Soft Mechanical Metamaterials Research Articles

Three-phase soft mechanical metamaterials for tunable negative expansion deformation and bandgaps

As the new artificial composite structures combing the smart materials and extensible topologies, the mechanical negative-expansion metamaterials deformation are promising in the fields of aerospace, robotics, medical devices, and flexible electronics. Based on the swelling characteristics of hydrogels, this work develops 2D and 3D soft mechanical metamaterials suitable for super large negative expansion deformations. The 2D and 3D metamaterials are fabricated by the multi-material 4D printing, and characterized by the experiments of self-driven negative expansion deformation and recovery. To accurately and quickly predict the deformation behavior of negative expansion response, a large-deformation theoretical model is developed based on finite element method and verified by the experimental characterizations. The influence of lattice parameters on the negative expansion response deformation and the corresponding adjustability are characterized and demonstrated through the theory, simulations and experiments. The 2D and 3D soft mechanical metamaterials show that their elastic wave bandgaps can be regulated actively and flexibly using the evolution of the lattice during the negative expansion deformation process. The present metamaterials can be used to design and manufacture instruments with adjustable negative expansion deformation and acoustic functionalities, showing the potential applications in the fields of smart soft robots and active metamaterial devices.

Study on influence of parameters of buckling behavior in soft mechanical metamaterials

Mechanical metamaterials are valued for their diverse properties and potential applications. Due to the instability and large deformability of soft mechanical metamaterials (SMMs), geometric reorganization will occur and lead to some unusual properties. It is possible to change the properties of materials by varying the parameters. Conventional SMMs contain a periodic distribution of holes with the same size and shape, which can be changed to a lesser extent. Periodic dispersion of regular through-hole patterns of various sizes or shapes into elastomers, resulting in metamaterials with more mechanical functionality and deformation scenarios. In this paper, we investigated the influence of parameters on the buckling mechanical behavior of SMMs and the buckling mechanical behavior of structures with multiple sizes and geometric shapes. The parameters studied include geometric parameters (pore shape, porosity and area ratio) and physical parameters (Poisson’s ratio and compression mode). Simulation of the buckling behavior of SMMs uses the finite element method. The finite element software ABAQUS is used, taking into account the almost incompressible characteristics of materials, the triangular quadratic plane strain hybrid element is selected (CPE6H). Numerical calculation gives the following results: Area ratio, pore shape and compression mode have obvious effects on buckling behavior, but Poisson’s ratio has little effect; the influence of parameters on the buckling critical strains varied for SMMs with various pore shapes; very different buckling behaviors will result from swapping out the pattern of holes with the same size or shape for holes with two different sizes or shapes; the expression of buckling behavior is also varied when the mix of hole shapes is modified. These findings demonstrate that the design parameters may be used to achieve the desired buckling behaviors. This is a new method that can be used to control the deformation of structures; modify the properties of the SMMs without changing stiffness; simplify the structures without significantly changing the material properties. The design path of mechanical metamaterials is increased.

Nonlinear elastic vector solitons in hard-magnetic soft mechanical metamaterials

We propose a design of a metamaterial for magnetically tunable propagation of nonlinear vector solitary waves. The metamaterial consists of a periodic array of units of hard-magnetic inclusion embedded in a soft matrix. The units are connected via thin and highly deformable ligaments. Our theoretical and numerical modeling results show that the configuration of the metamaterial undergoes drastic transformations when activated by a magnetic field. These controllable microstructural transformations significantly influence the propagation of vector solitary waves in the proposed metamaterial system. We report the magnetic field-enabled propagation of solitary waves. We show that the proposed soft magnetoactive metamaterial allows us to tune the key characteristics of the enabled nonlinear solitary waves, including their pulse width and amplitude. Our findings also highlight the potential of magneto-mechanical coupling in the development of untethered mechanical metamaterial systems for applications in nondestructive testing, energy harvesting, and smart soft wave devices.

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 orisolators.

