Compaction through buckling in 2D periodic, soft and porous structures: effect of pore shape

Harnessing plasticity in sequential metamaterials for ideal shock absorption

Mechanical metamaterials exhibit interesting properties such as high stiffness at low density1-3, enhanced energy absorption3,4, shape morphing5-7, sequential deformations8-11, auxeticity12-14 and robust waveguiding15,16. Until now, metamaterial design has primarily relied on geometry, and materials nonlinearities such as viscoelasticity, fracture and plasticity have been largely left out of the design rationale. In fact, plastic deformations have been traditionally seen as a failure mode and thereby carefully avoided1,3,17,18. Here we embrace plasticity instead and discover a delicate balance between plasticity and buckling instability, which we term 'yield buckling'. We exploit yield buckling to design metamaterials that buckle sequentially in an arbitrary large sequence of steps whilst keeping a load-bearing capacity. We make use of sequential yield buckling to create metamaterials that combine stiffness and dissipation-two properties that are usually incompatible-and that can be used several times. Hence, our metamaterials exhibit superior shock-absorption performance. Our findings add plasticity to the metamaterial toolbox and make mechanical metamaterials a burgeoning technology with serious potential for mass production.

Soft Magnetoelastic Tactile Multi-Sensors with Energy-Absorbing Properties for Self-Powered Human-Machine Interfaces

Tactile sensors play a key role in human-machine interfaces (HMIs) for augmented and virtual reality, point-of-care devices, and human-robot collaboration, which show the promise of revolutionizing our ways of life. Here, we present a sensor (EMTS) that utilizes the magnetoelastic effect in a soft metamaterial to convert mechanical pressure into electrical signals. With this unique mechanism, the proposed EMTS simultaneously possesses self-powering, waterproof, and compliant features. The soft metamaterial is essentially a porous magnetoelastomer structure designed based on the Fourier series expansion, which allows for programmable mechanical response and sensing performance of the EMTS. Fabricated by simple 3D-printed molds, the EMTS also holds potential for low-cost production. Particularly, the porous magnetoelastomer structure comes with selectable buckling instabilities that can significantly enhance biomechanical-to-electrical energy conversion. Also, with the embedded magnetic microparticles, the energy-absorbing performance of the sensor is greatly improved, which is highly beneficial to HMIs. To pursue practical applications, the EMTSs are further integrated with two systems as control and perception modules. It is demonstrated that the EMTS is able to identify different hand gestures to control a lighting system even in a high-humidity environment. Also, the EMTS stands out for its superior capability of simultaneous impact perception and energy absorption in drop tests. Overall, with its compelling array of features, the presented EMTS gives impetus to multi-sensing technology and practically enables a variety of HMI applications.

A seamless auxetic substrate with a negative Poisson's ratio of -1

Auxetic metamaterials are a unique class of materials or structures with a negative Poisson's ratio and a wide array of functionalities. However, their inherent porosity presents challenges in practical applications. Filling the inherent perforations while preserving their unique auxeticity is difficult because it demands the seamless integration of components that have highly distinct mechanical characteristics. Here we introduce a seamless auxetic substrate film capable of achieving a negative Poisson's ratio of -1, the theoretical limit of isotropic materials. This breakthrough is realized by incorporating a highly rigid auxetic structure reinforced by glass-fabric, with surface-flattening soft elastomers. We effectively optimize the mechanical properties of these components by systematic experimental and theoretical investigations into the effects of relative differences in the moduli of the constituents. Using the developed auxetic film we demonstrate an image distortion-free display having 25 PPI resolution of micro-LEDs that is capable of 25% stretching without performance degradation.

Suppressing torsional buckling in auxetic meta-shells

Take a thin cylindrical shell and twist it; it will buckle immediately. Such unavoidable torsional buckling can lead to systemic failure, for example by disrupting the blood flow through arteries. In this study, we prevent this torsional buckling instability using a combination of auxeticity and orthotropy in cylindrical metamaterial shells with a holey pattern. When the principal axes of the orthotropic meta-shell are relatively aligned with that of the compressive component of the applied stress during twisting, the meta-shell uniformly shrinks in the radial direction as a result of a local buckling instability. This shrinkage coincides with a softening-stiffening transition that leads to ordered stacking of unit cells along the compressive component of the applied stress. These transitions due to local instabilities circumvent the usual torsional instability even under a large twist angle. This study highlights the potential of tailoring anisotropy and programming instabilities in metamaterials, with potential applications in designing mechanical elements for soft robotics, biomechanics or fluidics. As an example of such applications, we demonstrate soft torsional compressor for generating pulsatile flows through a torsion release mechanism.

