Digital Mechanical Metamaterial with Programmable Functionality.

Digitization has brought a new era to the world, liberating information from physical media. The material structure-property relation is high-dimensional and nonlinear, and the digitization of structure-property relations may bring unprecedented functional programmability and diversity. Here, a new concept of digital mechanical metamaterial (DMM) is presented, where property design is realized by programming the digital states of the DMM to decouple the design of the structure and property. Transforming the binary stable states of a curved beam to the digital bit, one unit cell of DMM manifests three distinct deformation responses under compression, i.e., compression-twist coupling (CTC), compression-shear coupling (CSC), and pure compression (PC). These deformation modes show notable differences in motion and stiffness, which, by digitally programming a series of DMM, can yield a spectrum of functionalities, including information encryption, stress-strain relation customization, energy absorption in cushioning, effective vibration isolation, and tunable force transmission. This study pioneers a versatile material design paradigm that provides much greater freedom for the property design of intelligent mechanical metamaterials.

Tailoring Stress-Strain Curves of Flexible Snapping Mechanical Metamaterial for On-Demand Mechanical Responses via Data-Driven Inverse Design.

By incorporating soft materials into the architecture, flexible mechanical metamaterials enable promising applications, e.g., energy modulation, and shape morphing, with a well-controllable mechanical response, but suffer from spatial and temporal programmability towards higher-level mechanical intelligence. One feasible solution is to introduce snapping structures and then tune their responses by accurately tailoring the stress-strain curves. However, owing to the strongly coupled nonlinearity of structural deformation and material constitutive model, it is difficult to deduce their stress-strain curves using conventional ways. Here, a machine learning pipeline is trained with the finite element analysis data that considers those strongly coupled nonlinearities to accurately tailor the stress-strain curves of snapping metamaterialfor on-demand mechanical response with an accuracy of 97.41%, conforming well to experiment. Utilizing the established approach, the energy absorption efficiency of the snapping-metamaterial-based device can be tuned within the accessible range to realize different rebound heights of a falling ball, and soft actuators can be spatially and temporally programmed to achieve synchronous and sequential actuation with a single energy input. Purely relying on structure designs, the accurately tailored metamaterials increase the devices' tunability/programmability. Such an approach can potentially extend to similar nonlinear scenarios towards predictable or intelligent mechanical responses.

Adaptive plasticity of auxetic Kirigami hydrogel fabricated from anisotropic swelling of cellulose nanofiber film.

Hydrogels are flexible materials that typically accommodate elongation with positive Poisson's ratios. Auxetic property, i.e., the negative Poisson's ratio, of elastic materials can be macroscopically implemented by the structural design of the continuum. We realize it without mold for hydrogel made of cellulose nanofibers (CNFs). The complex structural design of auxetic Kirigami is first implemented on the dry CNF film, i.e., so-called nanopaper, by laser processing, and the CNF hydrogel is formed by dipping the film in liquid water. The CNF films show anisotropic swelling where drastic volumetric change mainly originates from increase in the thickness. This anisotropy makes the design and fabrication of the emergent Kirigami hydrogel straightforward. We characterize the flexibility of this mechanical metamaterial made of hydrogel by cyclic tensile loading starting from the initial end-to-end distance of dry sample. The tensile load at the maximum strain decreases with the increasing number of cycles. Furthermore, the necessary work up to the maximum strain even decreases to the negative value, while the work of restoration to the original end-to-end distance increases from the negative value to the positive. The equilibrium strain where the force changes the sign increases to reach a plateau. This plastic deformation due to the cyclic loading can be regarded as the adaptive response without fracture to the applied dynamic loading input.

Highly anisotropic swelling-based gelation of dry film of cellulose nanofibers enables development of emergent hydrogel Kirigami with auxetic behavior. Furthermore, adaptive response to the iterative loading condition is found.

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.

Piezo-Wormbots for Continuous Crawling.

