Auxetic Perforated Mechanical Metamaterials with Randomly Oriented Cuts

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

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

Generative models struggle with kirigami metamaterials

Generative machine learning models have shown notable success in identifying architectures for metamaterials-materials whose behavior is determined primarily by their internal organization-that match specific target properties. By examining kirigami metamaterials, in which dependencies between cuts yield complex design restrictions, we demonstrate that this perceived success in the employment of generative models for metamaterials might be akin to survivorship bias. We assess the performance of the four most popular generative models-the Variational Autoencoder (VAE), the Generative Adversarial Network (GAN), the Wasserstein GAN (WGAN), and the Denoising Diffusion Probabilistic Model (DDPM)-in generating kirigami structures. Prohibiting cut intersections can prevent the identification of an appropriate similarity measure for kirigami metamaterials, significantly impacting the effectiveness of VAE and WGAN, which rely on the Euclidean distance-a metric shown to be unsuitable for considered geometries. This imposes significant limitations on employing modern generative models for the creation of diverse metamaterials.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

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

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.

Studies of Auxetic Structures Assembled from Rotating Rectangles

The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson's ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure's linear dimensions and Poisson's ratio. The obtained findings suggest that Poisson's ratio is intricately tied to the structure's opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson's ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson's ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles.

Modeling of metamaterial based incision patterns for generating high expansions in skin grafts

BACKGROUND

Split-thickness skin grafting is a widely used treatment for burn patients. It requires removing a small portion of healthy skin, making parallel incisions on it, stretching it, and surgically implanting it into the burn site. Although skin graft mesher companies claim to significantly expand the size of the skin graft, in reality, the amount of expansion achieved is much smaller.

METHODS

This study aimed to improve the expansion potential of skin grafts by designing new incision patterns with auxetic properties, using a skin simulant material and additive manufacturing. The mechanical properties and digital image correlation was used to analyze the strain, effective Poisson's ratio, local strains, void area, and meshing ratio of the auxetic skin graft simulants.

FINDINGS

The results showed that the Y-shaped skin graft simulant had the highest effective negative Poisson's ratio, largest areal expansions, lowest maximum induced stresses and strains, and uniform strain distribution properties, making it the best choice for generating high expansions in skin grafts.

INTREPRETATION

The study found that the expansions were highly strain sensitive, with higher auxeticity observed at lower strains. The novel findings with auxetic skin graft simulants are expected to provide valuable insights for developing skin grafts with higher expansion potential in the future.

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

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

Auxetic Kirigami Metamaterials upon Large Stretching

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

A DFT-Based Quantitative and Geometric Analysis of the Effect of Pressure on Boron Arsenate

Boron arsenate, BAsO₄, is a β-cristobalite-like crystal which has been reported to exhibit the rather unusual property of negative linear compressibility behaviour at elevated pressures, that is expanding rather than shrinking in a linear dimension when subjected to pressure. This work proposes a ‘geometry—deformation mechanism’-based mathematical model to aid the discernment of the manner how this anomalous pressure behaviour is achieved. The model makes use of data obtained from DFT simulations over an extended range of pressures, including extreme pressure conditions, and rigorously explains the macroscopic properties of this material in terms of the nanoscale deformations. More specifically, through this model, it was possible to decipher the different contributions to the deformation mechanism and compressibility properties of BAsO₄. Moreover, for the first time, it was shown that a rule related to the sum of angles of tetrahedrally coordinated atoms is so robust that it applies at the extreme pressures studied here.

Review: Auxetic Polymer-Based Mechanical Metamaterials for Biomedical Applications

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

Biomechanical modeling of novel high expansion auxetic skin grafts

Over 20 million burn injuries are reported every year, with severe cases requiring skin grafting. Traditionally, split thickness skin grafts are prepared by excising a small portion of healthy skin and its incision patterning using a suitable meshing device, which allows the graft to be expanded beyond its capacity. To date, the maximum expansion achieved through skin grafting has been reported to be less than three times, which is not sufficient for covering large burn sites with limited donor site skin. In this work, we have attempted to study skin graft expansion potential with novel auxetic patterns, which are known to exhibit negative Poisson's effect. Two-layer skin graft models were developed using eight different auxetic incision patterns, and subjected to uniaxial and biaxial tensile strains. The Poisson's ratio, meshing ratio, and induced stresses were characterized for all graft models. The numerical results indicated expansion potentials greater than that of traditional skin grafts across all loads. Extremely high expansions (i.e., >30 times) were estimated for the I-Shaped Re-entrant and Rotating Triangles shaped auxetic models without rupture. Such pioneering findings are anticipated to initiate ground-breaking advances towards skin graft research and improved outcomes in burn surgeries.

