Isotropic Negative Thermal Expansion Metamaterials

Kirigami-Inspired Three-Dimensional Metamaterials with Programmable Isotropic and Orthotropic Thermal Expansion

Mechanical metamaterials with specifically designed cells can provide unusual thermal expansion properties for diverse applications. Limited by very few available cell topologies and complicated non-linear structural deformation, most existing thermal expansion metamaterials can only achieve orthogonally isotropic negative/zero/positive thermal expansion (NTE/ZTE/PTE) within a mild range, especially the 3D ones. Here, based on one-degree-of-freedom kirigami polyhedrons proposed with a kinematic design strategy, a family of 3D isotropic and orthotropic metamaterials capable of programmable NTE, PTE, and even ZTE over ultra-wide range is developed. Incorporating bi-material strips as creases for isotropic polyhedrons, NTE and PTE metamaterials with coefficients of thermal expansion (CTEs) ranging from -2354.3 to 3006.7 ppm/°C are designed and programmed by the theoretical model. Meanwhile, isotropic ZTE metamaterials are constructed by either homogeneous tessellation of ZTE cells or hybrid tessellation of NTE and PTE cells. Furthermore, by allowing distinct geometric parameters in the three orthogonal directions of the kirigami polyhedrons while preserving the kinematic motion, orthotropic metamaterials, in which each of the three directions can be assigned with an independently programmed NTE, ZTE, or PTE, are also achieved. This study paves a novel pathway for the development of thermal expansion metamaterials with potential applications for space optical systems, MEMS, and so on.

Homogenization of Thermal Properties in Metaplates

Three-dimensional metamaterials endowed with two-dimensional in-plane periodicity exhibit peculiar thermoelastic behaviour when heated or cooled. By proper design of the unit cell, the equivalent thermal expansion coefficient can be programmed and can also reach negative values. The heterogeneity in the third direction of such metamaterials also causes, in general, a thermal-induced deflection. The prediction of the equivalent thermal properties is important to design the metamaterial suitable for a specific application. Under the hypothesis of small thickness with respect to the global in-plane dimensions, we make use of asymptotic homogenization to describe the thermoelastic behaviour of these metamaterials as that of an equivalent homogenous plate. The method provides explicit expressions for the effective thermal properties, which allow for a cost-effective prediction of the thermoelastic response of these metaplates.

Inverse design of Bézier curve-based mechanical metamaterials with programmable negative thermal expansion and negative Poisson's ratio via a data augmented deep autoencoder

Controlling stress and deformation induced by thermo-mechanical stimulation in high-precision mechanical systems can be achieved by mechanical metamaterials (MM) exhibiting negative thermal expansion (NTE) and negative Poisson's ratio (NPR). However, the inverse design of MM exhibiting a wide range of arbitrary target NTEs and NPRs is a challenging task due to the low design flexibility of analytical methods and parametric studies based on numerical simulation. In this study, we propose Bézier curve-based programmable chiral mechanical metamaterials (BPCMs) and a deep autoencoder-based inverse design model (DAIM) for the inverse design of BPCMs. Through iterative transfer learning with data augmentation, DAIM can generate BPCMs with a curved rib shape inaccessible with the Bézier curve, which improves the inverse design performance of the DAIM in the data sparse domain. This approach decreases the mean absolute error of NTE and NPR between the inverse design target and the numerical simulation results of inverse designed BPCMs on the data-sparse domain by 79.25% and 83.33% on average, respectively. A 3D-printed BPCM is validated experimentally and exhibits good coincidence with the target NTE and NPR. Our proposed BPCM and the corresponding inverse design framework enable the inverse design of BPCMs with NTE in the range of -1100 to 0 ppm K-1 and NPR in the range of -0.6 to -0.1. Furthermore, programmable thermal deformation modes with a fixed Poisson's ratio are realized by combining various inverse designed BPCM unit cells. BPCMs and the DAIM for their inverse design are expected to improve the mechanical robustness of high-precision mechanical systems through tunable modulation of thermo-mechanical stimulation.

