Topology Optimized Architectures with Programmable Poisson's Ratio over Large Deformations

Imprinting reversible deformations on a compressed soft rod network

We present emergent behaviour of storing mechanical deformation in compressed soft cellular materials (a network of soft polymeric rods). Under an applied compressive strain field, the soft cellular material transits from an elastic regime to a 'pseudo-plastic' regime (not to be confused with pseudoplasticity in fluids). In the elastic phase, it is capable of forgetting (or relaxing) any applied indentation once the applied indentation is removed. This relaxation will be determined by the visco-elasticity and internal relaxation timescales in polymeric hyperelastic cellular materials. In the pseudo-plastic phase, however, the material is capable of storing local indentation (or deformation) indefinitely. This deformation can be erased via removal of the external strain field and is therefore reversible. We characterise this behaviour experimentally and present a simple model that makes use of friction for understanding this behavior.

Modulate stress distribution with bio-inspired irregular architected materials towards optimal tissue support

Natural materials typically exhibit irregular and non-periodic architectures, endowing them with compelling functionalities such as body protection, camouflage, and mechanical stress modulation. Among these functionalities, mechanical stress modulation is crucial for homeostasis regulation and tissue remodeling. Here, we uncover the relationship between stress modulation functionality and the irregularity of bio-inspired architected materials by a generative computational framework. This framework optimizes the spatial distribution of a limited set of basic building blocks and uses these blocks to assemble irregular materials with heterogeneous, disordered microstructures. Despite being irregular and non-periodic, the assembled materials display spatially varying properties that precisely modulate stress distribution towards target values in various control regions and load cases, echoing the robust stress modulation capability of natural materials. The performance of the generated irregular architected materials is experimentally validated with 3D printed physical samples - a good agreement with target stress distribution is observed. Owing to its capability to redirect loads while keeping a proper amount of stress to stimulate bone repair, we demonstrate the potential application of the stress-programmable architected materials as support in orthopedic femur restoration.

Hydrogel-Reactive-Microenvironment Powering Reconfiguration of Polymer Architectures

Reconfiguration of architected structures has great significance for achieving new topologies and functions of engineering materials. Existing reconfigurable strategies have been reported, including approaches based on heat, mechanical instability, swelling, origami/kirigami designs, and electromagnetic actuation. However, these approaches mainly involve physical interactions between the host materials and the relevant stimuli. Herein, a novel, easy-manipulated, and controllable reconfiguration strategy for polymer architectures is proposed by using a chemical reaction of host material within a hydrogel reactive microenvironment. 3D printed polycaprolactone (PCL) lattices transformed in an aqueous polyacrylamide (PAAm) hydrogel precursor solution, in which ultraviolet (UV) light triggered heterogeneous grafting polymerization between PCL and AAm. In situ microscopy shows that PCL beams go through volumetric expansion and cooperative buckling, resulting in transformation of PCL lattices into sinusoidal patterns. The transformation process can be tuned easily and patterned through the adjustment of the PCL beam diameter, unit cell width, and UV light on-off state. Controlling domain formation is achieved by using UV masks. This framework enables the design, fabrication, and programming of architected materials and inspires the development of novel 4D printing approaches.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Optimization of 3D printing parameters in polylactic acid bio-metamaterial under cyclic bending loading considering fracture features

3D printing has become a crucial additive manufacturing technique with the applications in various industries. Fused deposition modeling (FDM) is a common additive manufacturing process that offers considerable flexibility in the component fabrication through multiple parameters, which strongly influence the properties of the produced parts. This study focused on the impact of different printing parameters on the fatigue behavior of polylactic acid (PLA). The standard samples were 3D-printed with varying speed (5, 10, and 15 mm/s), print temperature (180, 210, and 240 °C), and nozzle diameter (0.2, 0.4, and 0.6 mm). The fatigue properties were evaluated through rotating bending fatigue tests, and a model was developed based on the results with a statistical analysis. The model accuracy was validated and the interactions between the parameters were analyzed. The optimization study found that a print speed of 5 mm/s, print temperature of 210 °C, and nozzle diameter of 0.2 mm were optimal. The fracture surfaces were also examined using a scanning electron microscopy, revealing the presence of crazing despite the brittle behavior of PLA.

Flexible Energy Storage Devices to Power the Future

The field of flexible electronics is a crucial driver of technological advancement, with a strong connection to human life and a unique role in various areas such as wearable devices and healthcare. Consequently, there is an urgent demand for flexible energy storage devices (FESDs) to cater to the energy storage needs of various forms of flexible products. FESDs can be classified into three categories based on spatial dimension, all of which share the features of excellent electrochemical performance, reliable safety, and superb flexibility. In this review, the application scenarios of FESDs are introduced and the main representative devices applied in disparate fields are summarized first. More specifically, it focuses on three types of FESDs in matched application scenarios from both structural and material aspects. Finally, the challenges that hinder the practical application of FESDs and the views on current barriers are presented.