Feasible strategy for simultaneously achieving excellent frequency selective characteristic and ultralight mechanical properties

Materials with both excellent frequency selective characteristic and ultralight mechanical properties are highly urgent demanded for its potential applications such as absorbing materials, artificial magnetic conductors, antenna and so on. However, although the research about materials with only excellent frequency selective characteristic or ultralight mechanical properties is advanced, in most cases, it is still a challenge that making a material possesses excellent frequency selective characteristic and ultralight mechanical properties simultaneously. So how to make the two properties achieving a high level simultaneously is a hot topic which remains to be solved. Herein, we proposed a novel and feasible strategy for achieving simultaneously excellent frequency selective characteristic and ultralight mechanical properties material. According to our strategy, the composite we designed behaviors as a FSS which can realize highly efficiency stop bands in 16.09-16.4GHz and 17.11-17.36GHz. At the same time, the composite can be regarded as an ultralight mechanical metamaterial. The relativity density of the composite can reduce to 431.99 Kg/m³, which have a distinct advantage compared with the dielectric layers that conversional FSS used. Moreover, Its elasticity modulus can reach 112.25 MPa and its bending stiffness can reach 90.54 N/mm. These performances show that although the density of the composite is reduced, the composite can still keep well mechanical properties. The strategy we proposed gives a good solution to the problem existing in the materials which desire both excellent frequency selective characteristic and ultralight mechanical properties. The composite is a designing example which can be applied in engineering. So the strategy is a guideline for researchers to achieve composite which owns both excellent frequency selective characteristic and ultralight mechanical properties.

Shearing Deformations of β-Cristobalite-Like Boron Arsenate

Boron arsenate, BAsO4, is crystalline material (I4¯ group) that was recently shown to be auxetic in its (001) plane for loading in any direction in this plane, and, which exhibits negative linear compressibility at elevated pressured in its [001] direction. This work presents and discusses the results of extensive density functional theory (DFT) based simulations aimed at studying deformations that such crystals undergo when subjected to shear loading in an attempt to obtain a better insight into the manner in which this material responds to mechanical loads. The deformations for shearing in the (001) plane are described in terms of the ‘rotating squares’ model, which was used to explain the auxeticity in the same plane where it was shown that shear loading results primarily in deformations which make the ‘squares’ become ‘parallelogram-like’ rather than rotate. This lack of rigidity in projected ‘squares’ was discussed by looking at changes in bond lengths and bond angles.

Elucidating the Mechanical Energy for Cyclization of a DNA Origami Tile

DNA origami has emerged as a versatile method to synthesize nanostructures with high precision. This bottom-up self-assembly approach can produce not only complex static architectures, but also dynamic reconfigurable structures with tunable properties. While DNA origami has been explored increasingly for diverse applications, such as biomedical and biophysical tools, related mechanics are also under active investigation. Here we studied the structural properties of DNA origami and investigated the energy needed to deform the DNA structures. We used a single-layer rectangular DNA origami tile as a model system and studied its cyclization process. This origami tile was designed with an inherent twist by placing crossovers every 16 base-pairs (bp), corresponding to a helical pitch of 10.67 bp/turn, which is slightly different from that of native B-form DNA (~10.5 bp/turn). We used molecular dynamics (MD) simulations based on a coarse-grained model on an open-source computational platform, oxDNA. We calculated the energies needed to overcome the initial curvature and induce mechanical deformation by applying linear spring forces. We found that the initial curvature may be overcome gradually during cyclization and a total of ~33.1 kcal/mol is required to complete the deformation. These results provide insights into the DNA origami mechanics and should be useful for diverse applications such as adaptive reconfiguration and energy absorption.

