Negative Stiffness Metamaterials Research Articles

OPTIMIZING THE GEOMETRICAL PARAMETERS OF 3D PRINTED NEGATIVE STIFFNESS METAMATERIAL USING TAGUCHI METHOD

The field of negative stiffness metamaterials (NSM) is a rapidly developing area within the realm of mechanical metamaterials. This work presents a novel negative stiffness metamaterial based on a bistable structure that consists of a straight beam with an elastic element shaped like a ring. Further, this work presents the findings of a Taguchi-based experiment aimed at optimizing geometrical parameters in negative stiffness metamaterial. The Taguchi method, known for its efficiency in experimental design and analysis, was employed to systematically study the effects of various factors on snapping force for a novel structure exhibiting negative stiffness. The experiment utilized L18 mixed level orthogonal array. All the test samples were fabricated using additive manufacturing technique. Signal-to-noise ratio analysis and analysis of variance were two statistical approaches that were used to comprehensively evaluate the acquired data. The results of this study provide valuable insights into the optimal geometrical configuration for maximizing snapping force of negative stiffness metamaterial.

3D bi-stable negative stiffness mechanical metamaterials for bandgap tuning

A recent topic of interest in dynamics research is bi-stable negative stiffness (NS) mechanical metamaterials that allow for the efficient control of wave propagation and bandgap (BG) tuning. In this study, a three-dimensional bi-stable NS mechanical metamaterial based on fan-shaped inclined beams was developed. It has BGs in multiple directions as well as significant BG tuning capability in specific direction, and the ability to design for multiple geometrical parameters. First, the requirements for NS mechanical metamaterials to achieve bi-stable properties were theoretically investigated. Subsequently, the deformation process of the unit cell of the metamaterial under uniaxial compression and the band structure and vibrational properties of the metamaterial under different steady states were analyzed through a combination of finite element method and experiments. The results showed that the BG range of the bi-stable NS metamaterials in the vertical direction changed with the switching of the steady state, whereas the out-of-plane BG in the horizontal direction remained constant. Therefore, this bi-stable NS mechanical metamaterial could realize modulation of the BG as well as control of wave propagation in multiple directions. In addition, bi-stable NS metamaterials with different angles exhibited different BG ranges. Finally, the vibrational transmittances of the metamaterials were investigated to verify the accuracy of the BG range.

A self-recoverable negative stiffness metamaterial with enhanced bearing and energy dissipation capacity

Because of their desirable properties, mechanical metamaterials have drawn increasing attention. Negative stiffness (NS) metamaterials can be used as reusable energy dissipation devices, but they usually have low bearing capacity. In this study, a self-recoverable NS structure with enhanced bearing and energy dissipation capacity was proposed. It breaks free from the size limitations of curved beams or thin rods, and can have high bearing and energy dissipation capacity through the mutual extrusion and friction between the snap plug and the layered snap groove. The mechanical properties of the proposed NS structure were studied by finite element analysis and experiments. The reusability of the structure was verified by cyclic loading experiments. The results show that compared with the traditional curved beam NS structure and the previously self-recoverable NS structure, the bearing and energy dissipation capacity of the proposed structure have been greatly improved.

Negative stiffness metamaterial with elastic energy dissipation based on conical shell: theoretical solution and experimental study

Negative stiffness (NS) metamaterials with the capability of elastic energy dissipation have gained substantial attention for their potential in shock absorption and vibration control. However, their practical application is often limited by their strength and stiffness. This study investigates an NS material that generates the NS phenomenon based on stretching and rotation of conical shells, akin to coned disk springs. This approach enhances the strength and loading capacity of the material compared to metamaterials based on conventional beam or shell structures. To fully understand the behavior of this material, a theoretical framework is presented, followed by a comprehensive validation process involving tests and numerical simulations. The applicability and constraints of the theoretical solution are discussed, and a parametric analysis is undertaken based on the solution. Finally, NS metamaterials based on the proposed mechanism are fabricated and tested, which showcases their strength and elastic energy dissipation capacity.

