedure, multiple materials with dissimilar properties are intelligently synthesized into composite structures to achieve arbitrary prescribed responses. Created structures possess unconventional geometry and seamless integration of multiple materials. Despite geometric complexity and varied material phases, these structures are fabricated by multimaterial manufacturing, and tested to demonstrate that wide-ranging nonlinear responses are physically and accurately realized. Upon heteroassembly, resulting structures provide architectures that exhibit highly complex yet navigable responses. The proposed strategy can benefit the design of function-oriented nonlinear mechanical devices, such as actuators and energy absorbers.

Wave manipulation using a bistable chain with reversible impurities

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal test beds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wave packets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend effect. Furthermore, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective "impurities." This behavior serves as a new mechanism for reversibly programming the dynamic response of bistable chains.

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.

Programmable Multistable Perforated Shellular

Developing bistable metamaterials has recently offered a new design paradigm for deployable structures and reusable dampers. While most bistable mechanisms possess inclined/curved struts, a new 3D multistable shellular metamaterial is developed by introducing delicate perforations on the surface of Schwarz's Primitive shellular, integrating the unique properties of shellular materials such as high surface area, stiffness, and energy absorption with the multistability concept. Denoting the fundamental snapping part by motif, certain shellular motifs with elliptical perforations exhibit mechanical bistability. To bring the concept of multistability to a single motif, multistable shellular motifs are developed by introducing multilayer staggered perforations that form hinges and facilitate local instability. Adopting an n-layer staggered perforation (n hinges) design leads to a maximum 2^n-1 stable states within one shellular motif during loading and unloading. Three-directional multistable shellulars are attained by extending the perforation design in three orthogonal directions. Harnessing snap-through and snap-back behaviors and self-contact, the introduced multistable perforated shellulars exhibit strong rigidity both in loading and unloading, and enhanced energy dissipation. The introduced design strategy opens up new horizons for creating multidirectional multistable metamaterials with load bearing capabilities for applications in soft robotics, shape-morphing architectures, and reusable and deployable energy absorbers/dampers.

Mechanical Metamaterials Gyro-Structure Piezoelectric Nanogenerators for Energy Harvesting under Quasi-Static Excitations in Ocean Engineering

In this study, we develop the mechanical metamaterial-enabled piezoelectric nanogenerators in the gyro-structure, which is reported as a novel green energy solution to generate electrical power under quasi-static excitations (i.e., <1 Hz) such as in the ocean environment. The plate-like mechanical metamaterials are designed with a hexagonal corrugation to improve their mechanical characteristics (i.e., effective bending stiffnesses), and the piezoelectric trips are bonded to the metaplates. The piezo-metaplates are placed in the sliding cells to obtain the post-buckling response for energy harvesting under low-frequency ocean motions. The corrugated mechanical metamaterials are fabricated using the three-dimensional additive manufacturing technique and are bonded with polyvinylidene fluoride strips, and the nanogenerator samples are investigated under the quasi-static loading. Theoretical and numerical models are developed to obtain the electrical power, and satisfactory agreements are observed. Optimization is conducted to maximize the generated electrical power with respect to the geometric consideration (i.e., changing the corrugation pattern of the mechanical metamaterials) and the material consideration (i.e., changing the mechanical metamaterials to anisotropic). In the end, we consider the piezoelectric nanogenerators as a potential green solution for the energy issues in other fields.

Self-Triggered Thermomechanical Metamaterials with Asymmetric Structures for Programmable Response under Thermal Excitations

In this study, we propose self-triggered thermomechanical metamaterials (ST-MM) by applying thermomechanical materials in mechanical metamaterials designed with asymmetric structures (i.e., microstructural hexagons and chiral legs). The thermomechanical metamaterials are observed with programmable mechanical response under thermal excitations, which are used in mechanical metamaterials to obtain chiral tubes with negative Poisson's ratio and microgrippers with temperature-induced grabbing response. Theoretical and numerical models are developed to analyze the thermomechanical response of the ST-MM from the material and structural perspectives. Finally, we envision advanced applications of the ST-MM as chiral stents and thermoresponsive microgrippers with maximum grabbing force of approximately 101.7 N. The emerging ST-MM provide a promising direction for the design and perception of smart mechanical metamaterials.