Auxetic Biomedical Metamaterials for Orthopedic Surgery Applications: A Comprehensive Review

Poisson's ratio in auxetic materials shifts from typically positive to negative, causing lateral expansion during axial tension. This scale-independent characteristic, originating from tailored architectures, exhibits specific physical properties, including energy adsorption, shear resistance, and fracture resistance. These metamaterials demonstrate exotic mechanical properties with potential applications in several engineering fields, but biomedical applications seem to be one of the most relevant, with an increasing number of articles published in recent years, which present opportunities ranging from cellular repair to organ reconstruction with outstanding mechanical performance, mechanical conduction, and biological activity compared with traditional biomedical metamaterials. Therefore, focusing on understanding the potential of these structures and promoting theoretical and experimental investigations into the benefits of their unique mechanical properties is necessary for achieving high-performance biomedical applications. Considering the demand for advanced biomaterial implants in surgical technology and the profound advancement of additive manufacturing technology that are particularly relevant to fabricating complex and customizable auxetic mechanical metamaterials, this review focuses on the fundamental geometric configuration and unique physical properties of negative Poisson's ratio materials, then categorizes and summarizes auxetic material applications across some surgical departments, revealing efficacy in joint surgery, spinal surgery, trauma surgery, and sports medicine contexts. Additionally, it emphasizes the substantial potential of auxetic materials as innovative biomedical solutions in orthopedics and demonstrates the significant potential for comprehensive surgical application in the future.

Superlative mechanical energy absorbing efficiency discovered through self-driving lab-human partnership

Energy absorbing efficiency is a key determinant of a structure's ability to provide mechanical protection and is defined by the amount of energy that can be absorbed prior to stresses increasing to a level that damages the system to be protected. Here, we explore the energy absorbing efficiency of additively manufactured polymer structures by using a self-driving lab (SDL) to perform >25,000 physical experiments on generalized cylindrical shells. We use a human-SDL collaborative approach where experiments are selected from over trillions of candidates in an 11-dimensional parameter space using Bayesian optimization and then automatically performed while the human team monitors progress to periodically modify aspects of the system. The result of this human-SDL campaign is the discovery of a structure with a 75.2% energy absorbing efficiency and a library of experimental data that reveals transferable principles for designing tough structures.

Digital Mechanical Metamaterial: Encoding Mechanical Information with Graphical Stiffness Pattern for Adaptive Soft Machines

Inspired by the adaptive features exhibited by biological organisms like the octopus, soft machines that can tune their shape and mechanical properties have shown great potential in applications involving unstructured and continuously changing environments. However, current soft machines are far from achieving the same level of adaptability as their biological counterparts, hampered by limited real-time tunability and severely deficient reprogrammable space of properties and functionalities. As a steppingstone toward fully adaptive soft robots and smart interactive machines, an encodable multifunctional material that uses graphical stiffness patterns is introduced here to in situ program versatile mechanical capabilities without requiring additional infrastructure. Through independently switching the digital binary stiffness states (soft or rigid) of individual constituent units of a simple auxetic structure with elliptical voids, in situ and gradational tunability is demonstrated here in various mechanical qualities such as shape-shifting and -memory, stress-strain response, and Poisson's ratio under compressive load as well as application-oriented functionalities such as tunable and reusable energy absorption and pressure delivery. This digitally programmable material is expected to pave the way toward multienvironment soft robots and interactive machines.

A Metamaterial Computational Multi-Sensor of Grip-Strength Properties with Point-of-Care Human-Computer Interaction

Grip strength is a biomarker of frailty and an evaluation indicator of brain health, cardiovascular morbidity, and psychological health. Yet, the development of a reliable, interactive, and point-of-care device for comprehensive multi-sensing of hand grip status is challenging. Here, a relation between soft buckling metamaterial deformations and built piezoelectric voltage signals is uncovered to achieve multiple sensing of maximal grip force, grip speed, grip impulse, and endurance indicators. A metamaterial computational sensor design is established by hyperelastic model that governs the mechanical characterization, machine learning models for computational sensing, and graphical user interface to provide visual cues. A exemplify grip measurement for left and right hands of seven elderly campus workers is conducted. By taking indicators of grip status as input parameters, human-computer interactive games are incorporated into the computational sensor to improve the user compliance with measurement protocols. Two elderly female schizophrenic patients are participated in the real-time interactive point-of-care grip assessment and training for potentially sarcopenia screening. The attractive features of this advanced intelligent metamaterial computational sensing system are crucial to establish a point-of-care biomechanical platform and advancing the human-computer interactive healthcare, ultimately contributing to a global health ecosystem.

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.

Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure

Nanopapers fabricated from cellulose nanofibers (CNFs) are flexible for bending while they are rather stiff against stretching, which is a common feature shared by conventional paper-based materials in contrast with typical elastomers. Cellulose nanopapers have therefore been expected to be adopted in flexible device applications, but their lack of stretching flexibility can be a bottleneck for specific situations. The high stretching flexibility of nanopapers can effectively be realized by the implementation of Kirigami structures, but there has never been discussion on the mechanical resilience where stretching is not a single event. In this study, we experimentally revealed the mechanical resilience of nanopapers implemented with Kirigami structures for stretching flexibility by iterative tensile tests with large strains. Although the residual strains are found to increase with larger maximum strains and a larger number of stretching cycles, the high mechanical resilience was also confirmed, as expected for moderate maximum strains. Furthermore, we also showed that the round edges of cut patterns instead of bare sharp ones significantly improve the mechanical resilience for harsh stretching conditions. Thus, the design principle of relaxing the stress focusing is not only important in circumventing fractures but also in realizing mechanical resilience.