Learning the nonlinear dynamics of mechanical metamaterials with graph networks

The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous works have shown tremendous success in describing the unique nonlinear dynamics of certain types of soft mechanical metamaterials. However, capturing the nonlinear dynamic response of these materials especially those with complex geometries, can be a challenge due to the strong nonlinearity and large computational cost. An efficient and reliable framework to predict the overall response of the metamaterials based on the geometry of their building blocks is not only key to understanding the unique behavior of metamaterials, but also vital to the rational design of such materials. In this work, we propose metamaterial graph network (MGN), a machine learning approach to address this challenge. MGN is based on a graph that represents the lattice-like metamaterial structure. The trained MGN is capable of simulating the dynamics of a metamaterial structure with over 200 by 200 unit cells, a task that is practically impossible for traditional direct numerical simulation using the finite element method. We also verify the accuracy of the proposed MGN against several representative numerical examples. In the first two examples, we show that MGN successfully captures the well-known pattern transformation behavior of porous metamaterials. In the later examples, we consider wave propagation in a dynamic setting and show that MGN produces quantitatively accurate results compared with direct numerical simulation. An additional feature of MGN is that defects/inhomogeneities can be easily incorporated into the metamaterial structure. We expect our method to open a new avenue for the study and modeling of mechanical metamaterials.

Self-adaptive acoustic cloak enabled by soft mechanical metamaterials

Acoustic cloaks enable exciting object concealment by manipulating sound waves and have attracted research efforts from different approaches such as transformation acoustics. However, the challenge still lies in the practical implementation of those cloaks that require complex material designs. Here, we show that an underwater acoustic cloak can be automatically achieved by deforming a soft mechanical metamaterial with Poisson’s ratio of -1. The deformation of such an auxetic structure is demonstrated to be able to automatically and passively fulfill the requirement of quasi-conformal mapping for cloak design. Such a self-adaptive acoustic cloak exhibits a wide frequency and angular bandwidth, which opens an avenue for convenient design of various kinds of acoustic metamaterials.

3D gradient auxetic soft mechanical metamaterials fabricated by additive manufacturing

Materials with a negative Poisson's ratio, also known as auxetics, have attracted a lot attention as they have shown innovation potential in applications for energy damping, modern fasteners, biomedical implants, piezoelectric sensors, and soft actuators. In this study, we introduce different patterns of graded distribution of unit cells with positive and negative Poisson's ratio in tubular configurations. Seven types of patterns are programmed into the fabric of the metamaterial to create desired shape changes upon applying far-field external loads. Two of the patterns demonstrate near-zero Poisson's ratio even at axial strains as high as 44%. Other pattern distributions convert the initially cylindrical shape of the tubes to vase, barrel, hourglass, nonsymmetrical vase, and nonsymmetrical hourglass geometries. The experimental Poisson's ratio values for the linear negative-to-positive-to-negative gradient (resulting in hourglass shape) and linear positive-to-negative-to-positive gradient (resulting in barrel shape) cases are +0.53 and −0.47, respectively. The measured Poisson's ratio values at tube level are in good accordance with the analytical values of +0.5 and −0.5. Benefits of the proposed designs in applications such as action-at-a-distance actuators and wrinkle-free jointless hinges in both 3D and 2D configurations are demonstrated.

Off/on switchable smart electromagnetic interference shielding aerogel

Summary Smart electromagnetic interference (EMI) shielding materials with tunable EM wave response characteristics are attractive for future EM devices. Here, we report an off/on switchable EMI shielding material that can be tuned from EM wave transmission to shielding and vice versa by mechanical compression and decompression. This smart material is prepared by filling conductive carbon nanoparticles into wood-derived lamellar carbon aerogel, showing reversible compressibility and strain-sensitive conductivity. The original aerogel has good impedance matching and low dielectric loss, allowing the EM wave to pass through. Mechanical compression enables the carbon nanoparticles to establish highly conductive pathways in the aerogel, which significantly increases the conductivity of aerogel and thus activates its EMI shielding performance. This function switch is reversible by repeatedly compressing and decompressing the aerogel. The availability of such a never-before-realized off/on switchable EMI shielding material provides an opportunity for the development of advanced smart EM devices.