Scalable Fabrication of High-Performance Thin-Shell Oxide Nanoarchitected Materials via Proximity-Field Nanopatterning

Nanoarchitected materials are considered as a promising research field, deriving distinctive mechanical properties by combining nanomechanical size effects with conventional structural engineering. Despite the successful demonstration of the superiority and feasibility of nanoarchitected materials, scalable and facile fabrication techniques capable of macroscopically producing such materials at a low cost are required to take advantage of the nanoarchitected materials for specific applications. Unlike conventional techniques, proximity-field nanopatterning (PnP) is capable of simultaneously obtaining high spatial resolution and mass producibility in synthesizing such nanoarchitected materials in the form of an inch-scale film. Herein, we focus on the feasibility of using PnP as a scalable fabrication technique for three-dimensional nanostructures and the superiority of the resultant thin-shell oxide nanoarchitected materials for specific applications, such as lightweight structural materials, mechanically robust nanocomposites, and high-performance piezoelectric materials. This review will discuss and summarize the relevant results obtained for nanoarchitected materials synthesized by PnP and provide suggestions for future research directions for scalable manufacturing and application.

Energy Absorption and Mechanical Performance of Functionally Graded Soft-Hard Lattice Structures

Today, the rational combination of materials and design has enabled the development of bio-inspired lattice structures with unprecedented properties to mimic biological features. The present study aims to investigate the mechanical performance and energy absorption capacity of such sophisticated hybrid soft–hard structures with gradient lattices. The structures are designed based on the diversity of materials and graded size of the unit cells. By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated. The simulations are implemented using ANSYS finite element modeling (FEM) (2020 R1, 2020, ANSYS Inc., Canonsburg, PA, USA) considering elastic-plastic and the hardening behavior of the materials and geometrical non-linearity. The numerical results are validated against experimental data on three-dimensional (3D)-printed lattices revealing the high accuracy of the FEM. Then, by combination of the dissimilar soft and hard polymeric materials in a homogenous hexagonal lattice structure, two dual-material mechanical lattice statures are designed, and their mechanical performance and energy absorption are studied. The results reveal that not only gradual changes in the unit cell size provide more energy absorption and improve mechanical performance, but also the rational combination of soft and hard materials make the lattice structure with the maximum energy absorption and stiffness, in comparison to those structures with a single material, interesting for multi-functional applications.

Generalized tessellations of superellipitcal voids in low porosity architected materials for stress mitigation

Stress concentration is a crucial source of mechanical failure in structural elements, especially those embedding voids. This paper examines periodic porous materials with porosity lower than 5%. We investigate their stress distribution under planar multiaxial loading, and presents a family of geometrically optimized void shapes for stress mitigation. We adopt a generalized description for both void geometry and planar tessellation patterns that can handle single and multiple voids of arbitrary void shape at a generic angle. The role of void shape evolution from diamond to rectellipse on the stress-distribution is captured at the edge of voids in a representative volume element (RVE) made of non-equal length periodic vectors. Theoretical derivations, numerical simulations along with experimental validation of the strain field in thermoplastic polymer samples fabricated by laser cutting unveil the role of geometric parameters, e.g. superellipse order, aspect ratio and rotation angle, that minimize stress peak and ameliorate stress distribution around voids. This work extends and complements classical theory by providing fundamental insights into the role that tessellation, void shape and inclination play in the stress distribution of low-porosity architected materials, thus introducing essential guidelines of broad application for stress-minimization and failure mitigation in diverse sectors.

Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation

Multistable mechanical metamaterials are artificial materials whose microarchitectures offer more than two different stable configurations. Existing multistable mechanical metamaterials mainly rely on origami/kirigami-inspired designs, snap-through instability, and microstructured soft mechanisms, with mostly bistable fundamental unit cells. Scalable, tristable structural elements that can be built up to form mechanical metamaterials with an extremely large number of programmable stable configurations remains illusive. Here, we harness the elastic tensile/compressive asymmetry of kirigami microstructures to design a class of scalable X-shaped tristable structures. Using these structure as building block elements, hierarchical mechanical metamaterials with one-dimensional (1D) cylindrical geometries, 2D square lattices, and 3D cubic/octahedral lattices are designed and demonstrated, with capabilities of torsional multistability or independent controlled multidirectional multistability. The number of stable states increases exponentially with the cell number of mechanical metamaterials. The versatile multistability and structural diversity allow demonstrative applications in mechanical ternary logic operators and amplitude modulators with unusual functionalities.

Mechanics of a Snap Fit

Snap fits are versatile mechanical designs in industrial products that enable the repeated assembling and disassembling of two solid parts. This important property is attributed to a fine balance between geometry, friction, and bending elasticity. In this Letter, we combine theory, simulation, and experiment to reveal the fundamental physical principles of snap-fit functions in the simplest possible setup consisting of a rigid cylinder and a thin elastic shell. We construct a phase diagram using geometric parameters and identify four distinct mechanical phases. We develop analytical predictions based on the linear elasticity theory combined with the law of static friction and rationalize the numerical and experimental results. The study reveals how an operational asymmetry of snap fits (i.e., easy to assemble but difficult to disassemble) emerges from an exquisite combination of geometry, elasticity, and friction and suggests optimization of the tunable functionalities for a range of mechanical designs.

Foundations for Soft, Smart Matter by Active Mechanical Metamaterials

Emerging interest to synthesize active, engineered matter suggests a future where smart material systems and structures operate autonomously around people, serving diverse roles in engineering, medical, and scientific applications. Similar to biological organisms, a realization of active, engineered matter necessitates functionality culminating from a combination of sensory and control mechanisms in a versatile material frame. Recently, metamaterial platforms with integrated sensing and control have been exploited, so that outstanding non-natural material behaviors are empowered by synergistic microstructures and controlled by smart materials and systems. This emerging body of science around active mechanical metamaterials offers a first glimpse at future foundations for autonomous engineered systems referred to here as soft, smart matter. Using natural inspirations, synergy across disciplines, and exploiting multiple length scales as well as multiple physics, researchers are devising compelling exemplars of actively controlled metamaterials, inspiring concepts for autonomous engineered matter. While scientific breakthroughs multiply in these fields, future technical challenges remain to be overcome to fulfill the vision of soft, smart matter. This Review surveys the intrinsically multidisciplinary body of science targeted to realize soft, smart matter via innovations in active mechanical metamaterials and proposes ongoing research targets that may deliver the promise of autonomous, engineered matter to full fruition.

Mechanical Metamaterials on the Way from Laboratory Scale to Industrial Applications: Challenges for Characterization and Scalability

Mechanical metamaterials promise a paradigm shift in materials design, as the classical processing-microstructure-property relationship is no longer exhaustively describing the material properties. The present review article provides an application-centered view on the research field and aims to highlight challenges and pitfalls for the introduction of mechanical metamaterials into technical applications. The main difference compared to classical materials is the addition of the mesoscopic scale into the materials design space. Geometrically designed unit cells, small enough that the metamaterial acts like a mechanical continuum, enabling the integration of a variety of properties and functionalities. This presents new challenges for the design of functional components, their manufacturing and characterization. This article provides an overview of the design space for metamaterials, with focus on critical factors for scaling of manufacturing in order to fulfill industrial standards. The role of experimental and simulation tools for characterization and scaling of metamaterial concepts are summarized and herewith limitations highlighted. Finally, the authors discuss key aspects in order to enable metamaterials for industrial applications and how the design approach has to change to include reliability and resilience.