Negative stiffness metamaterial with directional stability in uniform fields

Negative stiffness metamaterials have been widely studied due to their unusual properties and potential applications in shape reconfiguration, shock isolation, and reusable energy absorption, but their stability in fields has been less studied. In this work, a theoretical framework for determining the stability of negative stiffness metamaterials in a uniform field is established. More importantly, the concepts of directional stability and semi-directional stability are proposed for the metamaterials that have different stability in different field directions; metamaterials with different physical feature distributions are designed and prepared to achieve such ability, and the finite element simulation is used for theory verification and parameter study. The proposed metamaterial has the potential to be applied as field direction detectors and field-sensitive electrical relays.

Elastic architected mechanical metamaterials with negative stiffness effect for high energy dissipation and low frequency vibration suppression

In this research, mechanical metamaterials with negative stiffness (NS) effect were architected and fabricated for high energy dissipation and low frequency vibration suppression. Periodic cellular metamaterials formed by connecting multiple NS elements in series exhibited hysteresis and lengthy sawtooth loading and unloading plateaus, which made them desirable for use in energy dissipation applications. And the key point was that the deformation of these metamaterials was completely reversible. To determine the underlying cause of hysteresis, the mechanical behavior with phase-transition characteristics was analyzed. Then, a finite element model was built, and the numerical simulation results were compared to the experimental test findings of the metamaterials, and the two were in good agreement, verifying the validity of the model. Furthermore, the influences of structural parameters on mechanical characteristics were systematically investigated and discussed utilizing the numerical models that had undergone experimental validation. The energy dissipation effect resulting from the phase transformation mechanisms could also be applied to the field of vibration control. Corresponding hammer tests were performed to explore the dynamic behavior of the NS metamaterials. The results show that the proposed metamaterials exhibit excellent vibration suppression performance, especially for low frequency vibration mitigation.

An energy dissipation metamaterial based on Coulomb friction and vibration

Compared with traditional energy dissipation structures, negative stiffness metamaterials can repeatedly dissipate energy without incurring irreversible plastic deformation. The existing negative stiffness structures are generally multistable, and their energy dissipation mechanism is either through internal component vibration or friction. In this paper, a self-recoverable negative stiffness structure was proposed which can dissipate energy through both vibration and Coulomb friction. The structure consists of an external I-shaped structure and a buckle-like structure composed of a plug and cantilever beams inside. The proposed structure achieves monostable characteristics by utilizing the concept of self-contact. To investigate the mechanical properties, quasi-static loading-unloading experiments were performed and verified using finite element simulation. The energy dissipated in the proposed structure by vibration and friction was quantified theoretically. The influence of geometric parameters on energy dissipation was studied using simulation and analytical methods. This type of metamaterial has the potential to be employed in the production of multi-functional metamaterial structures such as deformable robots or reusable bumpers.

Additive Manufacturing of Composite Foam Metamaterial Springs for Vibration Isolation

This research introduces a novel approach for reducing the vibrations experienced by passengers in vehicles using metamaterials embedded in polyurethane foam to improve the existing vibration isolation capacity of car seats. An exploration of quasizero and negative stiffness metamaterials is conducted to develop metamaterial springs that exhibit a region of high‐static and low‐dynamic stiffness to achieve vibration isolation. Metamaterials are developed using low‐cost open‐source additive manufacturing methods and thermoplastic polyurethane filament. This investigation follows a process of determining the geometric, material, and systemic design requirements, to identify the quasizero and negative‐stiffness force–displacement regions. Small‐scale models of a car seat are developed by embedding the designed metamaterials into different grades of polyurethane foam and completing static and dynamic testing. The results demonstrate practical applications for implementing metamaterial springs into polyurethane foam to enhance vibration isolation under dynamic loading. The developed material library and the key geometric variables in the metamaterial design allow for application‐specific solutions where the selection of the appropriate metamaterial and foam combination can be tailored to suit the system requirements.