Folding-mediated soft elasticity and bandgap variation in mechanical metamaterials

Soft mechanical metamaterials with hinge-like elements can undergo multi-step reconfiguration through folding and contacts, and thus exhibit highly nonlinear responses. Numerical simulation of the nonlinear behaviors is essential for the design and control of the mechanical metamaterials, but it remains a challenge due to complicated nonlinear effects. Here, we report the finite element modeling of multi-step reconfiguration of a shape-changing metamaterial, and elucidate the underlying mechanism of soft elasticity. The predicted stress–strain curve together with the folding angles of hinge elements shows excellent agreement with experimental data reported in the literature. Moreover, we explore the influence of reconfiguration and folding-induced internal stress on the bandgap distribution of the mechanical metamaterials. Our efforts provide useful guidelines for the design and application of mechanical metamaterials for both static and dynamic situations.

Achieving selective snapping-back and enhanced hysteresis in soft mechanical metamaterials via fiber reinforcement

When a soft mechanical metamaterial, consisting of a regular array of representative volume elements (RVEs), is stressed up to a large strain, the delicately tailored behavior of the RVE does not prevail in the metamaterial due to the boundary effect and manufacturing imperfections. A metamaterial sheet comprising RVEs designed for snapping-back behavior exhibits random snapping-through instability when uniaxially stretched. We conceptualize that loss of representativeness of RVE can be avoided by introducing fiber reinforcement to regulate boundary conditions. Through a combination of experiments and numerical simulation, we demonstrate that fiber reinforcements tune behavior of a metamaterial sheet from random snapping-through to sequential and even selective snapping-back instability by introducing small structural variations. Ideal snapping-back instability, characterized by sharp variations of forces in both loading and unloading processes, is captured, while the latter is typically hard to observe in real experiments. Enhanced energy dissipation rate from 25.3% for the case without fiber to 46.4% for the case with fiber-reinforcement is recorded in experiments, when the metamaterial sheet is stretched up to 200% and then released to restore its original length.

A nonlinear mechanics model of soft network metamaterials with unusual swelling behavior and tunable phononic band gaps

Soft mechanical metamaterials with negative swelling responses represent a class of man-made materials with specially engineered micro-architectures, which are attractive for applications in areas such as biomedical engineering, aerospace and microelectronics. These soft mechanical metamaterials are usually constructed with laminated filaments that serve as building block structures in periodic lattices, with capabilities to convert hydraulic deformations of active materials into large bending deformations of the filamentary microstructures. The previous studies mainly relied on massive calculations of finite element analyses (FEA) as the core process of metamaterial designs to achieve targeted mechanical properties. The FEA calculations could, however, be very cumbersome and time-consuming, especially when the micro-architecture involves a large number of complex microstructures. This paper introduces a theoretical model that can predict accurately the swelling-induced deformations in such soft mechanical metamaterials consisting of sandwiched horseshoe microstructures. This model takes into account the evident shape change of sandwiched cross section observed in experiments, during the hydration process. Experimental and computational studies on mechanical metamaterials with a wide range of microstructure geometries were carried out to validate the developed model. These results unveil the significant role of out-of-plane deformations on the swellability of the mechanical metamaterials. The theoretical model sheds light on the essential microstructure-property relationship, which could serve as a reference of metamaterial designs to achieve desired swelling behavior. Furthermore, we leverage the active control of microstructure geometry during hydration to offer tunable phononic band structures, with potential applications in noise/vibration control and wave mitigation.

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.

Large deformation shape optimization of cut-mediated soft mechanical metamaterials

Cutting various patterns in elastomeric sheets has emerged as a simple yet effective way to fabricate soft mechanical metamaterials with unusual or auxetic properties. Upon stretching, the cut ligaments of the metamaterial deform severely and much higher stress is induced around the notch due to stress concentration. This would limit the stretchability or even result in fracture of the cut-mediated metamaterials. Optimization of cut-mediated mechanical materials has been rarely, if at all, been explored, partially due to the difficulty of nonlinear optimization and analysis of materials with large deformation. We present an integrated strategy and a platform based on commercial software to optimize cut-mediated soft mechanical metamaterials. Optimization of the metamaterial is realized by modifying the boundary shape of cut ligaments, which would reduce stress concentration, generate larger negative Poisson’s ratio, and allow enhanced stretchability. Our optimization scheme of metamaterials would aid design and fabrication of mechanical metamaterials and transforming structures.

