Strain rate-dependent mechanical metamaterials

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Diffusive kinks turn kirigami into machines

Kinks define boundaries between distinct configurations of a material. In the context of mechanical metamaterials, kinks have recently been shown to underpin logic, shape-changing and locomotion functionalities. So far such kinks propagate by virtue of inertia or of an external load. Here, we discover the emergence of propagating kinks in purely dissipative kirigami. To this end, we create kirigami that shape-change into different textures depending on how fast they are stretched. We find that if we stretch fast and wait, the viscoelastic kirigami can eventually snap from one texture to another. Crucially, such a snapping instability occurs in a sequence and a propagating diffusive kink emerges. As such, it mimics the slow sequential folding observed in biological systems, e.g., Mimosa Pudica. We finally demonstrate that diffusive kinks can be harnessed for basic machine-like functionalities, such as sensing, dynamic shape morphing, transport and manipulation of objects.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

Mechanical metamaterials are meticulously designed structures with exceptional mechanical properties determined by their microstructures and constituent materials. Tailoring their material and geometric distribution unlocks the potential to achieve unprecedented bulk properties and functions. However, current mechanical metamaterial design considerably relies on experienced designers' inspiration through trial and error, while investigating their mechanical properties and responses entails time-consuming mechanical testing or computationally expensive simulations. Nevertheless, recent advancements in deep learning have revolutionized the design process of mechanical metamaterials, enabling property prediction and geometry generation without prior knowledge. Furthermore, deep generative models can transform conventional forward design into inverse design. Many recent studies on the implementation of deep learning in mechanical metamaterials are highly specialized, and their pros and cons may not be immediately evident. This critical review provides a comprehensive overview of the capabilities of deep learning in property prediction, geometry generation, and inverse design of mechanical metamaterials. Additionally, this review highlights the potential of leveraging deep learning to create universally applicable datasets, intelligently designed metamaterials, and material intelligence. This article is expected to be valuable not only to researchers working on mechanical metamaterials but also those in the field of materials informatics.

A reprogrammable mechanical metamaterial with origami functional-group transformation and ring reconfiguration

Recent advancements in reprogrammable metamaterials have enabled the development of intelligent matters with variable special properties in situ. These metamaterials employ intra-element physical reconfiguration and inter-element structural transformation. However, existing mono-characteristic homo-element mechanical metamaterials have limited reprogramming functions. Here, we introduce a reprogrammable mechanical metamaterial composed of origami elements with heterogeneous mechanical properties, which achieves various mechanical behavior patterns by functional group transformations and ring reconfigurations. Through the anisotropic assembly of two heterogeneous elements into a functional group, we enable mechanical behavior switching between positive and negative stiffness. The resulting polygonal ring exhibits rotational deformation, zero Poisson's ratio stretching/compression deformation, and negative Poisson's ratio auxetic deformation. Arranging these rings periodically yields homogeneous metamaterials. The reconfiguration of quadrilateral rings allows for continuous fine-tunability of the mechanical response and negative Poisson's ratio. This mechanical metamaterial could provide a versatile material platform for reprogrammable mechanical computing, multi-purpose robots, transformable vehicles and architectures at different scales.

Non-reciprocal and non-Newtonian mechanical metamaterials

Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton's second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

Soft Mechanical Metamaterials with Transformable Topology Protected by Stress Caching

Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non-trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically-protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as "stress caching". This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers or isolators.