Cellular Auxetic Structures for Mechanical Metamaterials: A Review

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

Random auxetics from buckling fibre networks

Auxetic materials have gained increasing interest in the last decades, fostered by auspicious applications in various fields. While the design of new auxetics has largely focused on meta-materials with deterministic, periodically arranged structures, we show here by theoretical and numerical analysis that pronounced auxetic behaviour with negative Poisson's ratios of very large magnitude can occur in random fibre networks with slender, reasonably straight fibre segments that buckle and deflect. We further demonstrate in experiments that such auxetic fibre networks, which increase their thickness by an order of magnitude and more than quintuple their volume when moderately extended, can be produced by electrospinning. Our results thus augment the class of auxetics by a large group of straightforwardly fabricable meta-materials with stochastic microstructure.

Shape-morphing architected sheets with non-periodic cut patterns

We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause a sheet to buckle into three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. These global buckling modes are observed in experiments and rationalized by an in-plane kinematic analysis that highlights the role of the geometric frustration arising from non-periodicity. The study focuses on elastic sheets, and is later extended to elastic-plastic materials to achieve shape retention. Our work illustrates a scalable route towards the fabrication of three-dimensional objects with nonzero Gaussian curvature from initially-flat sheets.

Nanocardboard as a nanoscale analog of hollow sandwich plates

Corrugated paper cardboard provides an everyday example of a lightweight, yet rigid, sandwich structure. Here we present nanocardboard, a monolithic plate mechanical metamaterial composed of nanometer-thickness (25-400 nm) face sheets that are connected by micrometer-height tubular webbing. We fabricate nanocardboard plates of up to 1 centimeter-square size, which exhibit an enhanced bending stiffness at ultralow mass of ~1 g m-2. The nanoscale thickness allows the plates to completely recover their shape after sharp bending even when the radius of curvature is comparable to the plate height. Optimally chosen geometry enhances the bending stiffness and spring constant by more than four orders of magnitude in comparison to solid plates with the same mass, far exceeding the enhancement factors previously demonstrated at both the macroscale and nanoscale. Nanocardboard may find applications as a structural component for wings of microflyers or interstellar lightsails, scanning probe cantilevers, and other microscopic and macroscopic systems.

Stiff auxetics: Hierarchy as a route to stiff, strong lattice based auxetic meta-materials

Using a combination of analytic and computational methods, we examine the effect of adding hierarchical substructure to an auxetic lattice. Our novel methodology, involving a coarse grain approach, allows for the analysis of hierarchically sub-structured lattices where direct computation would prove intractable. We show that through hierarchy one can create ultra-lightweight auxetic meta-materials of high strength and stiffness. Through scaling law arguments, we show that the benefits of hierarchical design can also be obtained in the general class of bending-dominated lattices. Furthermore, we show that the hierarchical structures presented show a wide range of tailorability in their mechanical properties, and exhibit increased strength when optimised for buckling resistance. Auxetic materials have a broad range of potential applications, and thus the creation of ultra-light auxetic meta-materials with enhanced stiffness and strength is undoubtedly of practical importance.

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

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

Soft network materials with isotropic negative Poisson's ratios over large strains

Auxetic materials with negative Poisson's ratios have important applications across a broad range of engineering areas, such as biomedical devices, aerospace engineering and automotive engineering. A variety of design strategies have been developed to achieve artificial auxetic materials with controllable responses in the Poisson's ratio. The development of designs that can offer isotropic negative Poisson's ratios over large strains can open up new opportunities in emerging biomedical applications, which, however, remains a challenge. Here, we introduce deterministic routes to soft architected materials that can be tailored precisely to yield the values of Poisson's ratio in the range from -1 to 1, in an isotropic manner, with a tunable strain range from 0% to ∼90%. The designs rely on a network construction in a periodic lattice topology, which incorporates zigzag microstructures as building blocks to connect lattice nodes. Combined experimental and theoretical studies on broad classes of network topologies illustrate the wide-ranging utility of these concepts. Quantitative mechanics modeling under both infinitesimal and finite deformations allows the development of a rigorous design algorithm that determines the necessary network geometries to yield target Poisson ratios over desired strain ranges. Demonstrative examples in artificial skin with both the negative Poisson's ratio and the nonlinear stress-strain curve precisely matching those of the cat's skin and in unusual cylindrical structures with engineered Poisson effect and shape memory effect suggest potential applications of these network materials.