Algorithmic encoding of adaptive responses in temperature-sensing multimaterial architectures

We envision programmable matters that can alter their physical properties in desirable manners based on user input or autonomous sensing. This vision motivates the pursuit of mechanical metamaterials that interact with the environment in a programmable fashion. However, this has not been systematically achieved for soft metamaterials because of the highly nonlinear deformation and underdevelopment of rational design strategies. Here, we use computational morphogenesis and multimaterial polymer 3D printing to systematically create soft metamaterials with arbitrarily programmable temperature-switchable nonlinear mechanical responses under large deformations. This is made possible by harnessing the distinct glass transition temperatures of different polymers, which, when optimally synthesized, produce local and giant stiffness changes in a controllable manner. Featuring complex geometries, the generated structures and metamaterials exhibit fundamentally different yet programmable nonlinear force-displacement relations and deformation patterns as temperature varies. The rational design and fabrication establish an objective-oriented synthesis of metamaterials with freely tunable thermally adaptive behaviors. This imbues structures and materials with environment-aware intelligence.

A data-driven framework for structure-property correlation in ordered and disordered cellular metamaterials

Extracting the relation between microstructural features and resulting material properties is essential for advancing our fundamental knowledge on the mechanics of cellular metamaterials and to enable the design of novel material systems. Here, we present a unified framework that not only allows the prediction of macroscopic properties but, more importantly, also reveals their connection to key morphological characteristics, as identified by the integration of machine-learning models and interpretability algorithms. We establish the complex manner in which strut orientation can be critical in determining effective stiffness for certain microstructures and highlight cellular metamaterials with counterintuitive material behavior. We further provide a refined version of Maxwell's criteria regarding the rigidity of frame structures and their connection to cellular metamaterials. By examining the shear moduli of these metamaterials, the mean cell compactness emerges as a key morphological feature. The generality of the proposed framework allows its extension to broader classes of architected materials as well as different properties of interest.

Self-bridging metamaterials surpassing the theoretical limit of Poisson's ratios

A hallmark of mechanical metamaterials has been the realization of negative Poisson's ratios, associated with auxeticity. However, natural and engineered Poisson's ratios obey fundamental bounds determined by stability, linearity and thermodynamics. Overcoming these limits may substantially extend the range of Poisson's ratios realizable in mechanical systems, of great interest for medical stents and soft robots. Here, we demonstrate freeform self-bridging metamaterials that synthesize multi-mode microscale levers, realizing Poisson's ratios surpassing the values allowed by thermodynamics in linear materials. Bridging slits between microstructures via self-contacts yields multiple rotation behaviors of microscale levers, which break the symmetry and invariance of the constitutive tensors under different load scenarios, enabling inaccessible deformation patterns. Based on these features, we unveil a bulk mode that breaks static reciprocity, providing an explicit and programmable way to manipulate the non-reciprocal transmission of displacement fields in static mechanics. Besides non-reciprocal Poisson's ratios, we also realize ultra-large and step-like values, which make metamaterials exhibit orthogonally bidirectional displacement amplification, and expansion under both tension and compression, respectively.

3D Printed Graphene-Based Metamaterials: Guesting Multi-Functionality in One Gain

Advanced functional materials with fascinating properties and extended structural design have greatly broadened their applications. Metamaterials, exhibiting unprecedented physical properties (mechanical, electromagnetic, acoustic, etc.), are considered frontiers of physics, material science, and engineering. With the emerging 3D printing technology, the manufacturing of metamaterials becomes much more convenient. Graphene, due to its superior properties such as large surface area, superior electrical/thermal conductivity, and outstanding mechanical properties, shows promising applications to add multi-functionality into existing metamaterials for various applications. In this review, the aim is to outline the latest developments and applications of 3D printed graphene-based metamaterials. The structure design of different types of metamaterials and the fabrication strategies for 3D printed graphene-based materials are first reviewed. Then the representative explorations of 3D printed graphene-based metamaterials and multi-functionality that can be introduced with such a combination are further discussed. Subsequently, challenges and opportunities are provided, seeking to point out future directions of 3D printed graphene-based metamaterials.

Three-Dimensionally Printed Expandable Structural Electronics Via Multi-Material Printing Room-Temperature-Vulcanizing (RTV) Silicone/Silver Flake Composite and RTV

Three-dimensional (3D) printing has various applications in many fields, such as soft electronics, robotic systems, biomedical implants, and the recycling of thermoplastic composite materials. Three-dimensional printing, which was only previously available for prototyping, is currently evolving into a technology that can be utilized by integrating various materials into customized structures in a single step. Owing to the aforementioned advantages, multi-functional 3D objects or multi-material-designed 3D patterns can be fabricated. In this study, we designed and fabricated 3D-printed expandable structural electronics in a substrateless auxetic pattern that can be adapted to multi-dimensional deformation. The printability and electrical conductivity of a stretchable conductor (Ag-RTV composite) were optimized by incorporating a lubricant. The Ag-RTV and RTV were printed in the form of conducting voxels and frame voxels through multi-nozzle printing and were arranged in a negative Poisson's ratio pattern with a missing rib structure, to realize an expandable passive component. In addition, the expandable structural electronics were embedded in a soft actuator via one-step printing, confirming the possibility of fabricating stable interconnections in expanding deformation via a missing rib pattern.