Crystal-Inspired Cellular Metamaterials and Triply Periodic Minimal Surfaces

Triply periodic minimal surfaces (TPMSs) are found in many natural objects including butterfly wings, sea urchins, and biological membranes. They simultaneously have zero mean curvature at every point and a crystallographic group symmetry. A metamaterial can be created from such periodic surfaces or used as a reinforcement of a composite material. While a TPMS as a mathematical object has been known since 1865, only novel additive manufacturing (AM) technology made it possible to fabricate cellular materials with complex TPMS shapes. Cellular TPMS-based metamaterials have remarkable properties related to wetting/liquid penetration, shock absorption, and the absence of stress concentrators. Recent studies showed that TPMSs are also found in natural crystals when electron surfaces are considered. Artificial crystal-inspired metamaterials mimic such crystals including zeolites and schwarzites. These metamaterials are used for shock, acoustic waves, and vibration absorption, and as structural materials, heat exchangers, and for other applications. The choice of the crystalline cell of a material, as well as its microstructure, plays a decisive role in its properties. The new area of crystal-inspired materials has many common features with traditional biomimetics with models being borrowed from nature and adjusted for engineering applications.

3D Tiled Auxetic Metamaterial: A New Family of Mechanical Metamaterial with High Resilience and Mechanical Hysteresis

For artificial materials, desired properties often conflict. For example, engineering materials often achieve high energy dissipation by sacrificing resilience and vice versa, or desired auxeticity by losing their isotropy, which limits their performance and applications. To solve these conflicts, a strategy is proposed to create novel mechanical metamaterial via 3D space filling tiles with engaging key-channel pairs, exemplified via auxetic 3D keyed-octahedron-cuboctahedron metamaterials. This metamaterial shows high resilience while achieving large mechanical hysteresis synergistically under large compressive strain. Especially, this metamaterial exhibits ideal isotropy approaching the theoretical limit of isotropic Poisson's ratio, -1, as rarely seen in existing 3D mechanical metamaterials. In addition, the new class of metamaterials provides wide tunability on mechanical properties and behaviors, including an unusual coupled auxeticity and twisting behavior under normal compression. The designing methodology is illustrated by the integral of numerical modeling, theoretical analysis, and experimental characterization. The new mechanical metamaterials have broad applications in actuators and dampers, soft robotics, biomedical materials, and engineering materials/systems for energy dissipation.

Duality and Sheared Analytic Response in Mechanism-Based Metamaterials

Mechanical metamaterials designed around a zero-energy pathway of deformation known as a mechanism, challenge the conventional picture of elasticity and generate complex spatial response that remains largely uncharted. Here, we present a unified theoretical framework to showing that the presence of a unimode in a 2D structure generates a space of anomalous zero-energy sheared analytic modes. The spatial profiles of these stress-free strain patterns is dual to equilibrium stress configurations. We show a transition at an exceptional point between bulk modes in structures with conventional Poisson ratios (anauxetic) and evanescent surface modes for negative Poisson ratios (auxetic). We suggest a first application of these unusual response properties as a switchable signal amplifier and filter for use in mechanical circuitry and computation.

Multimaterial Additively Manufactured Metamaterials Functionalized with Customizable Thermal Expansion in Multiple Directions

Metamaterials functionalized with customizable multidirectional coefficient of thermal expansion (CTE) are urgently needed for advanced shape control or dimensional stability under temperature variations. The currently reported metamaterials still lack the development of diverse base material systems and exploration of the multimaterial fabrication process. Especially, the reported range of customizable CTEs for metamaterials in multiple directions is limited within [-68.1, 56.4] ppm/°C. Here, this work explicitly proposes a strategy for closely linking base materials, additive manufacturing (AM) process, architecture, and CTE tunability, in order to provide a general guideline for the design or customization of such metamaterials. In detail, first, we systematically identify the key process parameters and related performance for additive manufacturing of polymers and propose various multimaterial systems such as polypropylene-polycarbonate (PP-PC). Then, six types of metamaterials have been fabricated with high quality by the established multimaterial additive manufacturing. By measuring the effective CTEs in multiple directions, the CTE tunability of metamaterials, including large positive values (+523.36 ppm/°C) and large negative values (-230.61 ppm/°C), far beyond the literature-reported CTE range, has been experimentally verified. Further, we have developed a bidirectional requirement-solution strategy here that acts as a bridge between design and fabrication. This work opens advanced avenues for metamaterials with multidirectionally customizable and extensive CTE tunability for a variety of engineering applications such as actuators, thermal stress relief, and improved structural stability.