Review: Auxetic Polymer-Based Mechanical Metamaterials for Biomedical Applications

Over the last three decades but more particularly during the last 5 years, auxetic mechanical metamaterials constructed from precisely architected polymer-based materials have attracted considerable attention due to their fascinating mechanical properties. These materials present a negative Poisson's ratio and therefore unusual mechanical behavior, which has resulted in enhanced static modulus, energy adsorption, and shear resistance, as compared with the bulk properties of polymers. Novel advanced polymer processing and fabrication techniques, and in particular additive manufacturing, allow one to design complex and customizable polymer architectures that are particularly relevant to fabricate auxetic mechanical metamaterials. Although these metamaterials exhibit exotic mechanical properties with potential applications in several engineering fields, biomedical applications seem to be one of the most relevant with a growing number of articles published over recent years. As a result, special focus is needed to understand the potential of these structures and foster theoretical and experimental investigations on the potential benefits of the unusual mechanical properties of these materials on the way to high performance biomedical applications. The present Review provides up to date information on the recent progress of polymer-based auxetic mechanical metamaterials mainly fabricated using additive manufacturing methods with a special focus toward biomedical applications including tissue engineering as well as medical devices including stents and sensors.

Design for Additive Manufacturing and Investigation of Surface-Based Lattice Structures for Buckling Properties Using Experimental and Finite Element Methods

Additive Manufacturing (AM) is rapidly evolving due to its unlimited design freedom to fabricate complex and intricate light-weight geometries with the use of lattice structure that have potential applications including construction, aerospace and biomedical applications, where mechanical properties are the prime focus. Buckling instability in lattice structures is one of the main failure mechanisms that can lead to major failure in structural applications that are subjected to compressive loads, but it has yet to be fully explored. This study aims to investigate the effect of surface-based lattice structure topologies and structured column height on the critical buckling load of lattice structured columns. Four different triply periodic minimal surface (TPMS) lattice topologies were selected and three design configurations (unit cells in x, y, z axis), i.e., 2 × 2 × 4, 2 × 2 × 8 and 2 × 2 × 16 column, for each structure were designed followed by printing using HP MultiJet fusion. Uni-axial compression testing was performed to study the variation in critical buckling load due to change in unit cell topology and column height. The results revealed that the structured column possessing Diamond structures shows the highest critical buckling load followed by Neovius and Gyroid structures, whereas the Schwarz-P unit cell showed least resistance to buckling among the unit cells analyzed in this study. In addition to that, the Diamond design showed a uniform decrease in critical buckling load with a column height maximum of 5193 N, which makes it better for applications in which the column’s height is relatively higher while the Schwarz-P design showed advantages for low height column maximum of 2271 N. Overall, the variations of unit cell morphologies greatly affect the critical buckling load and permits the researchers to select different lattice structures for various applications as per load/stiffness requirement with different height and dimensions. Experimental results were validated by finite element analysis (FEA), which showed same patterns of buckling while the numerical values of critical buckling load show the variation to be up to 10%.

Investigation of Modified Auxetic Structures from Rigid Rotating Squares

Auxetic structures exhibit unusual changes in size, expanding laterally upon stretching instead of contracting. This paper presents this effect in a failsafe mode in structures made of rigid squares. We applied the concept of auxetic structures made of rigid rotating squares (from Grima and Evans) and offer a novel solution for connecting them. By introducing axes of rotation on the surface of the squares, a reliable working system is obtained, free from stress, in which the squares can come into contact with each other and completely cover the surface of the structure, or, in the open position, form regularly arranged pores. Herein, we present a new 2D auxetic metamaterial that is mathematically generated based on a theoretical relationship of the angle between the edges of a square and the position of the axis of rotation. Physical models were generated in the form of a planar structure and in the form of a circular closed structure. Such physical models confirmed our initial considerations and the geometrical relationships, offering new application possibilities. The novel structure that was designed and manufactured for the purpose of the paper can be considered as a new proposal in the market of auxetic materials.