Auxetic Kirigami Metamaterials upon Large Stretching

Auxetic kirigami metamaterials (KMs) attain negative Poisson's ratios with periodic slender cuts on thin sheets. The existing thin auxetic KMs forfeit auxeticity under large tensions because their auxeticity mainly arises from in-plane deformation, but out-of-plane buckling could arise to cause large deviations, and thicker KMs would suffer from stress failure. This paper proposes a novel family of KMs that can realize and retain auxeticity for up to 0.50 applied strains by fully exploiting out-of-plane buckling in the design model. Numerical and experimental results show that the designed KMs possess unique properties that are not exhibited by existing KMs, including a wide range of negative Poisson's ratios with designable variation modes under different applied strains, sheet thickness-insensitive auxeticity, and excellent shape recoverability. A potential application is exemplified with a scenario that they are designed as a stretchable display without image distortions under large tensions. The proposed auxetic KMs open new opportunities for the design of specific functional devices in areas of compliant robotics, bio-medical devices, and flexible electronics.

Engineering zero modes in transformable mechanical metamaterials

In the field of flexible metamaterial design, harnessing zero modes plays a key part in enabling reconfigurable elastic properties of the metamaterial with unconventional characteristics. However, only quantitative enhancement of certain properties succeeds in most cases rather than qualitative transformation of the metamaterials' states or/and functionalities, due to the lack of systematic designs on the corresponding zero modes. Here, we propose a 3D metamaterial with engineered zero modes, and experimentally demonstrate its transformable static and dynamic properties. All seven types of extremal metamaterials ranging from null-mode (solid state) to hexa-mode (near-gaseous state) are reported to be reversibly transformed from one state to another, which is verified by the 3D-printed Thermoplastic Polyurethanes prototypes. Tunable wave manipulations are further investigated in 1D-, 2D- and 3D-systems. Our work sheds lights on the design of flexible mechanical metamaterials, which can be potentially extended from the mechanical to the electro-magnetite, the thermal or other types.

Inverse Design of Energy-Absorbing Metamaterials by Topology Optimization

Compared with the forward design method through the control of geometric parameters and material types, the inverse design method based on the target stress-strain curve is helpful for the discovery of new structures. This study proposes an optimization strategy for mechanical metamaterials based on a genetic algorithm and establishes a topology optimization method for energy-absorbing structures with the desired stress-strain curves. A series of structural mutation algorithms and design-domain-independent mesh generation method are developed to improve the efficiency of finite element analysis and optimization iteration. The algorithm realizes the design of ideal energy-absorbing structures, which are verified by additive manufacturing and experimental characterization. The error between the stress-strain curve of the designed structure and the target curve is less than 5%, and the densification strain reaches 0.6. Furthermore, special attention is paid to passive pedestrian protection and occupant protection, and a reasonable solution is given through the design of a multiplatform energy-absorbing structure. The proposed topology optimization framework provides a new solution path for the elastic-plastic large deformation problem that is unable to be resolved by using classical gradient algorithms or genetic algorithms, and simplifies the design process of energy-absorbing mechanical metamaterials.

Embedded 3D Printing of Multimaterial Polymer Lattices via Graph-Based Print Path Planning

Recent advances in computational design and 3D printing enable the fabrication of polymer lattices with high strength-to-weight ratio and tailored mechanics. To date, 3D lattices composed of monolithic materials have primarily been constructed due to limitations associated with most commercial 3D printing platforms. Here, freeform fabrication of multi-material polymer lattices via embedded three-dimensional (EMB3D) printing is demonstrated. An algorithm is developed first that generates print paths for each target lattice based on graph theory. The effects of ink rheology on filamentary printing and the effects of the print path on resultant mechanical properties are then investigated. By co-printing multiple materials with different mechanical properties, a broad range of periodic and stochastic lattices with tailored mechanical responses can be realized opening new avenues for constructing architected matter.

Deep-learning-based inverse design of three-dimensional architected cellular materials with the target porosity and stiffness using voxelized Voronoi lattices

Architected cellular materials are a class of artificial materials with cellular architecture-dependent properties. Typically, designing cellular architectures paves the way to generate architected cellular materials with specific properties. However, most previous studies have primarily focused on a forward design strategy, wherein a geometry is generated using computer-aided design modeling, and its properties are investigated experimentally or via simulations. In this study, we developed an inverse design framework for a disordered architected cellular material (Voronoi lattices) using deep learning. This inverse design framework is a three-dimensional conditional generative adversarial network (3D-CGAN) trained based on supervised learning using a dataset consisting of voxelized Voronoi lattices and their corresponding relative densities and Young's moduli. A well-trained 3D-CGAN adopts variational sampling to generate multiple distinct Voronoi lattices with the target relative density and Young's modulus. Consequently, the mechanical properties of the 3D-CGAN generated Voronoi lattices are validated through uniaxial compression tests and finite element simulations. The inverse design framework demonstrates potential for use in bone implants, where scaffold implants can be automatically generated with the target relative density and Young's modulus.

Discrete breathers in a mechanical metamaterial

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

Flexible Metamaterial Electronics

Over the last decade, extensive efforts have been made on utilizing advanced materials and structures to improve the properties and functionalities of flexible electronics. While the conventional ways are approaching their natural limits, a revolutionary strategy, namely metamaterials, is emerging toward engineering structural materials to break the existing fetters. Metamaterials exhibit supernatural physical behaviors, in aspects of mechanical, optical, thermal, acoustic, and electronic properties that are inaccessible in natural materials, such as tunable stiffness or Poisson's ratio, manipulating electromagnetic or elastic waves, and topological and programmable morphability. These salient merits motivate metamaterials as a brand-new research direction and have inspired extensive innovative applications in flexible electronics. Here, such a groundbreaking interdisciplinary field is first coined as "flexible metamaterial electronics," focusing on enhancing and innovating functionalities of flexible electronics via the design of metamaterials. Herein, the latest progress and trends in this infant field are reviewed while highlighting their potential value. First, a brief overview starts with introducing the combination of metamaterials and flexible electronics. Then, the developed applications are discussed, such as self-adaptive deformability, ultrahigh sensitivity, and multidisciplinary functionality, followed by the discussion of potential prospects. Finally, the challenges and opportunities facing flexible metamaterial electronics to advance this cutting-edge field are summarized.