Modular reprogrammable 3D mechanical metamaterials with unusual hygroscopic deformation modes

The majority of polymer-based materials demonstrate expansion upon absorbing water from the air. Mechanical metamaterials provide an interesting way to achieve unusual hygroscopic deformation. However, previous studies have only accommodated the limited tunability of negative hygroscopic expansion by theoretical analysis but have never involved other deformation modes. This work proposes modular reprogrammable 3D moisture-sensitive mechanical metamaterials with switchable hygroscopic deformation modes, which are built up of multi-material 3D-printed bi-material curved strips and cubic nodes. Depending on the geometrical parameters and spatial layouts of the curved strips, the metamaterials exhibit tunable coefficient of hygroscopic expansion from negative to positive. In addition to homogeneous deformation, complex 3D hygroscopic deformation modes can be achieved including shear and twist. More interestingly, the metamaterials are reprogrammable since all the deformation modes can be switched by modular disassembling and reassembling of the curved strips, just like LEGO building blocks. This work demonstrates a feasible approach to achieve customized 3D hygroscopic deformation through easy block building for specific engineering applications including eliminating hygroscopic stress, shape morphing structures, and smart actuators.

Mechanical metamaterials and beyond

Mechanical metamaterials enable the creation of structural materials with unprecedented mechanical properties. However, thus far, research on mechanical metamaterials has focused on passive mechanical metamaterials and the tunability of their mechanical properties. Deep integration of multifunctionality, sensing, electrical actuation, information processing, and advancing data-driven designs are grand challenges in the mechanical metamaterials community that could lead to truly intelligent mechanical metamaterials. In this perspective, we provide an overview of mechanical metamaterials within and beyond their classical mechanical functionalities. We discuss various aspects of data-driven approaches for inverse design and optimization of multifunctional mechanical metamaterials. Our aim is to provide new roadmaps for design and discovery of next-generation active and responsive mechanical metamaterials that can interact with the surrounding environment and adapt to various conditions while inheriting all outstanding mechanical features of classical mechanical metamaterials. Next, we deliberate the emerging mechanical metamaterials with specific functionalities to design informative and scientific intelligent devices. We highlight open challenges ahead of mechanical metamaterial systems at the component and integration levels and their transition into the domain of application beyond their mechanical capabilities.

New Class of Multifunctional Bioinspired Microlattice with Excellent Sound Absorption, Damage Tolerance, and High Specific Strength

Although mutually independent, simultaneous sound absorption and superior mechanical properties are often sought after in a material. One main challenge in achieving such a material will be on how to design it. Herein, we propose a bamboo-inspired design strategy to overcome the aforementioned challenges. Building on top of the basic octet-truss design, we introduce a hollow-tube architecture to achieve lightweight property and mechanical robustness and a septum-chamber architecture to introduce acoustic resonant cells. The concept is experimentally verified through samples fabricated using selective laser melting with the Inconel 718 alloy. High sound absorption coefficients (>0.99) with broadband spectra, damage-tolerant behavior, high specific strength (up to 81.2 MPa·cm3/g), and high specific energy absorption of 40.1 J/g have been realized in this design. The sound absorption capability is attributed to Helmholtz resonance through the pore-and-cavity morphology of the structure. Microscopically speaking, dissipation primarily occurs via the viscous frictional flow and thermal boundary layers on the air and microlattice interactions at the narrow pores. The high strength is in turn attributed to the near-membrane state of stress in the plate structures and the excellent strength of the base material. Overall, this work presents a new design concept for developing multifunctional metamaterials.

Bifunctional Metamaterials Incorporating Unusual Geminations of Poisson's Ratio and Coefficient of Thermal Expansion