A New Polymer-Based Mechanical Metamaterial with Tailorable Large Negative Poisson's Ratios

Mechanical metamaterials have attracted significant attention due to their programmable internal structure and extraordinary mechanical properties. However, most of them are still in their prototype stage without direct applications. This research developed an easy-to-use mechanical metamaterial with tailorable large negative Poisson’s ratios. This metamaterial was microstructural, with cylindrical-shell-based units and was manufactured by the 3D-printing technique. It was found numerically that the present metamaterial could achieve large negative Poisson’s ratios up to −1.618 under uniaxial tension and −1.657 under uniaxial compression, and the results of the following verification tests agreed with simulation findings. Moreover, stress concentration in this new metamaterial is much smaller than that in most of existing re-entrance metamaterials.

Strain rate-dependent mechanical metamaterials

Mechanical metamaterials are usually designed to exhibit novel properties and functionalities that are rare or even unprecedented. What is common among most previous designs is the quasi-static nature of their mechanical behavior. Here, we introduce a previously unidentified class of strain rate-dependent mechanical metamaterials. The principal idea is to laterally attach two beams with very different levels of strain rate-dependencies to make them act as a single bi-beam. We use an analytical model and multiple computational models to explore the instability modes of such a bi-beam construct, demonstrating how different combinations of hyperelastic and viscoelastic properties of both beams, as well as purposefully introduced geometric imperfections, could be used to create robust and highly predictable strain rate-dependent behaviors of bi-beams. We then use the bi-beams to design and experimentally realize lattice structures with unique strain rate-dependent properties including switching between auxetic and conventional behaviors and negative viscoelasticity.

Inflatable soft jumper inspired by shell snapping

Fluidic soft actuators are enlarging the robotics toolbox by providing flexible elements that can display highly complex deformations. Although these actuators are adaptable and inherently safe, their actuation speed is typically slow because the influx of fluid is limited by viscous forces. To overcome this limitation and realize soft actuators capable of rapid movements, we focused on spherical caps that exhibit isochoric snapping when pressurized under volume-controlled conditions. First, we noted that this snap-through instability leads to both a sudden release of energy and a fast cap displacement. Inspired by these findings, we investigated the response of actuators that comprise such spherical caps as building blocks and observed the same isochoric snapping mechanism upon inflation. Last, we demonstrated that this instability can be exploited to make these actuators jump even when inflated at a slow rate. Our study provides the foundation for the design of an emerging class of fluidic soft devices that can convert a slow input signal into a fast output deformation.

Design of 3D Printed Programmable Horseshoe Lattice Structures Based on a Phase-Evolution Model

By 3D printing lattice structure with active materials, the structures can exhibit shape and functional changes under external stimulus. However, the programmable shape changes of the 3D printed lattice structures are limited due to the complex geometries, nonlinear behaviors of the active materials, and the diverse external stimuli. In this work, we propose a design framework combining experiments, theoretical modeling, and finite element simulations for the controllable shape changes of the 3D printed horseshoe under thermal stimulus. The theoretical model is based on a phase evolution model that combines the geometrical nonlinearity and the material nonlinearity. Results show that the shapes with positive or negative Poisson's ratio and bending intermediate shapes can be programmed by tuning the geometrical parameters and the temperature distribution. This work provides a method to aid the design of 3D printed functional lattice structures and have potential applications in soft robotics, biomedicine, and energy absorbing fields.

Soft three-dimensional network materials with rational bio-mimetic designs

Many biological tissues offer J-shaped stress–strain responses, since their microstructures exhibit a three-dimensional (3D) network construction of curvy filamentary structures that lead to a bending-to-stretching transition of the deformation mode under an external tension. The development of artificial 3D soft materials and device systems that can reproduce the nonlinear, anisotropic mechanical properties of biological tissues remains challenging. Here we report a class of soft 3D network materials that can offer defect-insensitive, nonlinear mechanical responses closely matched with those of biological tissues. This material system exploits a lattice configuration with different 3D topologies, where 3D helical microstructures that connect the lattice nodes serve as building blocks of the network. By tailoring geometries of helical microstructures or lattice topologies, a wide range of desired anisotropic J-shaped stress–strain curves can be achieved. Demonstrative applications of the developed conducting 3D network materials with bio-mimetic mechanical properties suggest potential uses in flexible bio-integrated devices.