A novel negative stiffness metamaterials: discrete assembly and enhanced design capabilities

In this study, a new negative stiffness metamaterial is designed using laminates with independent negative stiffness properties as the functional component and a discrete assembly method. In this paper, the metamaterial is designed by a mathematical model, which has been verified and analyzed systematically by experiment and finite element method. The influence of each laminate parameter on the design of metamaterials under uniform distribution and gradient distribution was investigated, and based on this, the load-bearing capacity enhancement strategy of metamaterials was further explored. The metamaterial has the advantages of discrete assembly and designability, which solves the defects of the previous performance constrained by the structure and enhances usability.

Design and compression-induced bandgap evolution of novel polygonal negative stiffness metamaterials

The paper proposes a novel polygonal negative stiffness (NS) metamaterial composed of folded beams and stiffening walls, which exhibits excellent performance in attenuating waves over a broad frequency range and shows compression-induced bandgap evolution characteristics. Dispersion relation and bandgaps for the propagation of elastic waves in NS metamaterials are calculated utilizing a semi-analytical periodic spectral method (PS-SAFE). The results demonstrate that broadband bandgaps can be achieved in the proposed polygonal NS metamaterials. Mode analysis and transmission spectrum are utilized to explain the underlying mechanisms of wave attenuation. Furthermore, appropriate deformation conditions are applied to the NS metamaterials to realize compression-induced bandgap evolution, which shows that compression-induced configuration variations significantly impact the frequency range and bandwidth of the bandgaps. As the deformation increases, folded beams enter the elastic instability stage, and the internal stress change strongly influence the vibration displacement modes, leading to various symmetric and antisymmetric displacement vibration modes within a similar frequency range, forming low-frequency broadband bandgaps. This work provides valuable insights into the design of advanced materials for low-frequency broadband wave attenuation.

A novel reinforced cylindrical negative stiffness metamaterial for shock isolation: Analysis and application

Negative stiffness (NS) metamaterials have been widely studied in the fields of shock isolation and energy absorption due to their special properties. For various application scenarios, many types of NS metamaterials have been proposed, such as 2D honeycomb, 3D cube, hollow cylinder. However, when installation space is limited, the hollow cylindrical NS metamaterials may not achieve buffering effect due to its weak stiffness. In this paper, a cylindrical negative stiffness structure with inner hollow parts filled by inclined beam elements is proposed, which can obtain enhanced stiffness and energy absorption by improving space utilization. Theoretical analysis, numerical simulation and experimental validation were carried out to study the quasi-static and dynamic mechanical properties of the structure. Finally, the structure was applied as a cushion in a non-pyrotechnic separator, which could achieve good cushion performance. This work is expected to provide more potential for the applications of cylindrical negative stiffness structures.

Buckling induced negative stiffness mechanical metamaterial for bandgap tuning

Negative-stiffness mechanical metamaterials that can achieve bandgap tuning are a novel area of intense interest, enabling vibration control as well as a wide range of mechanical properties. In this paper, a negative-stiffness mechanical metamaterial consists of beam elements that can be reconfigured for large deformations and the bandgap can be tuned by its deformation behavior. The deformation process of the proposed negative-stiffness metamaterial under uniaxial compression, as well as the band structure and vibration characteristics of the metamaterial under different deformation states are analyzed by a combination of numerical simulation and experiment. The research results show that the proposed negative-stiffness metamaterial suffers from buckling instability and large deformation during uniaxial compression., and has different band structures and band gap ranges under different deformation states. Thus, bandgap tuning can be achieved by the deformation of negative stiffness metamaterials. Furthermore, negative stiffness metamaterials with different angles exhibit different results in bandgap tuning. Finally, the performance of vibration transfer is verified by experiments. This study may provide a new avenue for the related research and design of negative-stiffness mechanical metamaterials with bandgap tuning capabilities.