Self-controlled wave propagation in hyperelastic media

We demonstrate theoretically that an ultrasonic wave propagating in a hyperelastic medium can self-control its phase velocities. This phenomenon occurs because the propagation of the ultrasonic wave generates acoustic radiation stresses in the medium, which can induce large deformation of the medium with significant stiffening effect. In turn, such deformation reshapes the wave propagation while the deformation stiffening changes significantly the phase velocities of the wave till the acoustic radiation stresses are balanced by elastic stresses in the current configuration of the hyperelastic medium. As a result of deformation stiffening, an initially isotropic medium becomes anisotropic, thus enabling self-control or self-bending of the wave propagation. We further reveal that, due to snap-through instability of acoustomechanical deformation in the hyperelastic medium, the ultrasonic wave can discontinuously switch its phase velocities from one state to another by jumping over a large unstable regime. This self-control and switchable mechanism of ultrasonic wave propagation in homogenous hyperelastic media offers innovative design opportunities for phononic, thermal and acoustic materials and devices.

Negative Poisson's ratio in graphene oxide

We perform molecular dynamics simulations to investigate the Poisson's ratio of graphene oxide. We find that the Poisson's ratio can be effectively tuned by increasing the degree of oxidation of graphene oxide. More specifically, the Poisson's ratio decreases linearly from positive to negative with increasing oxidation, turning negative at room temperature for a degree of oxidation of 0.27, and reaching a value of -0.567 for fully oxidized graphene. The oxidation dependence of the Poisson's ratio is attributed to the tension-induced suppression of the ripples resulting from the oxidation, whose amplitude increases with increasing oxidation. Finally, we also demonstrate the temperature dependence of the Poisson's ratio in the graphene oxide.

Effects of size and surface on the auxetic behaviour of monolayer graphene kirigami

Graphene is an active element used in the design of nano-electro-mechanical systems (NEMS) owing to its excellent in-plane physical properties on mechanical, electric and thermal aspects. Considering a component requiring negative Poisson’s ratio in NEMS, a graphene kirigami (GK) containing periodic re-entrant honeycombs is a natural option. This study demonstrates that a GK with specific auxetic property can be obtained by adjusting the sizes of its honeycombs. Using molecular dynamics experiments, the size effects on the auxetic behaviour of GK are investigated. In some cases, the auxetic difference between the hydrogenated GK and continuum kirigami (CK) is negligible, in which the results from macro CK can be used to predict auxetic behaviour of nano kirigami. Surface effect of GK is demonstrated from two aspects. One is to identify the difference of mechanical responses between the pure carbon GK and the hydrogenated GK at same geometry and loading condition. Another is from the difference of mechanical responses between the GK model and the CK model under same loading condition and geometric configuration. Generally, surface energy makes the GK possess higher variation of auxetic behaviour. It also results in higher modulus for the GK as comparing with that of the CK.

Negative Poisson's Ratio in Modern Functional Materials

Materials with negative Poisson's ratio attract considerable attention due to their underlying intriguing physical properties and numerous promising applications, particularly in stringent environments such as aerospace and defense areas, because of their unconventional mechanical enhancements. Recent progress in materials with a negative Poisson's ratio are reviewed here, with the current state of research regarding both theory and experiment. The inter-relationship between the underlying structure and a negative Poisson's ratio is discussed in functional materials, including macroscopic bulk, low-dimensional nanoscale particles, films, sheets, or tubes. The coexistence and correlations with other negative indexes (such as negative compressibility and negative thermal expansion) are also addressed. Finally, open questions and future research opportunities are proposed for functional materials with negative Poisson's ratios.

Tensional acoustomechanical soft metamaterials

We create acoustomechanical soft metamaterials whose response to uniaxial tensile stressing can be easily tailored by programming acoustic wave inputs, resulting in force versus stretch curves that exhibit distinct monotonic, s-shape, plateau and non-monotonic snapping behaviors. We theoretically demonstrate this unique metamaterial by considering a thin soft material sheet impinged by two counter-propagating ultrasonic wave inputs across its thickness and stretched by an in-plane uniaxial tensile force. We establish a theoretical acoustomechanical model to describe the programmable mechanics of such soft metamaterial, and introduce the first- and second-order tangential stiffness of its force versus stretch curve to boundary different behaviors that appear during deformation. The proposed phase diagrams for the underlying nonlinear mechanics show promising prospects for designing tunable and switchable photonic/phononic crystals and microfluidic devices that harness snap-through instability.