Robotic Materials Transformable Between Elasticity and Plasticity

Robotic materials, with coupled sensing, actuation, computation, and communication, have attracted increasing attention because they are able to not only tune their conventional passive mechanical property via geometrical transformation or material phase change but also become adaptive and even intelligent to suit varying environments. However, the mechanical behavior of most robotic materials is either reversible (elastic) or irreversible (plastic), but not transformable between them. Here, a robotic material whose behavior is transformable between elastic and plastic is developed, based upon an extended neutrally stable tensegrity structure. The transformation does not depend on conventional phase transition and is fast. By integrating with sensors, the elasticity-plasticity transformable (EPT) material is able to self-sense deformation and decides whether to undergo transformation or not. This work expands the capability of the mechanical property modulation of robotic materials.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Additive Manufacturing of Biomaterials-Design Principles and Their Implementation

Additive manufacturing (AM, also known as 3D printing) is an advanced manufacturing technique that has enabled progress in the design and fabrication of customised or patient-specific (meta-)biomaterials and biomedical devices (e.g., implants, prosthetics, and orthotics) with complex internal microstructures and tuneable properties. In the past few decades, several design guidelines have been proposed for creating porous lattice structures, particularly for biomedical applications. Meanwhile, the capabilities of AM to fabricate a wide range of biomaterials, including metals and their alloys, polymers, and ceramics, have been exploited, offering unprecedented benefits to medical professionals and patients alike. In this review article, we provide an overview of the design principles that have been developed and used for the AM of biomaterials as well as those dealing with three major categories of biomaterials, i.e., metals (and their alloys), polymers, and ceramics. The design strategies can be categorised as: library-based design, topology optimisation, bio-inspired design, and meta-biomaterials. Recent developments related to the biomedical applications and fabrication methods of AM aimed at enhancing the quality of final 3D-printed biomaterials and improving their physical, mechanical, and biological characteristics are also highlighted. Finally, examples of 3D-printed biomaterials with tuned properties and functionalities are presented.

Deployable mechanical metamaterials with multistep programmable transformation

Transformations in shape are critical to actuation in engineered metamaterials. Existing engineering metamaterials are typically limited to a small number of shape transformations that must be built-in during material synthesis. Here, inspired by the multistability and programmability of kirigami-based self-folding elements, a robust framework is introduced for the construction of sequentially programmable and reprogrammable mechanical metamaterials. The materials can be locked into multiple stable deployed configurations and then, using tunable bistability enabled by temperature-responsive constituent materials, return to their original reference configurations or undergo mode bifurcation. The framework provides a platform to design metamaterials with multiple deployable and reversible configurations in response to external stimuli.

Sequential snapping and pathways in a mechanical metamaterial

Materials that feature bistable elements, hysterons, exhibit memory effects. Often, these hysterons are difficult to observe or control directly. Here, we introduce a mechanical metamaterial in which slender elements, interacting with pushers, act as mechanical hysterons. We show how we can tune the hysteron properties and pathways under cyclic compression by the geometric design of these elements and how we can tune the pathways of a given sample by tilting one of the boundaries. Furthermore, we investigate the effect of the coupling of a global shear mode to the hysterons as an example of the interactions between hysteron and non-hysteron degrees of freedom. We hope our work will inspire further studies on designer matter with targeted pathways.

Synergistic Energy Absorption Mechanisms of Architected Liquid Crystal Elastomers

A unique rate-dependent energy absorption behavior of liquid crystal elastomer (LCE)-based architected materials is reported. The architected materials consist of repeating unit cells of bistable tilted LCE beams sandwiched between stiff supports. The viscoelastic behavior of the LCE causes the energy absorption to increase with strain rate according to a power-law relationship, which can be modulated by changing the degree of mesogen alignment and the loading direction relative to the director. For a strain rate of 600 s^-1 , the unit cell exhibits up to a 5 MJ m^-3 energy absorption density, which is two orders of magnitude higher than the same structure fabricated from poly(dimethylsiloxane) elastomer and is comparable to the dissipation from irreversible plastic deformation exhibited by denser metals. For a multilayered structure of unit cells, nonuniform buckling of the different layers produces additional viscoelastic dissipation. This synergistic interaction between viscoelastic dissipation and snap-through buckling causes the energy absorption density to increase with the number of layers. The sequence of cell collapse can be controlled by grading the beam thickness to further promote viscous dissipation and enhance the energy absorption density. It is envisioned that the study can contribute to the development of lightweight extreme energy-absorbing metamaterials.