Study on Energy Absorption Performances of Conical Negative Stiffness Metamaterials

Study on Energy Absorption Performances of Conical Negative Stiffness Metamaterials

A 3D metamaterial with negative stiffness for six-directional energy absorption and cushioning

To attenuate the impact acceleration under multidirectional loads, a mechanical metamaterial with six-directional cushioning and energy-absorbing properties is urgently needed. The study proposes a 3D negative stiffness (NS) metamaterial (NS-MM), which exhibits a bidirectional NS effect and cushion capacity under compressive and tensile loading in three principal directions. The unit cell of NS-MMs contains three pairs of parallel cross-curved beams mounted in a cubical frame, and the NS effect is obtained by controlled elastic buckling of the cross-curved beams. The mechanical analysis of one unit cell is conducted toward predicting the static response. The static performance of the NS-MMs composed of 1×1×1 and 2×2×2 unit cells in three principal directions is investigated by numerical calculations and experiments with quasi-static tension–compression conditions. Comprehensive results indicate the proposed structure has the characteristics of shape recovery, bidirectional NS property, and good energy absorption under tension and compressive loads in one principal direction and has the same mechanical properties in three principal directions. Transient dynamic analysis is exploited to investigate the cushioning performance. The obtained response acceleration (RA) is effectively attenuated in both directions and limited to a certain threshold.

A systematic group of multidirectional buckling-based negative stiffness metamaterials

Negative stiffness (NS) metamaterials are kinds of artificial mechanical materials that exhibit the negative stiffness effect governed by different mechanical mechanisms, among which the buckling-based negative stiffness (BNS) metamaterial consisting of prefabricated curved beams and rigid frames have attracted considerable concern. However, the variety of the reported geometrical configurations of BNS metamaterials is relatively limited, and the study of systematically developing multidirectional buckling-based negative stiffness (MDBNS) metamaterials has rarely been seen at present, especially their mechanical performance. Therefore, the novelty of this study is to design a systematic group of MDBNS metamaterials comprising flexible cosine curved beams and stiffened supporting frames based on Bravais lattices. The group contains 15 element members and has been classified into 5 categories including the 2D bi-directional, 2D tri-directional, 3D tri-directional, 3D quadri-directional, and 3D six-directional NS functional elements. The geometrical configurations of the proposed MDBNS functional elements are respectively constructed based on the systematic arrangement rule of the Bravais lattices that provides the design guidance for the systematic metamaterial group with a fixed number of group members. The mechanical performance of some typical functional elements with the most NS directions and the metamaterial lattices composed of the proposed MDBNS metamaterials have been verified via the Finite Element Analysis (FEA) with the periodic boundary condition (PBC), respectively, while the numerical study has been validated experimentally with 2D MDBNS functional elements via 3D additive manufacturing. The results strongly prove the mechanical NS effects of the proposed MDBNS metamaterials and also indicate that the mechanical behavior is independent if the NS directions are orthogonal, whereas it interacts with each other in the case of non-orthogonal NS directions. The study can also be adopted to develop multidirectional NS metamaterials with other NS functional components and induced mechanisms.

A novel bi-material negative stiffness metamaterial in sleeve-type via combining rigidity with softness

Negative stiffness metamaterials (NSM) can dissipate mechanical energy repeatedly based on a “snap-though” mechanism. However, this mechanism is only effective when many NSM cells are arranged in series or such cell is assembled with a spring. Limits of the mechanism bring a challenge to improve the energy dissipation capacity of the NSM. Here, a novel bi-material NSM in sleeve-type (BMST-NSM) is designed which can dissipate mechanical energy even if the metamaterial is only composed of one negative stiffness cell. The quasi-static loading–unloading experiment is conducted to investigate the characteristics of BMST-NSMs; a multilinear model is presented to characterize the load–displacement curve of BMST-NSMs; and the finite element method (FEM) is used to study the characteristic of strain distribution in BMST-NSMs. Research results show that BMST-NSM can be tailored to be recoverable or multi-stable through parameter design. BMST-NSMs are also tested under different loading speeds and high cyclic loading, which shows that the recoverable BMST-NSM is of good reusability and energy dissipation ability. Moreover, it indicates that BMST-NSM can exhibit a high energy absorption capability within a certain limited displacement range. The presented BMST-NSM has great prospects in low ultra-low frequency vibration isolation and energy dissipation in impacting protection.