Natural materials overwhelmingly shrink laterally under stretching and expand upon heating. Through incorporating Poisson's ratio and coefficient of thermal expansion (PR and CTE) in unusual geminations, such as positive PR and negative CTE, negative PR and positive CTE, and even zero PR and zero CTE, bifunctional metamaterials would generate attractive shape control capacity. However, reported bifunctional metamaterials are only theoretically constructed by simple skeletal ribs, and the magnitudes of the bifunctions are still in quite narrow ranges. Here, we propose a methodology for generating novel bifunctional metamaterials consisting of engineering polymers. From concept to refinement, the topology and shape optimization are integrated for programmatically designing bifunctional metamaterials in various germinations of the PR and CTE. The underlying deformation mechanisms of the obtained bifunctions are distinctly revealed. All of the designs with complex architectures and material layouts are fabricated using the multimaterial additive manufacturing, and their effective properties are experimentally characterized. Good agreements of the design, simulation, and experiments are achieved. Especially, the accessible range of the bifunction, namely, PR and CTE, is remarkably enlarged nearly 4 times. These developed approaches open an avenue to explore the bifunctional metamaterials, which are the basis of myriad mechanical- and temperature-sensitive devices, e.g., morphing structures and high-precision components of the sensors/actuators in aerospace and electronical domains.

Programmable Mechanical Metamaterials with Tailorable Negative Poisson's Ratio and Arbitrary Thermal Expansion in Multiple Thermal Deformation Modes

Mechanical metamaterials pave a way for designing and optimizing microstructure topology to achieve counterintuitive deformation including negative Poisson's ratio (NPR) and negative thermal expansion (NTE). Previous studies were always limited to single anomalous mechanical or thermal deformation, but current applications for high-precision mechanical or optical equipment always require their combination and customized and anisotropic deformation parameters. This work develops programmable two-dimensional (2D) mechanical metamaterials based on chiral and antichiral structures constructed with curved bimaterial strips to produce tailorable NPR and arbitrary thermal deformation. The coefficient of thermal expansion of the mechanical metamaterials is tunable on a large scale across negative, near-zero, and positive values depending on the bimaterial configurations and geometrical parameters of curved strips, while the value of NPR is mainly determined by the radian. Furthermore, it is programmable by coding the unit cells to exhibit customized and anisotropic thermal deformation combining homogeneous, gradient, and shear modes. The proposed mechanical metamaterials are fabricated by multimaterial three-dimensional (3D) printing, and the unusual deformation modes are verified experimentally, which is well in agreement with the results of finite element analysis. This work demonstrates a feasible approach to achieving customized mechanical and thermal deformation through easy block building for specific engineering applications including eliminating thermal stress, shape morphing, and smart actuators.

Elastic mechanics solution of thermal expansion of bi-material curved beam and its application to negative thermal expansion metamaterials

Thermal stress impacts various engineering fields significantly, such as aerospace and precision instruments. This adverse effect can be greatly reduced, if not eliminated, by the application of micro-thermal expansion materials, and bi-material beams are widely utilized in the design of micro-thermal expansion structures, thereby exhibiting great application potentials. The elasticity solution of bi-material curved beam under free thermal expansion has been proposed by scholars. Based on this solution, the simplified form is proposed in this paper, and extended to the case where the rotation angles at both ends of the circular arc are constrained under thermal loads. Besides, the geometric parameters and the nonlinear problems of the thermal expansion of bi-material curved beam are analyzed. In addition, a novel type of negative thermal expansion material has been designed by applying the bi-material curved beam to the tetra chiral and anti-tetra chiral materials. The proposed material has greater negative thermal expansion effect than the traditional tetra and anti-tetra chiral materials that are with straight beams.

Differences in thermal expansion and motion ability for herringbone and face-to-face π-stacked solids

A series of aromatic organic molecules functionalized with different halogen atoms (I/ Br), motion-capable groups (olefin, azo or imine) and molecular length were designed and synthesized. The molecules self-assemble in the solid state through halogen bonding and exhibit molecular packing sustained by either herringbone or face-to-face π-stacking, two common motifs in organic semiconductor molecules. Interestingly, dynamic pedal motion is only achieved in solids with herringbone packing. On average, solids with herringbone packing exhibit larger thermal expansion within the halogen-bonded sheets due to motion occurrence and molecular twisting, whereas molecules with face-to-face π-stacking do not undergo motion or twisting. Thermal expansion along the π-stacked direction is surprisingly similar, but slightly larger for the face-to-face π-stacked solids due to larger changes in π-stacking distances with temperature changes. The results speak to the importance of crystal packing and intermolecular interaction strength when designing aromatic-based solids for organic electronics applications.

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.