Responsive materials architected in space and time

Rationally designed architected materials have attained previously untapped territories in materials property space. The properties and behaviours of architected materials need not be stagnant after fabrication; they can be encoded with a temporal degree of freedom such that they evolve over time. In this Review, we describe the variety of materials architected in both space and time, and their responses to various stimuli, including mechanical actuation, changes in temperature and chemical environment, and variations in electromagnetic fields. We highlight the additive manufacturing methods that can precisely prescribe complex geometries and local inhomogeneities to make such responsiveness possible. We discuss the emergent physics phenomena observed in architected materials that are analogous to those in classical materials, such as the formation and behaviour of defects, phase transformations and topologically protected properties. Finally, we offer a perspective on the future of architected materials that have a degree of intelligence through mechanical logic and artificial neural networks.

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.

Profusion of transition pathways for interacting hysterons

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

Oligomodal metamaterials with multifunctional mechanics

Mechanical metamaterials are man-made materials with extraordinary properties that come from their geometrical structure rather than their chemical composition. For instance, they can be engineered to be extremely light and stiff; to shrink sideways when compressed, instead of expanding; or to exhibit programmable shape changes. Such properties often rely on zero-energy modes. In this work, we created a class of mechanical metamaterials with zero-energy modes that can exhibit multiple properties at the same time within a single structure. In particular, we created a metamaterial that can either shrink or expand on the side when compressed, depending on how fast it is compressed. These metamaterials could lead to novel adaptable devices for, for example, robotics and energy absorption applications.

Mechanical metamaterials are artificial composites that exhibit a wide range of advanced functionalities such as negative Poisson’s ratio, shape shifting, topological protection, multistability, extreme strength-to-density ratio, and enhanced energy dissipation. In particular, flexible metamaterials often harness zero-energy deformation modes. To date, such flexible metamaterials have a single property, for example, a single shape change, or are pluripotent, that is, they can have many different responses, but typically require complex actuation protocols. Here, we introduce a class of oligomodal metamaterials that encode a few distinct properties that can be selectively controlled under uniaxial compression. To demonstrate this concept, we introduce a combinatorial design space containing various families of metamaterials. These families include monomodal (i.e., with a single zero-energy deformation mode); oligomodal (i.e., with a constant number of zero-energy deformation modes); and plurimodal (i.e., with many zero-energy deformation modes), whose number increases with system size. We then confirm the multifunctional nature of oligomodal metamaterials using both boundary textures and viscoelasticity. In particular, we realize a metamaterial that has a negative (positive) Poisson’s ratio for low (high) compression rate over a finite range of strains. The ability of our oligomodal metamaterials to host multiple mechanical responses within a single structure paves the way toward multifunctional materials and devices.

Fractal-inspired soft deployable structure: a theoretical study

The study of soft deployable structures is an emergent field that is highly correlated with metamaterial design, soft robotics, medical devices, etc. This paper studies a novel two-dimensional (2D) soft deployable structure that has a fractal layout with hierarchically coupled thin walls, which buckles upon actuation and deforms into a "peacock tail" pattern that is over 10 fold its original dimension. Large deflection theory and finite-element (FE) modeling are used to characterize its mechanical performance and to investigate its potential application in multiple fields. Further, 2D FE homogenization is implemented to extend the novel design into an active plane lattice metamaterial, on which parametric studies are carried out to explore its effective stiffness and large strain properties. The results show that, besides excellent deformability, the "peacock tail" soft deployable structure and its lattice metamaterial derivates exhibit intriguing properties such as multi-stiffening, strong anisotropy, zero/negative Poisson's ratio, a unique post-buckling collapse mechanism, etc. Three-dimensional generalization of the fractal compliant system is modeled to elaborate on the practical use of the structures. This paper aims to enrich the spectrum of soft deployable structures, shedding light on the research of novel soft robots, hierarchical structures, and metamaterials.