Machine learning-based prediction and inverse design of 2D metamaterial structures with tunable deformation-dependent Poisson's ratio

With the aid of recent efficient and prior knowledge-free machine learning (ML) algorithms, extraordinary mechanical properties such as negative Poisson's ratio have extensively promoted the diverse designs of metamaterials with distinctive cellular structures. However, most existing ML approaches applied to the design of metamaterials are primarily based on a single property value with the assumption that the Poisson's ratio of a material is stationary, neglecting the dynamic variability of Poisson's ratio, termed deformation-dependent Poisson's ratio, during the loading process that a metamaterial other than conventional materials may experience. This paper first proposes a crystallographic symmetry-based methodology to build 2D metamaterials with complex but patterned topological structures, and then converts them into computational models suitable for molecular dynamics simulations. Then, we employ an integrated approach, consisting of molecular dynamics simulations capable of generating and collecting a large dataset for training/validation, in addition to ML algorithms (CNN and Cycle-GAN) able to predict the dynamic characteristics of Poisson's ratio and offer the inverse design of a metamaterial structure based on a target quasi-continuous Poisson's ratio-strain curve, to eventually unravel the underlying mechanism and design principles of 2D metamaterial structures with tunable Poisson's ratio. The close match between the predefined Poisson's ratio response and that from the generated structure validates the feasibility of the proposed ML model. Owing to the high efficiency and complete independence from prior knowledge, our proposed approach offers a novel and robust technique for the prediction and inverse design of metamaterial structures with tailored deformation-dependent Poisson's ratio, an unprecedented property attractive in flexible electronics, soft robotics, and nanodevices.

Auxetic structures used in kinesiology tapes can improve form-fitting and personalization

Each year 65% of young athletes and 25% of physically active adults suffer from at least one musculoskeletal injury that prevents them from continuing with physical activity, negatively influencing their physical and mental well-being. The treatment of musculoskeletal injuries with the adhesive elastic kinesiology tape (KT) decreases the recovery time. Patients can thus recommence physical exercise earlier. Here, a novel KT based on auxetic structures is proposed to simplify the application procedure and allow personalization. This novel KT exploits the form-fitting property of auxetics as well as their ability to simultaneously expand in two perpendicular directions when stretched. The auxetic contribution is tuned by optimizing the structure design using analytical equations and experimental measurements. A reentrant honeycomb topology is selected to demonstrate the validity of the proposed approach. Prototypes of auxetic KT to treat general elbow pains and muscle tenseness in the forearm are developed.

Tunable hydrogen enhancement of Ce3+ doped CdS with different Poisson's ratio support

In this article, a 3D photocatalytic support with different Poisson's ratio was used for the first time to control the photocatalytic production rate of hydrogen. It was created by a stereo-lithography method, and the support with the most negative Poisson's ratio got the best result. The Poisson's ratio of the 3D structure influences the rate of hydrogen production, and it is important for the photocatalyst supports to be porous for light to penetrate into them. A series of Ce doped CdS photocatalysts were produced and immobilized on 3D multicellular Al₂O₃ supports. By changing the proportion of Ce³⁺ doped into the CdS photocatalysts 1 % of Ce³⁺ exhibited optimal hydrogen production, which was 222.9 % compared to that of the pure CdS. Using the 3D photocatalytic support with different Poisson's ratio, the photocatalytic production rate of hydrogen increased by 128 %.

Transition fronts and their universality classes

Steadily moving transition (switching) fronts, associated with local transformation, symmetry breaking, or collapse, are among the most important dynamic coherent structures. The nonlinear mechanical waves of this type play a major role in many modern applications involving the transmission of mechanical information in systems ranging from crystal lattices and metamaterials to macroscopic civil engineering structures. While many different classes of such dynamic fronts are known, the interrelation between them remains obscure. Here we consider a minimal prototypical mechanical system, the Fermi-Pasta-Ulam (FPU) chain with piecewise linear nonlinearity, and show that there are exactly three distinct classes of switching fronts, which differ fundamentally in how (and whether) they produce and transport oscillations. The fact that all three types of fronts could be obtained as explicit Wiener-Hopf solutions of the same discrete FPU problem allows one to identify the exact mathematical origin of the particular features of each class. To make the underlying Hamiltonian dynamics analytically transparent, we construct a minimal quasicontinuum approximation of the FPU model that captures all three classes of the fronts and reveals interrelation between them. This approximation is of higher order than conventional ones (KdV, Boussinesq) and involves mixed space-time derivatives. The proposed framework unifies previous attempts to classify the mechanical transition fronts as radiative, dispersive, topological, or compressive and categorizes them instead as irreducible types of dynamic lattice defects.