Liquid Crystal Elastomer Metamaterials with Giant Biaxial Thermal Shrinkage for Enhancing Skin Regeneration

Liquid crystal elastomers (LCEs) are a class of soft active materials of increasing interest, because of their excellent actuation and optical performances. While LCEs show biomimetic mechanical properties (e.g., elastic modulus and strength) that can be matched with those of soft biological tissues, their biointegrated applications have been rarely explored, in part, due to their high actuation temperatures (typically above 60 °C) and low biaxial actuation performances (e.g., actuation strain typically below 10%). Here, unique mechanics-guided designs and fabrication schemes of LCE metamaterials are developed that allow access to unprecedented biaxial actuation strain (-53%) and biaxial coefficient of thermal expansion (-33 125 ppm K^-1 ), significantly surpassing those (e.g., -20% and -5950 ppm K^-1 ) reported previously. A low-temperature synthesis method with use of optimized composition ratios enables LCE metamaterials to offer reasonably high actuation stresses/strains at a substantially reduced actuation temperature (46 °C). Such biocompatible LCE metamaterials are integrated with medical dressing to develop a breathable, shrinkable, hemostatic patch as a means of noninvasive treatment. In vivo animal experiments of skin repair with both round and cross-shaped wounds demonstrate advantages of the hemostatic patch over conventional strategies (e.g., medical dressing and suturing) in accelerating skin regeneration, while avoiding scar and keloid generation.

Adjustable positive and negative hygrothermal expansion metamaterial inspired by the Maltese cross

A metamaterial that can manifest both positive and negative coefficients of moisture and thermal expansion is presented herein, based on inspiration from the Maltese cross. Each unit of the metamaterial consists of a pair of equal-armed crosses pin-joined at their junctions to permit rotation, but elastically restrained by a bimaterial spiral spring, and four pairs of hinge rods to translate the relative rotational motion of the pair of equal-armed crosses into translational motion of the connecting rods. The effective coefficients of moisture and thermal expansion models were developed for small and large changes in the hygrothermal conditions using infinitesimal (approximate) and finite (exact) motion analyses, respectively, with the former giving constant effective coefficients with respect to environmental changes. Results indicate that the approximate method underestimates the magnitude of both the effective expansion coefficients under cooling and drying but overestimates magnitudes of both coefficients during heating and moistening, and that the change in both expansion coefficients is more drastic during cooling and drying than during heating and moistening. In addition to providing another micro-lattice geometry for effecting expansion coefficients of either signs, this metamaterial exhibits auxetic property.

Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.

Elastic multipole method for describing deformation of infinite two-dimensional solids with circular inclusions

Elastic materials with holes and inclusions are important in a large variety of contexts ranging from construction material to biological membranes. More recently, they have also been exploited in mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson's ratio, mechanical cloaking, and tunable phononic band gaps. Understanding how such structures deform in response to applied external loads is thus crucial for designing novel mechanical metamaterials. Here we present a method for predicting the linear response of infinite 2D solid structures with circular holes and inclusions by employing analogies with electrostatics. Just like an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects, external stress induces elastic multipoles inside holes and inclusions. Stresses generated by these induced elastic multipoles then lead to interactions between holes and inclusions, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands the induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external stress field and also between them. The results of our method show good agreement with both linear finite element simulations and experiments.

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.

Optimization of Generatively Encoded Multi-Material Lattice Structures for Desired Deformation Behavior

Natural systems achieve favorable mechanical properties through coupling significantly different elastic moduli within a single tissue. However, when it comes to man-made materials and structures, there are a lack of methods which enable production of artifacts inspired by these phenomena. In this study, a method for design automation based on alternate deposition of soft and stiff struts within a multi-material 3D lattice structure with desired deformation behavior is proposed. These structures, once external forces are applied, conform to the geometry given in advance. For that purpose, a population-based algorithm was proposed and integrated with a multi-material physics simulator. To reduce the amount of data processed during optimization, a generative encoding method based on discrete cosine transform (DCT) was proposed. This enabled a compressed topological description and promoted symmetry in material distribution. The simulation results showed different three-dimensional lattice structures designed with proposed algorithm to meet a set of desired deformation behaviors. The relation between residual deformation error, targeted deformation geometry, and material distribution is discussed.