Inverted and Programmable Poynting Effects in Metamaterials

The Poynting effect generically manifests itself as the extension of the material in the direction perpendicular to an applied shear deformation (torsion) and is a material parameter hard to design. Unlike isotropic solids, in designed structures, peculiar couplings between shear and normal deformations can be achieved and exploited for practical applications. Here, a metamaterial is engineered that can be programmed to contract or extend under torsion and undergo nonlinear twist under compression. First, it is shown that the system exhibits a novel type of inverted Poynting effect, where axial compression induces a nonlinear torsion. Then the Poynting modulus of the structure is programmed from initial negative values to zero and positive values via a pre-compression applied prior to torsion. The work opens avenues for programming nonlinear elastic moduli of materials and tuning the couplings between shear and normal responses by rational design. Obtaining inverted and programmable Poynting effects in metamaterials inspires diverse applications from designing machine materials, soft robots, and actuators to engineering biological tissues, implants, and prosthetic devices functioning under compression and torsion.

Investigation of Compression and Buckling Properties of a Novel Surface-Based Lattice Structure Manufactured Using Multi Jet Fusion Technology

Lattice structures possess many superior properties over solid materials and conventional structures. Application-oriented lattice structure designs have become a choice in many industries, such as aerospace, automotive applications, construction, biomedical applications, and footwear. However, numerical and empirical analyses are required to predict mechanical behavior under different boundary conditions. In this article, a novel surface-based structure named O-surface structure is designed and inspired by existing Triply Periodic Minimal Surface morphologies in a particular sea urchin structure. For comparison, both structures were designed with two different height configurations and investigated for mechanical performance in terms of compression, local buckling, global buckling, and post-buckling behavior. Both simulation and experimental methods were carried out to reveal these aforementioned properties of samples fabricated by multi jet fusion technology. The sea urchin structure exhibited better mechanical strength than its counterpart, with the same relative density almost two-folds higher in the compressive response. However, the O-surface structure recorded more excellent energy absorption and flexible behavior under compression. Additionally, the compression behavior of the O-surface structure was progressive from top to bottom. In contrast, the sea urchin structure was collapsed randomly due to originated cracks from unit cells' centers with local buckling effects. Moreover, the buckling direction of structures in long columns was also affected by keeping the relative density constant. Finally, based on specific strength, the O-surface structure exhibited 16-folds higher specific strength than the sea urchin structure.

Magnetic Multimaterial Printing for Multimodal Shape Transformation with Tunable Properties and Shiftable Mechanical Behaviors

Magnetic soft materials (MSMs) have shown potential in soft robotics, actuators, metamaterials, and biomedical devices because they are capable of untethered, fast, and reversible shape reconfigurations as well as controllable dynamic motions under applied magnetic fields. Recently, magnetic shape memory polymers (M-SMPs) that incorporate hard magnetic particles in shape memory polymers demonstrated superior shape manipulation performance by realizing reprogrammable, untethered, fast, and reversible shape transformation and shape locking in one material system. In this work, we develop a multimaterial printing technology for the complex structural integration of MSMs and M-SMPs to explore their enhanced multimodal shape transformation and tunable properties. By cooperative thermal and magnetic actuation, we demonstrate multiple deformation modes with distinct shape configurations, which further enable active metamaterials with tunable physical properties such as sign-change Poisson's ratio. Because of the multiphysics response of the M-MSP/MSM metamaterials, one distinct feature is their capability of shifting between various global mechanical behaviors such as expansion, contraction, shear, and bending. We anticipate that the multimaterial printing technique opens new avenues for the fabrication of multifunctional magnetic materials.

The Effect of Void Arrangement on the Pattern Transformation of Porous Soft Solids under Biaxial Loading

Structural topology and loading condition have important influences on the mechanical behaviors of porous soft solids. The porous solids are usually set to be under uniaxial tension or compression. Only a few studies have considered the biaxial loads, especially the combined loads of tension and compression. In this study, porous soft solids with oblique and square lattices of circular voids under biaxial loadings were studied through integrated experiments and numerical simulations. For the soft solids with oblique lattices of circular voids, we found a new pattern transformation under biaxial compression, which has alternating elliptic voids with an inclined angle. This kind of pattern transformation is rarely reported under uniaxial compression. Introducing tensile deformation in one direction can hamper this kind of pattern transformation under biaxial loading. For the soft solids with square lattices of voids, the number of voids cannot change their deformation behaviors qualitatively, but quantitatively. In general, our present results demonstrate that void morphology and biaxial loading can be harnessed to tune the pattern transformations of porous soft solids under large deformation. This discovery offers a new avenue for designing the void morphology of soft solids for controlling their deformation patterns under a specific biaxial stress-state.

Exploring the property space of periodic cellular structures based on crystal networks

Finding genuine novelty in cellular structures is inherently difficult due to the numerous possible topological and geometrical configurations and their complex mechanical and physical interrelations. Here, we draw inspiration from the incredibly rich collection of crystallographic periodic networks that we interpret from a structural point of view to identify and design novel cellular structures with unique properties. We provide a ready-to-use catalog with more than 17,000 unique entries and show how crystallographic symmetries relate to their mechanical properties. Our work provides a foundation to support future applications in science and engineering, ranging from mechanical and optical metamaterials, over bone tissue engineering, to the design of electrochemical devices.

