Negative Stiffness Metamaterials Research Articles

Design exploration of additively manufactured metamaterials

Additive manufacturing (AM) is making a profound impact on our ability to realize complex metamaterials and structures, but fully realizing the manufacturing freedom afforded by AM requires some significant advances in engineering design methods and tools. For some additive manufacturing applications, simulation-based design tools may be required to explore a hierarchy of features, ranging in size from microns to meters. At the same time, these tools need to provide real-time feedback on the constraints and process-structure-property relationships relevant to specific AM technologies, and this Design-for-AM feedback is needed during the design process, rather than at the end. To address these challenges, a design exploration approach has been established for creating inverse maps of promising regions of a hierarchical structural/material design space. The approach utilizes machine learning classifiers for identifying sets of promising solutions to a materials design problem, combined with statistical characterization of geometric features and material properties to ensure that the designs are robustly manufacturable. The capabilities of the approach are demonstrated by applying it to the hierarchical design of negative stiffness metamaterials for energy absorption applicationsAdditive manufacturing (AM) is making a profound impact on our ability to realize complex metamaterials and structures, but fully realizing the manufacturing freedom afforded by AM requires some significant advances in engineering design methods and tools. For some additive manufacturing applications, simulation-based design tools may be required to explore a hierarchy of features, ranging in size from microns to meters. At the same time, these tools need to provide real-time feedback on the constraints and process-structure-property relationships relevant to specific AM technologies, and this Design-for-AM feedback is needed during the design process, rather than at the end. To address these challenges, a design exploration approach has been established for creating inverse maps of promising regions of a hierarchical structural/material design space. The approach utilizes machine learning classifiers for identifying sets of promising solutions to a materials design problem, combined with statistical char...

Tunable Mechanical Metamaterial with Constrained Negative Stiffness for Improved Quasi‐Static and Dynamic Energy Dissipation

This paper presents the computational design, fabrication, and experimental validation of a mechanical metamaterial in which the damping of the material is significantly increased without decreasing the stiffness by embedding a small volume fraction of negative stiffness (NS) inclusions within it. Unlike other systems that dissipate energy primarily through large‐amplitude deformation of nonlinear structures, this metamaterial dissipates energy by amplifying linear strains in the viscoelastic host material. By macroscopically tuning the pre‐strain of the metamaterial via mechanical loading, the embedded NS inclusions operate about a constrained buckling instability. When further macroscopic vibrational excitation is applied, the inclusions amplify the strains of the surrounding viscoelastic medium. This results in enhanced dissipation of mechanical energy when compared to voided or neat comparison media. Microstereolithography, an emerging high‐resolution additive manufacturing (AM) technology, is employed to fabricate the deeply subwavelength inclusions which ensures broadband damping behavior. The mechanically induced broadband energy dissipation and manufacturing approach further differentiate the metamaterial from other approaches that exploit resonances, large deformations, or non‐mechanical instabilities. The computational design, fabrication, and experimental evaluation reported is the first dynamic demonstration of such a mechanically tunable NS metamaterial, potentially enabling components with integrated structural and damping capabilities.

Design Exploration of Reliably Manufacturable Materials and Structures With Applications to Negative Stiffness Metamaterials and Microstereolithography1

One of the challenges in designing metamaterials for additive manufacturing (AM) is accounting for the differences between as-designed and as-built geometries and material properties. From a designer's perspective, these differences can lead to degradation of part and metamaterial performance, which is especially difficult to accommodate in small-lot or one-of-a-kind production. In this context, each part is unique, and therefore, extensive iteration is costly. Designers need a means of exploring the design space while simultaneously considering the reliability of additively manufacturing particular candidate designs. In this work, a design exploration approach, based on Bayesian network classifiers (BNC), is extended to incorporate manufacturing variation into the design exploration process and identify designs that reliably meet performance requirements when this variation is taken into account. The example application is the design of negative stiffness (NS) metamaterials, in which small volume fractions of NS inclusions are embedded within a host material. The resulting metamaterial or composite exhibits macroscopic mechanical stiffness and loss properties that exceed those of the base matrix material. The inclusions are fabricated with microstereolithography with features on the scale of tens of microns, but variability is observed in material properties and dimensions from specimen to specimen. This variability is measured and modeled via design, fabrication, and characterization of metrology parts. The quantified manufacturing variability is incorporated into the BNC approach as a manufacturability classifier to identify candidate designs that achieve performance targets reliably, even when manufacturing variability is taken into account.