Direct Ink Writing: A 3D Printing Technology for Diverse Materials

Additive manufacturing (AM) has gained significant attention due to its ability to drive technological development as a sustainable, flexible, and customizable manufacturing scheme. Among the various AM techniques, direct ink writing (DIW) has emerged as the most versatile 3D printing technique for the broadest range of materials. DIW allows printing of practically any material, as long as the precursor ink can be engineered to demonstrate appropriate rheological behavior. This technique acts as a unique pathway to introduce design freedom, multifunctionality, and stability simultaneously into its printed structures. Here, a comprehensive review of DIW of complex 3D structures from various materials, including polymers, ceramics, glass, cement, graphene, metals, and their combinations through multimaterial printing is presented. The review begins with an overview of the fundamentals of ink rheology, followed by an in-depth discussion of the various methods to tailor the ink for DIW of different classes of materials. Then, the diverse applications of DIW ranging from electronics to food to biomedical industries are discussed. Finally, the current challenges and limitations of this technique are highlighted, followed by its prospects as a guideline toward possible futuristic innovations.

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.

Sequential metamaterials with alternating Poisson's ratios

Mechanical metamaterials have been designed to achieve custom Poisson’s ratios via the deformation of their microarchitecture. These designs, however, have yet to achieve the capability of exhibiting Poisson’s ratios that alternate by design both temporally and spatially according to deformation. This capability would enable dynamic shape-morphing applications including smart materials that process mechanical information according to multiple time-ordered output signals without requiring active control or power. Herein, both periodic and graded metamaterials are introduced that leverage principles of differential stiffness and self-contact to passively achieve sequential deformations, which manifest as user-specified alternating Poisson’s ratios. An analytical approach is provided with a complementary software tool that enables the design of such materials in two- and three-dimensions. This advance in design capability is due to the fact that the tool computes sequential deformations more than an order of magnitude faster than contemporary finite-element packages. Experiments on macro- and micro-scale designs validate their predicted alternating Poisson’s ratios.

Mechanical metamaterials with alternating Poisson’s ratios are desirable for shape-morphing applications. Here the authors achieve this by utilizing self-contacting hard stops and flexible elements of different stiffnesses to achieve time-ordered sequential deformation.

Review on Development and Application of 3D-Printing Technology in Textile and Fashion Design

Three-dimensional printing (3DP) allows for the creation of highly complex products and offers customization for individual users. It has generated significant interest and shows great promise for textile and fashion design. Here, we provide a timely and comprehensive review of 3DP technology for the textile and fashion industries according to recent advances in research. We describe the four 3DP methods for preparing textiles; then, we summarize three routes to use 3DP technology in textile manufacturing, including printing fibers, printing flexible structures and printing on textiles. In addition, the applications of 3DP technology in fashion design, functional garments and electronic textiles are introduced. Finally, the challenges and prospects of 3DP technology are discussed.

Origin of nonlinear force distributions in a composite system

Composite materials have been actively developed in recent years because they are highly functional such as lightweight, high yield strength, and superior load response. In spite of importance of the composite materials, mechanisms of the mechanical responses of composites have been unrevealed. Here, in order to understand the mechanical responses of composites, we investigated the origin and nature of the force distribution in heterogeneous materials using a soft particle model. We arranged particles with different softness in a lamellar structure and then we applied homogeneous pressure to the top surface of the system. It is found that the density in each region differently changes and then the density difference induces a nonlinear force distribution. In addition, it is found that the attractive interaction suppresses the density difference and then the force distribution is close to the theoretical prediction. Those findings may lead material designs for functional composite materials.

Recent Progress in Active Mechanical Metamaterials and Construction Principles

Active mechanical metamaterials (AMMs) (or smart mechanical metamaterials) that combine the configurations of mechanical metamaterials and the active control of stimuli-responsive materials have been widely investigated in recent decades. The elaborate artificial microstructures of mechanical metamaterials and the stimulus response characteristics of smart materials both contribute to AMMs, making them achieve excellent properties beyond the conventional metamaterials. The micro and macro structures of the AMMs are designed based on structural construction principles such as, phase transition, strain mismatch, and mechanical instability. Considering the controllability and efficiency of the stimuli-responsive materials, physical fields such as, the temperature, chemicals, light, electric current, magnetic field, and pressure have been adopted as the external stimuli in practice. In this paper, the frontier works and the latest progress in AMMs from the aspects of the mechanics and materials are reviewed. The functions and engineering applications of the AMMs are also discussed. Finally, existing issues and future perspectives in this field are briefly described. This review is expected to provide the basis and inspiration for the follow-up research on AMMs.

An Aggregation-Free Local Volume Fraction Formulation for Topological Design of Porous Structure

Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such as the p-norm aggregation and implicit porosity control, the violation of the maximum local volume constraint is inevitable. To this end, the primary optimization problem with bounds of local volume constraints is transformed into unconstrained programming by setting up a sequence of minimization sub-problems in terms of the augmented Lagrangian method. The approximation and algorithm using the concept of moving asymptotes is employed as the optimizer. Several numerical tests are provided to illustrate the effectiveness of the proposed approach in comparison with existing approaches. The effects of the global and local volume percentage, influence radius and mesh discretization on the final designs are investigated. In comparison to existing methods, the proposed method is capable of accurately limiting the upper bound of global and local volume fractions, which opens up new possibilities for additive manufacturing.