Biomimetic soft robots are typically made of soft materials with bioinspired configurations. However, their locomotion is activated and manipulated by externally controlled soft actuators. In this study, piezo-wormbots were developed by automatically triggering the mechanical metamaterial-inspired soft actuator to mimic the continuous crawling of inchworms without manipulation, where crawling was controlled by the deformation of the piezo-wormbots themselves. We designed the flexible piezo-wormbots with an actuator to generate bending deformation under continuous inflation, piezoelectric rubber to automatically create internal excitation voltage to trigger deflation, as well as true legs and prolegs to convert the bending-recovering sequence into continuous crawling. We tailored the actuator to enhance the crawling performance and found that the response was critically affected by the leg pattern, inflation-to-deflation time duration ratio, air pressure, and ground environment. We observed satisfactory locomotion performance for the following tasks (pushing boxes and approaching a predefined target) through accurate self-actuated crawling under up to 51 continuous bending cycles. The maximum crawling velocity of the piezo-wormbots was found to be 16.6 mm/s, resulting in a maximum body length per second (BL/s) of 0.13, which is comparable to those of most natural inchworms (0.1-0.3 BL/s). This study offers new insight into bioinspired soft robotics and expands its biomimetic performance to continuously autonomous locomotion.

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.

Omnidirectional Configuration of Stretchable Strain Sensor Enabled by the Strain Engineering with Chiral Auxetic Metamaterial.

An electromechanical interface plays a pivotal role in determining the performance of a stretchable strain sensor. The intrinsic mechanical property of the elastomer substrate prevents the efficient modulation of the electromechanical interface, which limits the further evolution of a stretchable strain sensor. In this study, a chiral auxetic metamaterial (CAM) is incorporated into the elastomer substrate of a stretchable strain sensor to override the deformation behavior of the pristine device and regulate the device performance. The tunable isotropic Poisson's ratio (from 0.37 to -0.25) achieved by the combination of CAM and elastomer substrate endows the stretchable strain sensor with significantly enhanced sensitivity (53-fold improvement) and excellent omnidirectional sensing ability. The regulation mechanism associated with crack propagation on the deformed substrate is also revealed with finite element simulations and experiments. The demonstration of on-body monitoring of human physiological signals and a smart training assistant for trampoline gymnastics with the CAM-incorporated strain sensor further illustrates the benefits of omnidirectionally enhanced performance.

A bioinspired 3D-printable flexure joint with cellular mechanical metamaterial architecture for soft robotic hands.

Compliant flexure joints have been widely used for cable-driven soft robotic hands and grippers due to their safe interaction with humans and objects. This paper presents a soft and compliant revolute flexure joint based on the auxetic cellular mechanical metamaterials with a heterogeneous structure. The heterogeneous architecture of the proposed metamaterial flexure joint (MFJ), which is inspired by the human finger joints, provides mechanically tunable multi-stiffness bending motion and large range of bending angle in comparison to conventional flexure joints. The multi-level variation of the joint stiffness over the range of bending motion can be tuned through the geometrical parameters of the cellular mechanical metamaterial unit cells. The proposed flexure joints are 3D printed with single flexible material in monolithic fashion using a standard benchtop 3D printer. The application of the MFJ is demonstrated in robotic in-hand manipulation and grasping thin and deformable objects such as wires and cables. The results show the capability and advantages of the proposed MFJ in soft robotic grippers and highly functional bionic hands.

Disrupting Density-Dependent Property Scaling in Hierarchically Architected Foams.

Creating lightweight architected foams as strong and stiff as their bulk constituent material has been a long-standing effort. Typically, the strength, stiffness, and energy dissipation capabilities of materials severely degrade with increasing porosity. We report nearly constant stiffness-to-density and energy dissipation-to-density ratios─a linear scaling with density─in hierarchical vertically aligned carbon nanotube (VACNT) foams with a mesoscale architecture of hexagonally close-packed thin concentric cylinders. We observe a transformation from an inefficient higher-order density-dependent scaling of the average modulus and energy dissipated to a desirable linear scaling as a function of the increasing internal gap between the concentric cylinders. From the scanning electron microscopy of the compressed samples, we observe an alteration in the deformation modality from local shell buckling at a smaller gap to column buckling at a larger gap, governed by an enhancement in the number density of CNTs with the increasing internal gap, leading to better structural stiffness at low densities. This transformation simultaneously improves the foams' damping capacity and energy absorption efficiency as well and allows us to access the ultra-lightweight regime in the property space. Such synergistic scaling of material properties is desirable for protective applications in extreme environments.

Bioinspired Nanonetwork Hydroxyapatite from Block Copolymer Templated Synthesis for Mechanical Metamaterials.