Mechanical Performance of Multidirectional Buckling-Based Negative Stiffness Metamaterials: An Analytical and Numerical Study.

Unidirectional, bidirectional and tridirectional Buckling-based Negative Stiffness (BNS) lattice metamaterials are designed by adding prefabricated curved beams into multidimensional rigid frames. Finite Element Analysis models are built, and their mechanical performance is investigated and discussed. First, geometric parameters of the curved beam were systematically studied with numerical analyses and the results were validated by theoretical solutions. Next, within unidirectional designs of different layer numbers, the basic properties of multilayer BNS metamaterials were revealed via quasi-static compressions. Then, the bidirectional and tridirectional designs were loaded on orthogonal axes to research both the quasi-static and dynamic behaviors. For dynamic analysis conditions, simulation scenarios of different impact velocities were implemented and compared. The results demonstrate that the proposed numerical analysis step has accurately predicted the force-displacement relations of both the curved beam and multilayer designs and the relations can be tuned via different geometric parameters. Moreover, the macroscopic performance of the metamaterials is sensitive to the rigidity of supporting frames. The shock force during impact is reduced down below the buckling thresholds of metamaterial designs and sharp impact damage is avoided. The presented metamaterials are able to undergo multiaxial stress conditions while retaining the negative stiffness effect and energy-absorbing nature and possess abundant freedom of parametric design, which is potentially useful in shock and vibration engineering.

Hierarchical Design of Negative Stiffness Metamaterials Using a Bayesian Network Classifier1

A set-based approach is presented for exploring multilevel design problems. The approach is applied to design negative stiffness metamaterials with mechanical stiffness and loss properties that surpass those of conventional composites. Negative stiffness metamaterials derive their properties from their internal structure, specifically by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design involves managing complex interdependencies among design variables across a range of length scales. Hierarchical material models are created for length scales ranging from the structure of the microscale negative stiffness inclusions to the effective properties of mesoscale metamaterials to the performance of an illustrative macroscale component. Bayesian network classifiers (BNCs) are used to map promising regions of the design space at each hierarchical modeling level, and the maps are intersected to identify sets of multilevel solutions that are likely to provide desirable system performance. The approach is particularly appropriate for highly efficient, top-down, performance-driven, multilevel design, as opposed to bottom-up, trial-and-error multilevel modeling.

Negative stiffness metamaterials and periodic composites

The creation of negative stiffness (NS) metamaterials is of interest for damping treatments, vibration isolation, and even more exotic applications such as acoustic lenses displaying negative refraction. This work will present ongoing efforts to produce NS metamaterial elements that rely on a bistable microscale geometry that leads to NS under quasistatic loading conditions. A candidate bistable microstructure employing thermal mismatch will be introduced along with finite element simulations predicting its full stiffness tensor. Effective medium modeling will show the broadband utility of these elements to enhance acoustic absorption for low volume fraction bi-material composites. The special case of a bi-material periodic composite containing NS inclusions will then be explored. It will be shown that a periodic composite containing NS inclusions permits the simultaneous elimination of the acoustic branch and reduction of the lower frequency of the optical branch passband to arbitrarily low frequencies. Physical interpretations of these results and potential applications will be discussed. This material is based upon work supported by the U. S. Army Research Office under grant number W911NF-11-1-0032.

Constrained negative stiffness metamaterials.

Acoustics‐oriented metamaterial research has focused primarily on the use of subwavelength resonant structures to elicit unconventional macroscale properties such as negative mass, anisotropic density, and negative stiffness. Unfortunately, reliance on resonant behavior limits the usefulness of these types of metamaterials to a narrow band of frequencies. One intriguing manifestation of negative stiffness, however, does not require resonant behavior and is therefore useful over a broader range of frequencies. This type of negative stiffness relies on constrained bistable structures and is known as constrained negative stiffness (CNS). The present work investigates the use of CNS mechanisms for vibration isolation and acoustic wave attenuation. A linearized analytical model of a constrained buckled beam structure is presented to predict system behavior and stability, and investigate the fundamental physical behavior leading to increased energy absorption. Experimental studies are then shown confirming model predictions. Finally, a 1‐D candidate acoustical metamaterial containing CNS inclusions is modeled and analyzed.