Robust topological designs for extreme metamaterial micro-structures

We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson's ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson's ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

Design of Kinematic Connectors for Microstructured Materials Produced by Additive Manufacturing

The main characteristic of materials with a functional gradient is the progressive composition or the structure variation across its geometry. This results in the properties variation in one or more specific directions, according to the functional application requirements. Cellular structure flexibility in tailoring properties is employed frequently to design functionally-graded materials. Topology optimisation methods are powerful tools to functionally graded materials design with cellular structure geometry, although continuity between adjacent unit-cells in gradient directions remains a restriction. It is mandatory to attain a manufacturable part to guarantee the connectedness between adjoining microstructures, namely by ensuring that the solid regions on the microstructure’s borders i.e., kinematic connectors) match the neighboring cells that share the same boundary. This study assesses the kinematic connectors generated by imposing local density restrictions in the initial design domain (i.e., nucleation) between topologically optimised representative unit-cells. Several kinematic connector examples are presented for two representatives unit-cells topology optimised for maximum bulk and shear moduli with different volume fractions restrictions and graduated Young’s modulus. Experimental mechanical tests (compression) were performed, and comparison studies were carried out between experimental and numerical Young’s modulus. The results for the single maximum bulk for the mean values for experimental compressive Young’s modulus (Ex¯) with 60%Vf show a deviation of 9.15%. The single maximum shear for the experimental compressive Young’s modulus mean values (Ex¯) with 60%Vf, exhibit a deviation of 11.73%. For graded structures, the experimental mean values of compressive Young’s moduli (Ex¯), compared with predicted total Young’s moduli (ESe), show a deviation of 6.96 for the bulk graded structure. The main results show that the single type representative unit-cell experimental Young’s modulus with higher volume fraction presents a minor deviation compared with homogenized data. Both (i.e., bulk and shear moduli) graded microstructures show continuity between adjacent cells. The proposed method proved to be suitable for generating kinematic connections for the design of shear and bulk graduated microstructured materials.

Effect of Fillets on Mechanical Properties of Lattice Structures Fabricated Using Multi-Jet Fusion Technology

Cellular structures with tailored topologies can be fabricated using additive manufacturing (AM) processes to obtain the desired global and local mechanical properties, such as stiffness and energy absorption. Lattice structures usually fail from the sharp edges owing to the high stress concentration and residual stress. Therefore, it is crucial to analyze the failure mechanism of lattice structures to improve the mechanical properties. In this study, several lattice topologies with fillets were designed, and the effects of the fillets on the stiffness, energy absorption, energy return, and energy loss of an open-cell lattice structure were investigated at a constant relative density. A recently developed high-speed AM multi-jet fusion technology was employed to fabricate lattice samples with two different unit cell sizes. Nonlinear simulations using ANSYS software were performed to investigate the mechanical properties of the samples. Experimental compression and loading–unloading tests were conducted to validate the simulation results. The results showed that the stiffness and energy absorption of the lattice structures can be improved significantly by the addition of fillets and/or vertical struts, which also influence other properties such as the failure mechanism and compliance. By adding the fillets, the failure location can be shifted from the sharp edges or joints to other regions of the lattice structure, as observed by comparing the failure mechanisms of type B and C structures with that of the type A structure (without fillets). The results of this study suggest that AM software designers should consider filleted corners when developing algorithms for generating various types of lattice structures automatically. Additionally, it was found that the accumulation of unsintered powder in the sharp corners of lattice geometries can also be minimized by the addition of fillets to convert the sharp corners to curved edges.

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.

A Review of Vat Photopolymerization Technology: Materials, Applications, Challenges, and Future Trends of 3D Printing

Additive manufacturing (3D printing) has significantly changed the prototyping process in terms of technology, construction, materials, and their multiphysical properties. Among the most popular 3D printing techniques is vat photopolymerization, in which ultraviolet (UV) light is deployed to form chains between molecules of liquid light-curable resin, crosslink them, and as a result, solidify the resin. In this manuscript, three photopolymerization technologies, namely, stereolithography (SLA), digital light processing (DLP), and continuous digital light processing (CDLP), are reviewed. Additionally, the after-cured mechanical properties of light-curable resin materials are listed, along with a number of case studies showing their applications in practice. The manuscript aims at providing an overview and future trend of the photopolymerization technology to inspire the readers to engage in further research in this field, especially regarding developing new materials and mathematical models for microrods and bionic structures.

A reprogrammable mechanical metamaterial with stable memory

Metamaterials are designed to realize exotic physical properties through the geometric arrangement of their underlying structural layout^1,2. Traditional mechanical metamaterials achieve functionalities such as a target Poisson's ratio³ or shape transformation^4-6 through unit-cell optimization^7-9, often with spatial heterogeneity^10-12. These functionalities are programmed into the layout of the metamaterial in a way that cannot be altered. Although recent efforts have produced means of tuning such properties post-fabrication^13-19, they have not demonstrated mechanical reprogrammability analogous to that of digital devices, such as hard disk drives, in which each unit can be written to or read from in real time as required. Here we overcome this challenge by using a design framework for a tileable mechanical metamaterial with stable memory at the unit-cell level. Our design comprises an array of physical binary elements (m-bits), analogous to digital bits, with clearly delineated writing and reading phases. Each m-bit can be independently and reversibly switched between two stable states (acting as memory) using magnetic actuation to move between the equilibria of a bistable shell^20-25. Under deformation, each state is associated with a distinctly different mechanical response that is fully elastic and can be reversibly cycled until the system is reprogrammed. Encoding a set of binary instructions onto the tiled array yields markedly different mechanical properties; specifically, the stiffness and strength can be made to range over an order of magnitude. We expect that the stable memory and on-demand reprogrammability of mechanical properties in this design paradigm will facilitate the development of advanced forms of mechanical metamaterials.