Simultaneous energy harvesting and vibration attenuation in piezo-embedded negative stiffness metamaterial

Mechanical metamaterials are uniquely engineered form of periodically arranged unit cells that exhibit interesting frequency-dependent physical properties like negative effective mass, Young’s modulus and Poisson’s ratio. These extreme engineering properties are beyond the natural properties of a material, which can modulate the propagation of wave. In this article, a mechanical realization of one of these uncommon properties called negative stiffness is emulated through analytical simulation. Wave propagation in metamaterials is contingent on frequency, which in turn results in transmission and attenuation bands. Simultaneous vibration control and energy harvesting can be executed by embedding energy harvesting smart material within the resonating units of the metamaterial. However, this needs careful design studies to outline the range of parameters. In this work, first, the band structure of a piezo-embedded negative stiffness metamaterial is studied using generalized Bloch’s theorem. Subsequently, harvested power along with the transmissibility is computed for a chain of finite number of metamaterial units by using backward substitution method. The results of the parametric studies elucidate that piezo-embedded negative stiffness metamaterial can enhance the performance in terms of vibration attenuation and harvested energy.

Quasi‐All‐Directional Negative Stiffness Metamaterials Based on Negative Rotation Stiffness Elements

Most negative stiffness metamaterials exhibit negative stiffness effects in only one direction. Herein, based on the theory of anisotropy, the concept of “negative stiffness” is redefined. A method to determine whether a material has all‐directional negative stiffness is proposed. The possibility and difficulty of achieving all‐directional negative stiffness are discussed. A new type of negative stiffness metamaterial comprising negative stiffness rotation hinges and rigid trusses is studied. The results show that quasi‐all‐directional negative stiffness is achievable.

Novel multidirectional negative stiffness mechanical metamaterials

This paper presents a novel tri-directional negative stiffness (NS) mechanical metamaterial, consisting of disk structure elements arranged in three-dimensions. The NS behavior was achieved through the elastic instability of the disk structure. Through the combination of numerical simulations and experiments, the NS property, the deformation mechanisms, and the basic mechanical performance of the disk structure and the novel NS mechanical metamaterial were systematically investigated. The influence of the geometric parameters on the snap-through behaviors of the NS metamaterial was investigated through the experimentally verified numerical method, and further designs were conducted on the disk structure to tailor its mechanical responses. Also based on the instability of the disk structure, several novel multidirectional NS structures, which can achieve NS behavior along five and seven loading directions, were firstly proposed. This innovation improves the homogeneity of the NS metamaterials, and is expected to expand the application scope of such metamaterial, considering that the previous reported NS metamaterial can exhibit NS behavior along three-dimensions at most. Moreover, the mechanical performance of the proposed NS metamaterial is tunable, benefited from the special structure form of itself. To our knowledge, this work is first to design NS metamaterial using the disk structures, and report the multidirectional (more than tri-directions) NS metamaterials.

Programmable Buckling-based negative stiffness metamaterial

Programmable mechanical metamaterials, whose properties would vary once their service environment changed, have a great prospect in many application scenarios. In this paper, a novel buckling-based negative stiffness (NS) mechanical metamaterial, consisting of pre-compressed elastic curved beams, is proposed, and its mechanical properties can be programmed by lateral confinement. Experiments and numerical simulations were both conducted to investigate its mechanical properties. Research results showed that multi-stability of the proposed NS metamaterial was programmable and it could be applied to tune the elastic wave propagation. Moreover, some improvement was made to simplify the structure and increase the efficiency of programming process.