The properties of periodic cellular structures strongly depend on the regular spatial arrangement of their constituent base materials and can be controlled by changing the topology and geometry of the repeating unit cell. Recent advances in three-dimensional (3D) fabrication technologies more and more expand the limits of fabricable real-world architected materials and strengthen the need of novel microstructural topologies for applications across all length scales and fields in both fundamental science and engineering practice. Here, we systematically explore, interpret, and analyze publicly available crystallographic network topologies from a structural point of view and provide a ready-to-use unit cell catalog with more than 17,000 unique entries in total. We show that molecular crystal networks with atoms connected by chemical bonds can be interpreted as cellular structures with nodes connected by mechanical bars. By this, we identify new structures with extremal properties as well as known structures such as the octet-truss or the Kelvin cell and show how crystallographic symmetries are related to the mechanical properties of the structures. Our work provides inspiration for the discovery of novel cellular structures and paves the way for computational methods to explore and design microstructures with unprecedented properties, bridging the gap between microscopic crystal chemistry and macroscopic structural engineering.

3D printable biomimetic rod with superior buckling resistance designed by machine learning

Our mother nature has been providing human beings with numerous resources to inspire from, in building a finer life. Particularly in structural design, plenteous notions are being drawn from nature in enhancing the structural capacity as well as the appearance of the structures. Here plant stems, roots and various other structures available in nature that exhibit better buckling resistance are mimicked and modeled by finite element analysis to create a training database. The finite element analysis is validated by uniaxial compression to buckling of 3D printed biomimetic rods using a polymeric ink. After feature identification, forward design and data filtering are conducted by machine learning to optimize the biomimetic rods. The results show that the machine learning designed rods have 150% better buckling resistance than all the rods in the training database, i.e., better than the nature's counterparts. It is expected that this study opens up a new opportunity to design engineering rods or columns with superior buckling resistance such as in bridges, buildings, and truss structures.

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.

A data-driven computational scheme for the nonlinear mechanical properties of cellular mechanical metamaterials under large deformation

Cellular mechanical metamaterials are a special class of materials whose mechanical properties are primarily determined by their geometry. However, capturing the nonlinear mechanical behavior of these materials, especially those with complex geometries and under large deformation, can be challenging due to inherent computational complexity. In this work, we propose a data-driven multiscale computational scheme as a possible route to resolve this challenge. We use a neural network to approximate the effective strain energy density as a function of cellular geometry and overall deformation. The network is constructed by "learning" from the data generated by finite element calculation of a set of representative volume elements at cellular scales. This effective strain energy density is then used to predict the mechanical responses of cellular materials at larger scales. Compared with direct finite element simulation, the proposed scheme can reduce the computational time up to two orders of magnitude. Potentially, this scheme can facilitate new optimization algorithms for designing cellular materials of highly specific mechanical properties.

Cellular Auxetic Structures for Mechanical Metamaterials: A Review

Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called "designed materials" or "architectured materials" and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson's ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.

Engineering Acoustic Metamaterials for Sound Absorption: From Uniform to Gradient Structures

The traditional sound absorption problem has not been completely resolved over the last 200 years. At every stage, its research has changed depending on practical requirements and current technologies. Phononic crystals (PCs) and acoustic metamaterials (AMs) have gained attention because of their extensive investigation and development over the past 30 years. Especially, the use of these materials brings new vitality into the traditional sound absorption problem to figure out broad working band and low-frequency absorption. This review highlights recent progress in sound absorption—from airborne to waterborne absorption—and gradient-index AMs. Progress in gradient-index AMs is singled out because of their favorable impedance matching, good viscous and thermal dissipation, and lengthened propagation paths compared with those of other materials. The progress in sound absorption of PCs and AMs is promising to serve as the next-generation sound absorbing materials, trap and reuse acoustic energy, and attenuate earthquake/tsunami wave in the future.

Effect of Two-Dimensional Re-Entrant Honeycomb Configuration on Elastoplastic Performance of Perforated Steel Plate

Perforated steel plates with regularly shaped holes are already widely employed as steel dampers, which dissipate seismic energy through plastic deformation of steel. As a typical auxetic structure, two-dimensional (2D) re-entrant honeycomb configurations have characteristics of large deformation and good energy absorption. However, research on the effects of these configurations on the mechanical performance of steel is limited. This paper investigated the auxetic properties of perforated steel plates with re-entrant hexagon holes. Repetitive units are controlled by three parameters, hole ratio, re-entrant angle, and chamfer radius. Elastoplastic behavior and damage under large deformation were studied via tension tests and finite element (FE) analysis based on a micromechanics-based ductile fracture model. The effects of different parameters on mechanical properties of configurations were analyzed and discussed. The static performance of the perforated steel plates obtained in this study provides a good basis for its further dynamic study under large deformation.