Design and Optimization of Lattice Structures: A Review

Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.

Direct Ink Writing Based 4D Printing of Materials and Their Applications

4D printing has attracted academic interest in the recent years because it endows static printed structures with dynamic properties with the change of time. The shapes, functionalities, or properties of the 4D printed objects could alter under various stimuli such as heat, light, electric, and magnetic field. Briefly, 4D printing is the development of 3D printing with the fourth dimension of time. Among the fabrication techniques that have been employed for 4D printing, the direct ink writing technique shows superiority due to its open source for various types of materials. Herein, the state-of-the-art achievements about the topic of 4D printing through direct ink writing are summarized. The types of materials, printing strategies, actuated methods, and their potential applications are discussed in detail. To date, most efforts have been devoted to shape-shifting materials, including shape memory polymers, hydrogels, and liquid crystal elastomers, showing great prospects in areas ranging from the biomedical field to robotics. Finally, the current challenges and outlook toward 4D printing based on direct ink writing are also pointed out to leave open a significant space for future innovation.

Liquid-Crystal-Elastomer-Based Dissipative Structures by Digital Light Processing 3D Printing

Digital Light Processing (DLP) 3D printing enables the creation of hierarchical complex structures with specific micro- and macroscopic architectures that are impossible to achieve through traditional manufacturing methods. Here, this hierarchy is extended to the mesoscopic length scale for optimized devices that dissipate mechanical energy. A photocurable, thus DLP-printable main-chain liquid crystal elastomer (LCE) resin is reported and used to print a variety of complex, high-resolution energy-dissipative devices. Using compressive mechanical testing, the stress-strain responses of 3D-printed LCE lattice structures are shown to have 12 times greater rate-dependence and up to 27 times greater strain-energy dissipation compared to those printed from a commercially available photocurable elastomer resin. The reported behaviors of these structures provide further insight into the much-overlooked energy-dissipation properties of LCEs and can inspire the development of high-energy-absorbing device applications.

A Unidirectional Soft Dielectric Elastomer Actuator Enabled by Built-In Honeycomb Metastructures

Dielectric elastomer actuators (DEAs) are able to undergo large deformation in response to external electric stimuli and have been widely used to drive soft robotic systems, due to their advantageous attributes comparable to biological muscles. However, due to their isotropic material properties, it has been challenging to generate programmable actuation, e.g., along a predefined direction. In this paper, we provide an innovative solution to this problem by harnessing honeycomb metastructures to program the mechanical behavior of dielectric elastomers. The honeycomb metastructures not only provide mechanical prestretches for DEAs but, more importantly, transfer the areal expansion of DEAs into directional deformation, by virtue of the inherent anisotropy. To achieve uniaxial actuation and maximize its magnitude, we develop a finite element analysis model and study how the prestretch ratios and the honeycomb structuring tailor the voltage-induced deformation. We also provide an easy-to-implement and scalable fabrication solution by directly printing honeycomb lattices made of thermoplastic polyurethane on dielectric membranes with natural bonding. The preliminary experiments demonstrate that our designed DEA is able to undergo unidirectional motion, with the nominal strain reaching up to 15.8%. Our work represents an initial step to program deformation of DEAs with metastructures.

3D Printing of Textiles: Potential Roadmap to Printing with Fibers

3D printing (3DP) has transformed engineering, manufacturing, and the use of advanced materials due to its ability to produce objects from a variety of materials, ranging from soft polymers to rigid ceramics. 3DP offers the advantage of being able to print at a variety of lengths scales; from a few micrometers to many meters. 3DP has the unique ability to produce customized small lots, efficiently. Yet, one crucial industry that has not been able to adequately explore its potential is textile manufacturing. The research in 3DP of textiles has lagged behind other areas primarily due to the difficulty in obtaining some of the unique characteristics of strength, flexibility, etc., of textiles, utilizing a fundamentally different manufacturing technology. Textiles are their own class of materials due to the specific structural developments that occur during the various stages of textile manufacturing: from fiber extrusion to assembly of the fibers to fabrics. Here, the current 3DP technologies are reviewed with emphasis on soft and anisotropic structures, as well as the efforts toward 3DP of textiles. Finally, a potential pathway to 3DP of textiles, dubbed as printing with fibers to create textile structures is proposed for further exploration.

2D Mechanical Metamaterials with Widely Tunable Unusual Modes of Thermal Expansion

Most natural materials expand uniformly in all directions upon heating. Artificial, engineered systems offer opportunities to tune thermal expansion properties in interesting ways. Previous reports exploit diverse design principles and fabrication techniques to achieve a negative or ultralow coefficient of thermal expansion, but very few demonstrate tunability over different behaviors. This work presents a collection of 2D material structures that exploit bimaterial serpentine lattices with micrometer feature sizes as the basis of a mechanical metamaterials system capable of supporting positive/negative, isotropic/anisotropic, and homogeneous/heterogeneous thermal expansion properties, with additional features in unusual shearing, bending, and gradient modes of thermal expansion. Control over the thermal expansion tensor achieved in this way provides a continuum-mechanics platform for advanced strain-field engineering, including examples of 2D metamaterials that transform into 3D surfaces upon heating. Integrated electrical and optical sources of thermal actuation provide capabilities for reversible shape reconfiguration with response times of less than 1 s, as the basis of dynamically responsive metamaterials.