Inspired by Mantis shrimp, this work aims to suggest a bottom-up approach for the fabrication of nanonetwork hydroxyapatite (HAp) thin film using self-assembled polystyrene-block-polydimethylsiloxane (PS-b-PDMS) block copolymer (BCP) with a diamond nanostructure as a template for templated sol-gel reaction. By introducing poly(vinylpyrrolidone) (PVP) into precursors of calcium nitrate tetrahydrate and triethyl phosphite, which limits the growth of forming HAp nanoparticles, well-ordered nanonetwork HAp thin film can be fabricated. Based on nanoindentation results, the well-ordered nanonetwork HAp shows high energy dissipation compared to the intrinsic HAp. Moreover, the uniaxial microcompression test for the nanonetwork HAp shows high energy absorption per volume and high compression strength, outperforming many cellular materials due to the topologic effect of the well-ordered network at the nanoscale. This work highlights the potential of exploiting BCP templated synthesis to fabricate ionic solid materials with a well-ordered nanonetwork monolith, giving rise to the brittle-to-ductile transition, and thus appealing mechanical properties with the character of mechanical metamaterials.

Programming Soft Shape-Morphing Systems by Harnessing Strain Mismatch and Snap-Through Bistability: A Review.

Multi-modal and controllable shape-morphing constitutes the cornerstone of the functionalization of soft actuators/robots. Involving heterogeneity through material layout is a widely used strategy to generate internal mismatches in active morphing structures. Once triggered by external stimuli, the entire structure undergoes cooperative deformation by minimizing the potential energy. However, the intrinsic limitation of soft materials emerges when it comes to applications such as soft actuators or load-bearing structures that require fast response and large output force. Many researchers have explored the use of the structural principle of snap-through bistability as the morphing mechanisms. Bistable or multi-stable mechanical systems possess more than one local energy minimum and are capable of resting in any of these equilibrium states without external forces. The snap-through motion could overcome energy barriers to switch among these stable or metastable states with dramatically distinct geometries. Attributed to the energy storage and release mechanism, such snap-through transition is quite highly efficient, accompanied by fast response speed, large displacement magnitude, high manipulation strength, and moderate driving force. For example, the shape-morphing timescale of conventional hydrogel systems is usually tens of minutes, while the activation time of hydrogel actuators using the elastic snapping instability strategy can be reduced to below 1 s. By rationally embedding stimuli-responsive inclusions to offer the required trigger energy, various controllable snap-through actuations could be achieved. This review summarizes the current shape-morphing programming strategies based on mismatch strain induced by material heterogeneity, with emphasis on how to leverage snap-through bistability to broaden the applications of the shape-morphing structures in soft robotics and mechanical metamaterials.

Complex pathways and memory in compressed corrugated sheets.

The nonlinear response of driven complex materials-disordered magnets, amorphous media, and crumpled sheets-features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry. We show how manipulation of the boundaries allows us to elicit multiple targeted pathways from a single sample. In all cases, each state in the pathway can be encoded by the binary state of material bits called hysterons, and the strength of their interactions plays a crucial role. In particular, as function of increasing interaction strength, we observe Preisach pathways, expected in systems of independently switching hysterons; scrambled pathways that evidence hitherto unexplored interactions between these material bits; and accumulator pathways which leverage these interactions to perform an elementary computation. Our work opens a route to probe, manipulate, and understand complex pathways, impacting future applications in soft robotics and information processing in materials.

Auxetic vibration behaviours of periodic tetrahedral units with a shared edge.

A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress-strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus.

Nanolatticed Architecture Mitigates Damage in Shark Egg Cases.

Structural versatility and multifunctionality of biological materials have resulted in countless bioinspired strategies seeking to emulate the properties of nature. The nanostructured egg case of swell sharks is one of the toughest permeable membranes known and, thus, presents itself as a model system for materials where the conflicting properties, strength and porosity, are desirable. The egg case possesses an intricately ordered structure that is designed to protect delicate embryos from the external environment while enabling respiratory and metabolic exchange, achieving a tactical balance between conflicting properties. Herein, structural analyses revealed an enabling nanolattice architecture that constitutes a Bouligand-like nanoribbon hierarchical assembly. Three distinct hierarchical architectural adaptations enhance egg case survival: Bouligand-like organization for in-plane isotropic reinforcement, noncylindrical nanoribbons maximizing interfacial stress distribution, and highly ordered nanolattices enabling permeability and lattice-governed toughening mechanisms. These discoveries provide fundamental insights for the improvement of multifunctional membranes, fiber-reinforced soft composites, and mechanical metamaterials.

Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study.

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson's ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts-one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson's ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler-Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson's ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson's ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson's ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.

Comparison of Transmission Measurement Methods of Elastic Waves in Phononic Band Gap Materials.

Periodic cellular structures can exhibit metamaterial properties, such as phononic band gaps. In order to detect these frequency bands of strong wave attenuation experimentally, several devices for wave excitation and measurement can be applied. In this work, piezoelectric transducers are utilized to excite two additively manufactured three-dimensional cellular structures. For the measurement of the transmission factor, we compare two methods. First, the transmitted waves are measured with the same kind of piezoelectric transducer. Second, a laser Doppler vibrometer is employed to scan the mechanical vibrations of the sample on both the emitting and receiving surfaces. The additional comparison of two different methods of spatial averaging of the vibrometer data, that is, the quadratic mean and arithmetic mean, provides insight into the way the piezoelectric transducers convert the transmitted signal. Experimental results are supported by numerical simulations of the dispersion relation and a simplified transmission simulation.

Characterization, stability, and application of domain walls in flexible mechanical metamaterials.

Domain walls, commonly occurring at the interface of different phases in solid-state materials, have recently been harnessed at the structural scale to enable additional modes of functionality. Here, we combine experimental, numerical, and theoretical tools to investigate the domain walls emerging upon uniaxial compression in a mechanical metamaterial based on the rotating-squares mechanism. We first show that these interfaces can be generated and controlled by carefully arranging a few phase-inducing defects. We establish an analytical model to capture the evolution of the domain walls as a function of the applied deformation. We then employ this model as a guideline to realize interfaces of complex shape. Finally, we show that the engineered domain walls modify the global response of the metamaterial and can be effectively exploited to tune its stiffness as well as to guide the propagation of elastic waves.

Analysis of Antichiral Thermomechanical Metamaterials with Continuous Negative Thermal Expansion Properties.

Negative thermal expansion is an interesting and appealing phenomenon for various scientific and engineering applications, while rarely occurring in natural materials. Here, using a universal antichiral metamaterial model with bimetal beams or strips, a generic theory has been developed to predict magnitude of the negative thermal expansion effect from model parameters. Thermal expansivity of the metamaterial is written as an explicit function of temperature and only three design parameters: relative node size, chirality angle, and a bimetal constant. Experimental measurements follow theoretical predictions well, where thermal expansivity in the range of negative 0.0006-0.0041 °C-1 has been seen.

Guided transition waves in multistable mechanical metamaterials.

Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave's direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces). The outcome is a predictable and programmable strongly nonlinear metamaterial motion with potential for, for example, propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

Femur Auxetic Meta-Implants with Tuned Micromotion Distribution.

Stress shielding and micromotions are the most significant problems occurring at the bone-implants interface due to a mismatch of their mechanical properties. Mechanical 3D metamaterials, with their exceptional behaviour and characteristics, can provide an opportunity to solve the mismatch of mechanical properties between the bone and implant. In this study, a new porous femoral hip meta-implant with graded Poisson's ratio distribution was introduced and its results were compared to three other femoral hip implants (one solid implant, and two porous meta-implants, one with positive and the other with a negative distribution of Poisson's ratio) in terms of stress and micromotion distributions. For this aim, first, a well-known auxetic 3D re-entrant structure was studied analytically, and precise closed-form analytical relationships for its elastic modulus and Poisson's ratio were derived. The results of the analytical solution for mechanical properties of the 3D re-entrant structure presented great improvements in comparison to previous analytical studies on the structure. Moreover, the implementation of the re-entrant structure in the hip implant provided very smooth results for stress and strain distributions in the lattice meta-implants and could solve the stress shielding problem which occurred in the solid implant. The lattice meta-implant based on the graded unit cell distribution presented smoother stress-strain distribution in comparison with the other lattice meta-implants. Moreover, the graded lattice meta-implant gave minimum areas of local stress and local strain concentration at the contact region of the implants with the internal bone surfaces. Among all the cases, the graded meta-implant also gave micromotion levels which are the closest to values reported to be desirable for bone growth (40 µm).