Designing Mechanical Metamaterials with Kirigami-Inspired, Hierarchical Constructions for Giant Positive and Negative Thermal Expansion

Advanced mechanical metamaterials with unusual thermal expansion properties represent an area of growing interest, due to their promising potential for use in a broad range of areas. In spite of previous work on metamaterials with large or ultralow coefficient of thermal expansion (CTE), achieving a broad range of CTE values with access to large thermally induced dimensional changes in structures with high filling ratios remains a key challenge. Here, design concepts and fabrication strategies for a kirigami-inspired class of 2D hierarchical metamaterials that can effectively convert the thermal mismatch between two closely packed constituent materials into giant levels of biaxial/uniaxial thermal expansion/shrinkage are presented. At large filling ratios (>50%), these systems offer not only unprecedented negative and positive biaxial CTE (i.e., -5950 and 10 710 ppm K^-1 ), but also large biaxial thermal expansion properties (e.g., > 21% for 20 K temperature increase). Theoretical modeling of thermal deformations provides a clear understanding of the microstructure-property relationships and serves as a basis for design choices for desired CTE values. An Ashby plot of the CTE versus density serves as a quantitative comparison of the hierarchical metamaterials presented here to previously reported systems, indicating the capability for substantially enlarging the accessible range of CTE.

Controlling thermal expansion within mixed cocrystals by tuning molecular motion capability

Thermal expansion behavior is tuned by incorporating motion-capable or -incapable molecules into organic solids.

Controlling thermal expansion (TE) behaviors of organic materials is challenging because several mechanisms can govern TE, such as noncovalent interaction strength and structural motions. Here, we report the first demonstration of tuning TE within organic solids by using a mixed cocrystal approach. The mixed cocrystals contain three unique molecules, two of which are present in variable ratios. These two molecules either lack or exhibit the ability to undergo molecular motion in the solid state. Incorporation of higher ratios of motion-capable molecules results in larger, positive TE along the motion direction. Addition of a motion-incapable molecule affords solids that undergo less TE. Fine-tuned TE behavior was attained by systematically controlling the ratio of motion-capable and -incapable molecules in each solid.

Analysis of Antichiral Thermomechanical Metamaterials with Continuous Negative Thermal Expansion Properties

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

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.

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.

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.

Mechanical performance of additively manufactured meta-biomaterials

Additive manufacturing (AM) (=3D printing) and rational design techniques have enabled development of meta-biomaterials with unprecedented combinations of mechanical, mass transport, and biological properties. Such meta-biomaterials are usually topologically ordered and are designed by repeating a number of regular unit cells in different directions to create a lattice structure. Establishing accurate topology-property relationships is of critical importance for these materials. In this paper, we specifically focus on AM metallic meta-biomaterials aimed for application as bone substitutes and orthopaedic implants and review the currently available evidence regarding their mechanical performance under quasi-static and cyclic loading conditions. The topology-property relationships are reviewed for regular beam-based lattice structures, sheet-based lattice structures including those based on triply periodic minimal surface, and graded designs. The predictive models used for establishing the topology-property relationships including analytical and computational models are covered as well. Moreover, we present an overview of the effects of the AM processes, material type, tissue regeneration, biodegradation, surface bio-functionalization, post-manufacturing (heat) treatments, and loading profiles on the quasi-static mechanical properties and fatigue behavior of AM meta-biomaterials. AM meta-biomaterials exhibiting unusual mechanical properties such as negative Poisson's ratios (auxetic meta-biomaterials), shape memory behavior, and superelasitcity as well as the potential applications of such unusual behaviors (e.g. deployable implants) are presented too. The paper concludes with some suggestions for future research. STATEMENT OF SIGNIFICANCE: Additive manufacturing enables fabrication of meta-biomaterials with rare combinations of topological, mechanical, and mass transport properties. Given that the micro-scale topological design determines the macro-scale properties of meta-biomaterials, establishing topology-property relationships is the central research question when rationally designing meta-biomaterials. The interest in understanding the relationship between the topological design and material type on the one hand and the mechanical properties and fatigue behavior of meta-biomaterials on the other hand is currently booming. This paper presents and critically evaluates the most important trends and findings in this area with a special focus on the metallic biomaterials used for skeletal applications to enable researchers better understand the current state-of-the-art and to guide the design of future research projects.