The development of artificial 3D soft materials and device systems that can reproduce the nonlinear, anisotropic mechanical properties of biological tissues remains challenging. Here, the authors design a class of soft 3D network materials that can offer defect-insensitive, nonlinear mechanical responses closely matched with those of biological tissues.

Solitary waves in a nonintegrable chain with double-well potentials

We study solitary waves in a one-dimensional lattice of identical masses that are connected in series by nonlinear springs. The potential of each spring is nonconvex, where two disjoint convex regions, phase I and phase II, are separated by a concave, spinodal region. Consequently, the force-strain relation of the spring is nonmonotonous, which gives rise to a bistable behavior. Based on analytical treatment, with some approximations, combined with extensive numerical simulations, we are able to reveal important insights. For example, we find that the solitary-wave solution is indifferent to the energy barrier that separates the two energy wells associated with phase I and phase II, and that the shape of the wave can be described by means of merely two scalar properties of the potential of the springs, namely, the ratio of stiffness in phase II and phase I, and the ratio between the Maxwell's force and corresponding transition strain. The latter ratio provides a useful measure for the significance of the spinodal region. Linear stability of the solitary-wave solution is studied analytically using the Vakhitov-Kolokolov criterion applied to the approximate solutions obtained in the first part. These results are validated by numerical simulations. We find that the solitary-wave solution is stable provided that its velocity is higher than some critical value. It is shown that, practically, the solitary waves are stable for almost the entire range of possible wave velocities. This is also manifested in the interaction between two solitary waves or between a solitary wave and a wall (rigid boundary). Such interaction results in a minor change of height and shape of the solitary wave along with the formation of a trail of small undulations that follow the wave, as expected in a nonintegrable system. Even after a significant number of interactions the changes in the wave height and shape are minor, suggesting that the bistable chain may be a useful platform for delivering information over long distances, even concurrently with additional information (other solitary waves) passing through the chain.

Propagation of pop ups in kirigami shells

Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets, the ligaments buckle simultaneously as Euler columns, leading to a continuous phase transition; here, we demonstrate that kirigami shells can also support discontinuous phase transitions. Specifically, we show via a combination of experiments, numerical simulations, and theoretical analysis that, in cylindrical kirigami shells, the snapping-induced curvature inversion of the initially bent ligaments results in a pop-up process that first localizes near an imperfection and then, as the deformation is increased, progressively spreads through the structure. Notably, we find that the width of the transition zone as well as the stress at which propagation of the instability is triggered can be controlled by carefully selecting the geometry of the cuts and the curvature of the shell. Our study significantly expands the ability of existing kirigami metamaterials and opens avenues for the design of the next generation of responsive surfaces as demonstrated by the design of a smart skin that significantly enhances the crawling efficiency of a simple linear actuator.

Toughening stretchable fibers via serial fracturing of a metallic core

Tough, biological materials (e.g., collagen or titin) protect tissues from irreversible damage caused by external loads. Mimicking these protective properties is important in packaging and in emerging applications such as durable electronic skins and soft robotics. This paper reports the formation of tough, metamaterial-like core-shell fibers that maintain stress at the fracture strength of a metal throughout the strain of an elastomer. The shell experiences localized strain enhancements that cause the higher modulus core to fracture repeatedly, increasing the energy dissipated during extension. Normally, fractures are catastrophic. However, in this architecture, the fractures are localized to the core. In addition to dissipating energy, the metallic core provides electrical conductivity and enables repair of the fractured core for repeated use. The fibers are 2.5 times tougher than titin and hold more than 15,000 times their own weight for a period 100 times longer than a hollow elastomeric fiber.

3D printing of twisting and rotational bistable structures with tuning elements

Three-dimensional (3D) printing is ideal for the fabrication of various customized 3D components with fine details and material-design complexities. However, most components fabricated so far have been static structures with fixed shapes and functions. Here we introduce bistability to 3D printing to realize highly-controlled, reconfigurable structures. Particularly, we demonstrate 3D printing of twisting and rotational bistable structures. To this end, we have introduced special joints to construct twisting and rotational structures without post-assembly. Bistability produces a well-defined energy diagram, which is important for precise motion control and reconfigurable structures. Therefore, these bistable structures can be useful for simplified motion control in actuators or for mechanical switches. Moreover, we demonstrate tunable bistable components exploiting shape memory polymers. We can readjust the bistability-energy diagram (barrier height, slope, displacement, symmetry) after printing and achieve tunable bistability. This tunability can significantly increase the use of bistable structures in various 3D-printed components.

Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study

Unidirectional, bidirectional and tridirectional Buckling-based Negative Stiffness (BNS) lattice metamaterials are designed by adding prefabricated curved beams into multidimensional rigid frames. Finite Element Analysis models are built, and their mechanical performance is investigated and discussed. First, geometric parameters of the curved beam were systematically studied with numerical analyses and the results were validated by theoretical solutions. Next, within unidirectional designs of different layer numbers, the basic properties of multilayer BNS metamaterials were revealed via quasi-static compressions. Then, the bidirectional and tridirectional designs were loaded on orthogonal axes to research both the quasi-static and dynamic behaviors. For dynamic analysis conditions, simulation scenarios of different impact velocities were implemented and compared. The results demonstrate that the proposed numerical analysis step has accurately predicted the force-displacement relations of both the curved beam and multilayer designs and the relations can be tuned via different geometric parameters. Moreover, the macroscopic performance of the metamaterials is sensitive to the rigidity of supporting frames. The shock force during impact is reduced down below the buckling thresholds of metamaterial designs and sharp impact damage is avoided. The presented metamaterials are able to undergo multiaxial stress conditions while retaining the negative stiffness effect and energy-absorbing nature and possess abundant freedom of parametric design, which is potentially useful in shock and vibration engineering.

Magnetoactive Acoustic Metamaterials

Acoustic metamaterials with negative constitutive parameters (modulus and/or mass density) have shown great potential in diverse applications ranging from sonic cloaking, abnormal refraction and superlensing, to noise canceling. In conventional acoustic metamaterials, the negative constitutive parameters are engineered via tailored structures with fixed geometries; therefore, the relationships between constitutive parameters and acoustic frequencies are typically fixed to form a 2D phase space once the structures are fabricated. Here, by means of a model system of magnetoactive lattice structures, stimuli-responsive acoustic metamaterials are demonstrated to be able to extend the 2D phase space to 3D through rapidly and repeatedly switching signs of constitutive parameters with remote magnetic fields. It is shown for the first time that effective modulus can be reversibly switched between positive and negative within controlled frequency regimes through lattice buckling modulated by theoretically predicted magnetic fields. The magnetically triggered negative-modulus and cavity-induced negative density are integrated to achieve flexible switching between single-negative and double-negative. This strategy opens promising avenues for remote, rapid, and reversible modulation of acoustic transportation, refraction, imaging, and focusing in subwavelength regimes.

Programmable Self-Locking Origami Mechanical Metamaterials

Developing mechanical metamaterials with programmable properties is an emerging topic receiving wide attention. While the programmability mainly originates from structural multistability in previously designed metamaterials, here it is shown that nonflat-foldable origami provides a new platform to achieve programmability via its intrinsic self-locking and reconfiguration capabilities. Working with the single-collinear degree-4 vertex origami tessellation, it is found that each unit cell can self-lock at a nonflat configuration and, therefore, possesses wide design space to program its foldability and relative density. Experiments and numerical analyses are combined to demonstrate that by switching the deformation modes of the constituent cell from prelocking folding to postlocking pressing, its stiffness experiences a sudden jump, implying a limiting-stopper effect. Such a stiffness jump is generalized to a multisegment piecewise stiffness profile in a multilayer model. Furthermore, it is revealed that via strategically switching the constituent cells' deformation modes through passive or active means, the n-layer metamaterial's stiffness is controllable among 2ⁿ target stiffness values. Additionally, the piecewise stiffness can also trigger bistable responses dynamically under harmonic excitations, highlighting the metamaterial's rich dynamic performance. These unique characteristics of self-locking origami present new paths for creating programmable mechanical metamaterials with in situ controllable mechanical properties.