Exploring multistability in prismatic metamaterials through local actuation

Metamaterials are artificial materials that derive their unusual properties from their periodic architecture. Some metamaterials can deform their internal structure to switch between different properties. However, the precise control of these deformations remains a challenge, as these structures often exhibit non-linear mechanical behavior. We introduce a computational and experimental strategy to explore the folding behavior of a range of 3D prismatic building blocks that exhibit controllable multifunctionality. By applying local actuation patterns, we are able to explore and visualize their complex mechanical behavior. We find a vast and discrete set of mechanically stable configurations, that arise from local minima in their elastic energy. Additionally these building blocks can be assembled into metamaterials that exhibit similar behavior. The mechanical principles on which the multistable behavior is based are scale-independent, making our designs candidates for e.g., reconfigurable acoustic wave guides, microelectronic mechanical systems and energy storage systems.

So far, mostly 2D building blocks have been used to make origami-type multistable metamaterials that can keep their shape when deformed. Here, the authors introduce a local actuation strategy to explore the energy landscape of multistable metamaterials fabricated from 3D prismatic building blocks.

Buckling and Post-Buckling Behavior of Uniform and Variable-Density Lattice Columns Fabricated Using Additive Manufacturing

Lattice structures are known for their high strength-to-weight ratio, multiple functionalities, lightweight, stiffness, and energy absorption capabilities and potential applications in aerospace, automobile, and biomedical industry. To reveal the buckling (global and local) and post-buckling behavior of different lattice morphologies, both experimental and simulation-based studies were carried out. Additionally, a variable-density lattice structure was designed and analyzed to achieve the optimal value of critical buckling load. Latticed columns were fabricated using polyamide 12 material on multi jet fusion 3D printer. The results exhibited that the buckling in lattice columns depends on the distribution of mass, second moment of inertia I, diameter and position of vertical beams, number of horizontal or inclined beams, and location and angle of the beams that support the vertical beams. The number of horizontal and inclined beams and their thickness has an inverse relation with buckling; however, this trend changes after approaching a critical point. It is revealed that vertical beams are more crucial for buckling case, when compared with horizontal or inclined beams; however, material distribution in inclined or horizontal orientation is also critical because they provide support to vertical beams to behave as a single body to bear the buckling load. The results also revealed that the critical buckling load could be increased by designing variable density cellular columns in which the beams at the outer edges of the column are thicker compared with inner beams. However, post-buckling behavior of variable density structures is brittle and local when compared with uniform density lattice structures.

Exploiting spatial heterogeneity and response characterization in non-uniform architected materials inspired by slime mould growth

Inspired by shape-shifting features of slime mould growth, we implement a computational algorithm to study the nutrient-induced pattern formation and transition of slime mould. We then translate the learned principles into the design and characterization of cellular materials, with particular focus on the issue of spatial heterogeneity due to the nature of the non-uniform, asymmetric pattern. Guided by clustering analysis, compression tests on 3D-printed samples, and numerical simulations by finite element models, we were able to categorize patterns with certain geometric features (such as layout and symmetry) and found similar mechanical response features, indicating high tailorability of non-uniform architected materials. This study paves the road for the advanced computer-aided design of architected materials and its potential in the development of innovative engineering mechanical devices and structural systems.

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multibranched. We study the number Δ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that Δ is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.

3D Printing of Auxetic Metamaterials with Digitally Reprogrammable Shape

Two-dimensional lattice structures with specific geometric features have been reported to have a negative Poisson's ratio, termed as auxetic metamaterials, that is, stretching-induced expansion in the transversal direction. In this paper, we designed a novel auxetic metamaterial; by utilizing the shape memory effect of the constituent materials, the in-plane moduli and Poisson's ratios can be continuously tailored. During deformation, the curved meshes ensure the rotation of the mesh joints to achieve auxetics. The rotations of these mesh joints are governed by the mesh curvature, which continuously changes during deformation. Because of the shape memory effect, the mesh curvature after printing can be programmed, which can be used to tune the rotation of the mesh joints and the mechanical properties of auxetic metamaterial structures, including Poisson's ratios, moduli, and fracture strains. Using the finite element method, the deformation of these auxetic meshes was analyzed. Finally, we designed and fabricated gradient/digital patterns and cylindrical shells and used the auxetics and shape memory effects to reshape the printed structures.

Complexity in phase transforming pin-jointed auxetic lattices

We demonstrate the complexity that can exist in the modelling of auxetic lattices. By introducing pin-jointed members and large deformations to the analysis of a re-entrant structure, we create a material which has both auxetic and non-auxetic phases. Such lattices exhibit complex equilibrium behaviour during the highly nonlinear transition between these two states. The local response is seen to switch many times between stable and unstable states, exhibiting both positive and negative stiffnesses. However, there is shown to exist an underlying emergent modulus over the transitional phase, to describe the average axial stiffness of a system comprising a large number of cells.