Multimaterial Control of Instability in Soft Mechanical Metamaterials

Soft mechanical metamaterials working on the basis of instability have numerous potential applications in the context of machine materials. Controlling the onset of instability is usually required when rationally designing such metamaterials. We study the isolated and modulated effects of geometrical design and material distribution on the onset of instability in multimaterial cellular metamaterials. We use multimaterial additive manufacturing to fabricate cellular specimens whose unit cells are divided into void space, a square element, and an intermediate ligament. The ratio of the elastic modulus of the ligament to that of the square element [(EL)/(ES)] is changed by using different material types. Computational models are also developed, validated against experimental observations, and used to study a wide range of possible designs. The critical stress can be adjusted independently from the critical strain by changing the material type while keeping [(EL)/(ES)] constant. The critical strain shows a power-law relationship with [(EL)/(ES)] within the range [(EL)/(ES)]=0.1-10. The void shape design alters the critical strain by up to threefold, while the combined effects of the void shape and material distribution cause up to a ninefold change in the critical strain. Our findings highlight the strong influence of material distribution on the onset of the instability and buckling mode.

Soft mechanical metamaterials with unusual swelling behavior and tunable stress-strain curves.

Soft adaptable materials that change their shapes, volumes, and properties in response to changes under ambient conditions have important applications in tissue engineering, soft robotics, biosensing, and flexible displays. Upon water absorption, most existing soft materials, such as hydrogels, show a positive volume change, corresponding to a positive swelling. By contrast, the negative swelling represents a relatively unusual phenomenon that does not exist in most natural materials. The development of material systems capable of large or anisotropic negative swelling remains a challenge. We combine analytic modeling, finite element analyses, and experiments to design a type of soft mechanical metamaterials that can achieve large effective negative swelling ratios and tunable stress-strain curves, with desired isotropic/anisotropic features. This material system exploits horseshoe-shaped composite microstructures of hydrogel and passive materials as the building blocks, which extend into a periodic network, following the lattice constructions. The building block structure leverages a sandwiched configuration to convert the hydraulic swelling deformations of hydrogel into bending deformations, thereby resulting in an effective shrinkage (up to around -47% linear strain) of the entire network. By introducing spatially heterogeneous designs, we demonstrated a range of unusual, anisotropic swelling responses, including those with expansion in one direction and, simultaneously, shrinkage along the perpendicular direction. The design approach, as validated by experiments, allows the determination of tailored microstructure geometries to yield desired length/area changes. These design concepts expand the capabilities of existing soft materials and hold promising potential for applications in a diverse range of areas.

Shape-matching soft mechanical metamaterials

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce “shape-matching” metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier’s series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices.

Rational design of soft mechanical metamaterials: Independent tailoring of elastic properties with randomness

The elastic properties of mechanical metamaterials are direct functions of their topological designs. Rational design approaches based on computational models could, therefore, be used to devise topological designs that result in the desired properties. It is of particular importance to independently tailor the elastic modulus and Poisson's ratio of metamaterials. Here, we present patterned randomness as a strategy for independent tailoring of both properties. Soft mechanical metamaterials incorporating various types of patterned randomness were fabricated using an indirect additive manufacturing technique and mechanically tested. Computational models were also developed to predict the topology-property relationship in a wide range of proposed topologies. The results of this study show that patterned randomness allows for independent tailoring of the elastic properties and covering a broad area of the elastic modulus-Poisson's ratio plane. The uniform and homogenous topologies constitute the boundaries of the covered area, while topological designs with patterned randomness fill the enclosed area.

Switching of deformation modes in soft mechanical metamaterials

ABSTRACTMechanical metamaterials have attracted tremendous interests, owing to their fruitfulness of underlying physics and mechanics as well as diverse potential applications. Conventional soft mechanical metamaterials contain periodic distribution of holes having identical sizes, which can only display one mechanical function. Periodically dispersing a regular pattern of through-holes with two sizes into an elastomer results in metamaterials with more mechanical functions and deformation scenarios. We numerically investigate the deformation behaviors of this type of metamaterials. Switching of modes from the buckling-dominated deformation to a loss-of-instability deformation is emphasized. Replacing the pattern of holes with the same sizes by a pattern of holes with two sizes imposes higher compliance and even loss of negative Poisson’s ratio of the material.