Positive and Negative Two-Dimensional Thermal Expansion via Relaxation of Node Distortions

The ability to tune physical properties is attractive for the development of new materials for myriad applications. Understanding and controlling the structural dynamics in complicated network structures like coordination polymers (CPs) is particularly challenging. We report a series of two-dimensional CPs [Mn(salen)]₂[M(CN)₄]· xH₂O (M = Pt (1), PtI₂ (2), and MnN (3)) incorporating zigzag cyano-network layers that display composition-dependent anisotropic thermal expansion properties. Variable-temperature single-crystal X-ray structural analyses demonstrated that the thermal expansion behavior is caused by double structural distortions involving [Mn(salen)]⁺ units incorporated into the zigzag layers. Thermal relaxations produce structural transformations resulting in positive thermal expansion for 2·H₂O and negative thermal expansion for 3. In the case of 1·H₂O, the relaxation does not occur and zero thermal expansion results in the plane between 200 to 380 K. The present study proposes a new strategy based on structural distortions in coordination networks to control thermal responsivities of frameworks.

Deformation mechanism of innovative 3D chiral metamaterials

Rational design of artificial microstructured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is very important. Making use of node rotation and ligament bending deformation features of chiral materials, two types of innovative 3D chiral metamaterials are proposed, namely chiral- chiral- antichiral and chiral- antichiral- antichiral metamaterials. In-situ compression and uniaxial tensile tests are performed for studying the mechanical properties and deformation mechanisms of these two types of 3D chiral metamaterials. Novel deformation mechanisms along different directions are explored and analyzed, such as: uniform spatial rotation deformation, tensile-shearing directed (compression-shearing directed), tensile-expansion directed (compression-shrinkage directed) deformation mechanisms of 3D chiral metamaterials, and competitions between different types of deformation mechanisms are discussed. The proposed 3D chiral metamaterials represents a series of metamaterials with robust microstructures design feasibilities.

Multi-material Additive Manufacturing of Metamaterials with Giant, Tailorable Negative Poisson's Ratios

Nature has evolved with a recurring strategy to achieve unusual mechanical properties through coupling variable elastic moduli from a few GPa to below KPa within a single tissue. The ability to produce multi-material, three-dimensional (3D) micro-architectures with high fidelity incorporating dissimilar components has been a major challenge in man-made materials. Here we show multi-modulus metamaterials whose architectural element is comprised of encoded elasticity ranging from rigid to soft. We found that, in contrast to ordinary architected materials whose negative Poisson’s ratio is dictated by their geometry, these type of metamaterials are capable of displaying Poisson’s ratios from extreme negative to zero, independent of their 3D micro-architecture. The resulting low density metamaterials is capable of achieving functionally graded, distributed strain amplification capabilities within the metamaterial with uniform micro-architectures. Simultaneous tuning of Poisson’s ratio and moduli within the 3D multi-materials could open up a broad array of material by design applications ranging from flexible armor, artificial muscles, to actuators and bio-mimetic materials.

Giant Thermal Expansion in 2D and 3D Cellular Materials

When temperature increases, the volume of an object changes. This property was quantified as the coefficient of thermal expansion only a few hundred years ago. Part of the reason is that the change of volume due to the variation of temperature is in general extremely small and imperceptible. Here, abnormal giant linear thermal expansions in different types of two-ingredient microstructured hierarchical and self-similar cellular materials are reported. The cellular materials can be 2D or 3D, and isotropic or anisotropic, with a positive or negative thermal expansion due to the convex or/and concave shape in their representative volume elements respectively. The magnitude of the thermal expansion coefficient can be several times larger than the highest value reported in the literature. This study suggests an innovative approach to develop temperature-sensitive functional materials and devices.

Four-dimensional Printing of Liquid Crystal Elastomers

Three-dimensional structures capable of reversible changes in shape, i.e., four-dimensional-printed structures, may enable new generations of soft robotics, implantable medical devices, and consumer products. Here, thermally responsive liquid crystal elastomers (LCEs) are direct-write printed into 3D structures with a controlled molecular order. Molecular order is locally programmed by controlling the print path used to build the 3D object, and this order controls the stimulus response. Each aligned LCE filament undergoes 40% reversible contraction along the print direction on heating. By printing objects with controlled geometry and stimulus response, magnified shape transformations, for example, volumetric contractions or rapid, repetitive snap-through transitions, are realized.