Electrochemically reconfigurable architected materials

Architected materials can actively respond to external stimuli-such as mechanical forces, hydration and magnetic fields-by changing their geometries and thereby achieve novel functionalities. Such transformations are usually binary and volatile because they toggle between 'on' and 'off' states and require persistent external stimuli. Here we develop three-dimensional silicon-coated tetragonal microlattices that transform into sinusoidal patterns via cooperative beam buckling in response to an electrochemically driven silicon-lithium alloying reaction. In situ microscopy reveals a controllable, non-volatile and reversible structural transformation that forms multiple ordered buckling domains separated by distorted domain boundaries. We investigate the mechanical dynamics of individual buckling beams, cooperative coupling among neighbouring beams, and lithiation-rate-dependent distributions of domain sizes through chemo-mechanical modelling and statistical mechanics analysis. Our results highlight the critical role of defects and energy fluctuations in the dynamic response of architected materials. We further demonstrate that domain boundaries can be programmed to form particular patterns by pre-designing artificial defects, and that a variety of reconfigurational degrees of freedom can be achieved through micro-architecture design. This framework enables the design, fabrication, modelling, behaviour prediction and programming of electrochemically reconfigurable architected materials, and could open the way to beyond-intercalation battery electrodes, tunable phononic crystals and bio-implantable devices.

Cnoidal wave propagation in an elastic metamaterial

Advances in fabrication techniques have led to a proliferation of studies on new mechanical metamaterials, particularly on elastic and linear phenomena (for example, their phonon spectrum and acoustic band gaps). More recently, there has been a growing interest in nonlinear wave phenomena in these systems, and particularly how geometric parameters affect the propagation of high-amplitude nonlinear waves. In this paper, we analytically, numerically, and experimentally demonstrate the propagation of cnoidal waves in an elastic architected material. This class of traveling waves constitutes a general family of nonlinear waves, which reduce to phonons and solitons under suitable limits. Although cnoidal waves were first discovered as solutions to the conservation laws for shallow water, they have subsequently appeared in contexts as diverse as ion plasmas and nonlinear optics, but have rarely been explored in elastic solids. We show that geometrically nonlinear deformations in architected soft elastic solids can result in cnoidal waves. Insights from our analysis will be critical to controlling the propagation of stress waves in advanced materials.

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.

Giant Poisson's Effect for Wrinkle-Free Stretchable Transparent Electrodes

The next generation of flexible electronics will require highly stretchable and transparent electrodes, many of which consist of a relatively stiff metal network (or carbon materials) and an underlying soft substrate. Typically, such a stiff-soft bilayer suffers from wrinkling or folding when subjected to strains, causing high surface roughness and seriously deteriorated optical transparency. In this work, a network with a giant effective Poisson's ratio on a soft substrate is found to be under biaxial tension upon deformation, and thus does not wrinkle or fold, but maintains smooth surfaces and high transparency. Soft tactile sensors employing such network electrodes exhibit high transparency and low fatigue over many stretching cycles. Such a giant Poisson's ratio has the same effect in other systems. This work offers a new understanding of surface instabilities and a general strategy to prevent them not only in flexible electronics, but also in other materials and mechanical structures that require flat surfaces.

Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial

Soft mechanical metamaterials can support a rich set of dynamic responses, which, to date, have received relatively little attention. Here, we report experimental, numerical, and analytical results describing the behavior of an anisotropic two-dimensional flexible mechanical metamaterial when subjected to impact loading. We not only observe the propagation of elastic vector solitons with three components-two translational and one rotational-that are coupled together, but also very rich direction-dependent behaviors such as the formation of sound bullets and the separation of pulses into different solitary modes.

Multimaterial 3D Printing of Highly Stretchable Silicone Elastomers

3D printing of silicone elastomers with the direct ink writing (DIW) process has demonstrated great potential in areas as diverse as flexible electronics, medical devices, and soft robotics. However, most of current silicones are not printable because of their low viscosity and long curing time. The lack of systematic research on materials, devices, and processes during printing makes it a huge challenge to apply the DIW process more deeply and widely. In this report, aiming at the dilemmas in materials, devices, and processes, we proposed a comprehensive guide for printing highly stretchable silicone. Specifically, to improve the printability of silicone elastomers, nanosilica was added as a rheology modifier without sacrificing any stretching ability. To effectively control print speed and accuracy, a theoretical model was built and verified. With this strategy, silicone elastomers with different mechanical properties can all be printed and can realize infinite time and high speed printing (>25 mm/s) while maintaining accuracy. Here, super-stretchable silicone that can be stretched to 2000% was printed for the first time, and complex structures can be printed with high quality. For further demonstration, prosthetic nose, data glove capable of detecting fingers' movement, and artificial muscle that can lift objects were printed directly. We believe that this work could provide a guide for further work using the DIW process to print soft matters in a wide range of application scenarios.