Auxetic Mechanical Metamaterials to Enhance Sensitivity of Stretchable Strain Sensors

Stretchable strain sensors play a pivotal role in wearable devices, soft robotics, and Internet-of-Things, yet these viable applications, which require subtle strain detection under various strain, are often limited by low sensitivity. This inadequate sensitivity stems from the Poisson effect in conventional strain sensors, where stretched elastomer substrates expand in the longitudinal direction but compress transversely. In stretchable strain sensors, expansion separates the active materials and contributes to the sensitivity, while Poisson compression squeezes active materials together, and thus intrinsically limits the sensitivity. Alternatively, auxetic mechanical metamaterials undergo 2D expansion in both directions, due to their negative structural Poisson's ratio. Herein, it is demonstrated that such auxetic metamaterials can be incorporated into stretchable strain sensors to significantly enhance the sensitivity. Compared to conventional sensors, the sensitivity is greatly elevated with a 24-fold improvement. This sensitivity enhancement is due to the synergistic effect of reduced structural Poisson's ratio and strain concentration. Furthermore, microcracks are elongated as an underlying mechanism, verified by both experiments and numerical simulations. This strategy of employing auxetic metamaterials can be further applied to other stretchable strain sensors with different constituent materials. Moreover, it paves the way for utilizing mechanical metamaterials into a broader library of stretchable electronics.

Shape-matching soft mechanical metamaterials

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce "shape-matching" metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier's series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices.

Thermal wave: from nonlocal continuum to molecular dynamics

To accommodate effects of thermomass and size-dependency of thermophysical properties on heat transport and to remove the theoretical singularity of temperature gradients across the thermal wavefront NL FTPL heat conduction, corroborated with MD simulation, is introduced.

Multistable Shape-Reconfigurable Architected Materials

Multistable shape-reconfigurable architected materials encompassing living hinges and enabling combinations of high strength, high volumetric change, and complex shape-morphing patterns are introduced. Analytical and numerical investigations, validated by experiments, are performed to characterize the mechanical behavior of the proposed materials. The proposed architected materials can be constructed from virtually any base material, at any length scale and dimensionality.

Three-Dimensional Polymeric Mechanical Metamaterials Fabricated by Multibeam Interference Lithography with the Assistance of Plasma Etching

The pentamode structure is a type of mechanical metamaterial that displays dramatically different bulk and shear modulus responses. In this study, a face-centered cubic (FCC) polymeric microstructure was fabricated by using SU8 negative-type photoresists and multibeam interference exposure. Isotropic plasma etching is used to control the solid-volume fraction; for the first time, we obtained a structure with the minimum solid-volume fraction as low as 15% that still exhibited high structural integrity. Using this method, we reduced the width of atom-to-atom connections by up to 40 nm. We characterize the effect of the connection area on the anisotropy of the mechanical properties using simulations. Nanoindentation measurements were also conducted to evaluate the energy dissipation by varying the connection area. The Young's/shear modulus ratio is 5 times higher for the etched microstructure than that of the bulk SU8 materials. The use of interference lithography may enable the properties of microscale materials to be engineered for various applications, such as MEMS.

Tensional acoustomechanical soft metamaterials

We create acoustomechanical soft metamaterials whose response to uniaxial tensile stressing can be easily tailored by programming acoustic wave inputs, resulting in force versus stretch curves that exhibit distinct monotonic, s-shape, plateau and non-monotonic snapping behaviors. We theoretically demonstrate this unique metamaterial by considering a thin soft material sheet impinged by two counter-propagating ultrasonic wave inputs across its thickness and stretched by an in-plane uniaxial tensile force. We establish a theoretical acoustomechanical model to describe the programmable mechanics of such soft metamaterial, and introduce the first- and second-order tangential stiffness of its force versus stretch curve to boundary different behaviors that appear during deformation. The proposed phase diagrams for the underlying nonlinear mechanics show promising prospects for designing tunable and switchable photonic/phononic crystals and microfluidic devices that harness snap-through instability.