Dielectric meta-atom with tunable resonant frequency temperature coefficient

In this paper, we present a proof-of-concept of a new approach to achieving tailored resonant frequency temperature coefficients in dielectric meta-atoms. The technique involves introducing a thermally expanding or contracting material joining the active high permittivity dielectric absorbers. Both simulation and experiment show that by careful design of the element size and appropriate choice of thermomechanical intermediate layer material, increased or decreased resonant frequency shift temperature sensitivity is possible. Once the active dielectric material is chosen, and a meta-atom design determined, we show the resonant frequency shift depends on the thermal expansion coefficient of the intermediate layer. This work demonstrates the feasibility of manipulating the blue or red shift of metamaterial devices by introducing temperature responsive intermediate layers into meta-atoms.

Enhanced Absorption Performance of Carbon Nanostructure Based Metamaterials and Tuning Impedance Matching Behavior by an External AC Electric Field

Metamaterials have surprisingly broadened the range of available practical applications in new devices such as shielding, microwave absorbing, and novel antennas. More research has been conducted related to tuning DNG frequency bands of ordered or disordered metamaterials, and far less research has focused on the importance of impedance matching behavior, with little effort and attention given to adjusting the magnitude of negative permittivity values. This is particularly important if devices deal with low-amplitude signals such as radio or TV antennas. The carbon/hafnium nickel oxide (C/Hf_0.9Ni_0.1O_y) nanocomposites with simultaneously negative permittivity and negative permeability, excellent metamaterial performance, and good impedance matching could become an efficient alternative for the ordered metamaterials in wave-transparent, microwave absorbing, and solar energy harvesting fields. In this study, we prepared C/Hf_0.9Ni_0.1O_y nanocomposites by the solvothermal method, and we clarified how the impedance matching and double-negative (DNG) behaviors of C/Hf_0.9Ni_0.1O_y can be tuned by an external AC electric field created by an electric quadrupole system. An external electric field allows for the alignment of the well-dispersed nanoparticles of carbon with long-range orientations order. We believe that this finding broadens our understanding of moderate conductive material-based random metamaterials (MCMRMs) and provides a novel strategy for replacing high-loss ordered or disordered metamaterials with MCMRMs.

Reversibly Actuating Solid Janus Polymeric Fibers

It is commonly assumed that the substantial element of reversibly actuating soft polymeric materials is chemical cross-linking, which is needed to provide elasticity required for the reversible actuation. On the example of melt spun and three-dimensional printed Janus fibers, we demonstrate here for the first time that cross-linking is not an obligatory prerequisite for reversible actuation of solid entangled polymers, since the entanglement network itself can build elasticity during crystallization. Indeed, we show that not-cross-linked polymers, which typically demonstrate plastic deformation in melt, possess enough elastic behavior to actuate reversibly. The Janus polymeric structure bends because of contraction of the polymer and due to entanglements and formation of nanocrystallites upon cooling. Actuation upon melting is simply due to relaxation of the stressed nonfusible component. This approach opens perspectives for design of solid active materials and actuator for robotics, biotechnology, and smart textile applications. The great advantage of our principle is that it allows design of non-cross-linked self-moving materials, which are able to actuate in both water and air, which are not cross-linked. We demonstrate application of actuating fibers for design of walkers, structures with switchable length, width, and thickness, which can be used for smart textile applications.

Micro-Structured Two-Component 3D Metamaterials with Negative Thermal-Expansion Coefficient from Positive Constituents

Controlling the thermal expansion of materials is of great technological importance. Uncontrolled thermal expansion can lead to failure or irreversible destruction of structures and devices. In ordinary crystals, thermal expansion is governed by the asymmetry of the microscopic binding potential, which cannot be adjusted easily. In artificial crystals called metamaterials, thermal expansion can be controlled by structure. Here, following previous theoretical work, we fabricate three-dimensional (3D) two-component polymer micro-lattices by using gray-tone laser lithography. We perform cross-correlation analysis of optical microscopy images taken at different sample temperatures. The derived displacement-vector field reveals that the thermal expansion and resulting bending of the bi-material beams leads to a rotation of the 3D chiral crosses arranged onto a 3D checkerboard pattern within one metamaterial unit cell. These rotations can compensate the expansion of the all positive constituents, leading to an effectively near-zero thermal length-expansion coefficient, or over-compensate the expansion, leading to an effectively negative thermal length-expansion coefficient. This evidences a striking level of thermal-expansion control.