Domain Formations and Pattern Transitions via Instabilities in Soft Heterogeneous Materials

Experimental observations of domain formations and pattern transitions in soft particulate composites under large deformations are reported herein. The system of stiff inclusions periodically distributed in a soft elastomeric matrix experiences dramatic microstructure changes upon the development of elastic instabilities. In the experiments, the formation of microstructures with antisymmetric domains and their geometrically tailored evolution into a variety of patterns of cooperative particle rearrangements are observed. Through experimental and numerical analyses, it is shown that these patterns can be tailored by tuning the initial microstructural periodicity and concentration of the inclusions. Thus, these fully determined new patterns can be achieved by fine tuning of the initial microstructure.

Vacuum-Actuated Bending for Grasping

Soft robotic devices typically are actuated with the application of a positive pressure (compared to ambient pressure), but some exciting work has been done with negative pressure application, with advantages for safety and robustness. Here, we present a negative pressure bending actuator inspired by previous work by Yang et al., fabricated using rapid prototyping techniques and elastomeric polymers. We describe the mechanical behavior of the system from a cellular solids perspective, showing the steps needed for the analysis and characterization of future similar systems. We find good agreement between experimentally measured values of displacement and force generated in atmospheric pressure conditions.

Auxetic multiphase soft composite material design through instabilities with application for acoustic metamaterials

We investigate the instability-induced pattern transformations in 3D-printed soft composites consisting of stiff inclusions and voids periodically distributed in a soft matrix. These soft auxetic composites are prone to elastic instabilities giving rise to negative Poisson's ratio (NPR) behavior. Upon reaching the instability point, the composite microstructure rearranges into a new morphology attaining an NPR regime. Remarkably, identical composites can morph into distinct patterns depending on the loading direction. These fully determined instability-induced distinct patterns are characterized by significantly different NPR behaviors, thus, giving rise to enhanced tunability of the composite properties. Finally, we illustrate a potential application of these reversible pattern transformations as tunable acoustic-elastic metamaterials capable of selectively filtering low frequency ranges controlled by deformation.

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.

Design for Additive Bio-Manufacturing: From Patient-Specific Medical Devices to Rationally Designed Meta-Biomaterials

Recent advances in additive manufacturing (AM) techniques in terms of accuracy, reliability, the range of processable materials, and commercial availability have made them promising candidates for production of functional parts including those used in the biomedical industry. The complexity-for-free feature offered by AM means that very complex designs become feasible to manufacture, while batch-size-indifference enables fabrication of fully patient-specific medical devices. Design for AM (DfAM) approaches aim to fully utilize those features for development of medical devices with substantially enhanced performance and biomaterials with unprecedented combinations of favorable properties that originate from complex geometrical designs at the micro-scale. This paper reviews the most important approaches in DfAM particularly those applicable to additive bio-manufacturing including image-based design pipelines, parametric and non-parametric designs, metamaterials, rational and computationally enabled design, topology optimization, and bio-inspired design. Areas with limited research have been identified and suggestions have been made for future research. The paper concludes with a brief discussion on the practical aspects of DfAM and the potential of combining AM with subtractive and formative manufacturing processes in so-called hybrid manufacturing processes.

Tailoring broadband acoustic energy suppression characteristics of double porosity metamaterials with compression constraints and mass inclusions

A metamaterial that capitalizes on a double porosity architecture is introduced for controlling broadband acoustic energy suppression properties. When the metamaterial is subjected to static compressive stress, a global rotation of the internal metamaterial architecture is induced that softens the effective stiffness and results in a considerable means to tailor wave transmission and absorption properties. The influences of mass inclusions and compression constraints are examined by computational and experimental efforts. The results indicate that the mass inclusions and applied constraints can significantly impact the absorption and transmission properties of double porosity metamaterials, while the appropriate utilization of the underlying poroelastic media can further magnify these parametric influences. Based on the widespread implementation of compressed poroelastic media in applications, the results of this research uncover how internal metamaterial architecture and constraints may be exploited to enhance engineering noise control properties while using less poroelastic material mass.

Auxetic mechanical metamaterials

We review the topology–property relationship and the spread of Young's modulus–Poisson's ratio duos in three main classes of auxetic metamaterials.

Programmable mechanical metamaterials: the role of geometry

We experimentally and numerically study the role of geometry for the mechanics of biholar metamaterials, which are quasi-2D slabs of rubber patterned by circular holes of two alternating sizes. We recently showed how the response to uniaxial compression of these metamaterials can be programmed by lateral confinement. In particular, there is a range of confining strains ε_x for which the resistance to compression becomes non-trivial-non-monotonic or hysteretic-in a range of compressive strains ε_y. Here we show how the dimensionless geometrical parameters t and χ, which characterize the wall thickness and size ratio of the holes that pattern these metamaterials, can significantly tune these ranges over a wide range. We study the behavior for the limiting cases where the wall thickness t and the size ratio χ become large, and discuss the new physics that arises there. Away from these extreme limits, the variation of the strain ranges of interest is smooth with porosity, but the variation with size ratio evidences a cross-over at low χ from biholar to monoholar (equal sized holes) behavior, related to the elastic instabilities in purely monoholar metamaterials. Our study provides precise guidelines for the rational design of programmable biholar metamaterials, tailored to specific applications, and indicates that the widest range of programmability arises for moderate values of both t and χ.

Tensile Instability in a Thick Elastic Body

A range of instabilities can occur in soft bodies that undergo large deformation. While most of them arise under compressive forces, it has previously been shown analytically that a tensile instability can occur in an elastic block subjected to equitriaxial tension. Guided by this result, we conducted centimeter-scale experiments on thick elastomeric samples under generalized plane strain conditions and observed for the first time this elastic tensile instability. We found that equibiaxial stretching leads to the formation of a wavy pattern, as regions of the sample alternatively flatten and extend in the out-of-plane direction. Our work uncovers a new type of instability that can be triggered in elastic bodies, enlarging the design space for smart structures that harness instabilities to enhance their functionality.

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.

Tailored Buckling Microlattices as Reusable Light-Weight Shock Absorbers

Structures and materials absorbing mechanical (shock) energy commonly exploit either viscoelasticity or destructive modifications. Based on a class of uniaxial light-weight geometrically nonlinear mechanical microlattices and using buckling of inner elements, either a sequence of snap-ins followed by irreversible hysteretic - yet repeatable - self-recovery or multistability is achieved, enabling programmable behavior. Proof-of-principle experiments on three-dimensional polymer microstructures are presented.

Kirigami Nanocomposites as Wide-Angle Diffraction Gratings

Beam steering devices represent an essential part of an advanced optics toolbox and are needed in a spectrum of technologies ranging from astronomy and agriculture to biosensing and networked vehicles. Diffraction gratings with strain-tunable periodicity simplify beam steering and can serve as a foundation for light/laser radar (LIDAR/LADAR) components of robotic systems. However, the mechanical properties of traditional materials severely limit the beam steering angle and cycle life. The large strain applied to gratings can severely impair the device performance both in respect of longevity and diffraction pattern fidelity. Here, we show that this problem can be resolved using micromanufactured kirigami patterns from thin film nanocomposites based on high-performance stiff plastics, metals, and carbon nanotubes, etc. The kirigami pattern of microscale slits reduces the stochastic concentration of strain in stiff nanocomposites including those made by layer-by-layer assembly (LBL). The slit patterning affords reduction of strain by 2 orders of magnitude for stretching deformation and consequently enables reconfigurable optical gratings with over a 100% range of period tunability. Elasticity of the stiff nanocomposites and plastics makes possible cyclic reconfigurability of the grating with variable time constant that can also be referred to as 4D kirigami. High-contrast, sophisticated diffraction patterns with as high as fifth diffraction order can be obtained. The angular range of beam steering can be as large as 6.5° for a 635 nm laser beam compared to ∼1° in surface-grooved elastomer gratings and ∼0.02° in MEMS gratings. The versatility of the kirigami patterns, the diversity of the available nanocomposite materials, and their advantageous mechanical properties of the foundational materials open the path for engineering of reconfigurable optical elements in LIDARs essential for autonomous vehicles and other optical devices with spectral range determined by the kirigami periodicity.

Auxetic Perforated Mechanical Metamaterials with Randomly Oriented Cuts

Perforated systems with quasi-disordered arrays of slits are found to exhibit auxetic characteristics almost as much as their traditional ordered "rotating-squares" counterparts. This provides a highly robust methodology for constructing auxetics that may be used for various practical applications such as skin grafting, where a high degree of precision may not always be achievable.

Geometry-based control of instability patterns in cellular soft matter

Rationally designing of geometrical features can control the functionality of cellular soft matter.

Dimpled elastic sheets: a new class of non-porous negative Poisson's ratio materials

In this study, we report a novel periodic material with negative Poisson’s ratio (also called auxetic materials) fabricated by denting spherical dimples in an elastic flat sheet. While previously reported auxetic materials are either porous or comprise at least two phases, the material proposed here is non-porous and made of a homogeneous elastic sheet. Importantly, the auxetic behavior is induced by a novel mechanism which exploits the out-of-plane deformation of the spherical dimples. Through a combination of experiments and numerical analyses, we demonstrate the robustness of the proposed concept, paving the way for developing a new class of auxetic materials that significantly expand their design space and possible applications.

Snapping mechanical metamaterials under tension

A snapping mechanical metamaterial is designed, which exhibits a sequential snap-through behavior under tension. The tensile response of this mechanical metamaterial can be altered by tuning the architecture of the snapping segments to achieve a range of nonlinear mechanical responses, including monotonic, S-shaped, plateau, and non-monotonic snap-through behavior.

Discontinuous Buckling of Wide Beams and Metabeams

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.

Lattice mechanics of origami tessellations

Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there have been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.