Negative Stiffness Honeycombs Research Articles

Design and testing of novel three-dimensional modular negative stiffness honeycomb structures as reusable crash absorbers

Conventional crash absorbers dissipate kinetic energy of impacts into plastic irreversible deformation, needing an immediate replacement to restore safety of the structure, highly increasing cost and inconvenience of the system. Aim of the present work was to develop innovative prototypes of reusable crash absorbers, able to withstand multiple collisions . A novel design was proposed, based on a modified Negative Stiffness Honeycomb (NSH) approach, using a three-dimensional modular layout with the objective of improving performance, reliability, and functionality of the device in repeated impacts. Two prototypes were manufactured to prove the concept. The first was produced in Nylon PA 6/66 by fused deposition modelling, while the second was obtained from laser-cut plates of stainless steel AISI 304. The nylon prototype was evaluated in cyclic static compression and dynamic impact tests, while the performance of the steel prototype was assessed only in impact tests. Results show improved values of energy absorption with respect to previous studies using bidimensional NSH energy absorbers and a highly reliable behaviour in multiple dynamic compression tests. Moreover, the nylon prototype featured a novel behaviour during impact tests, with autonomous delayed recovery of deformation after the collision. Our data show that three-dimensional modular NSH approach is effective in obtaining a reusable crash absorber, with improved performance and functionality compared to previously proposed design. This work can be considered a step forward in the search for alternative crash absorbers able to sustain multiple impactsbefore substitution, with potential advantages when their replacement is either impossible or too expensive.

Numerical and experimental investigation of negative stiffness beams and honeycomb structures

Metamaterial structures that exhibit negative stiffness (MSNS) behavior have shown the potential to be used as energy dissipation systems in different applications. Negative stiffness honeycomb structures consist of multiple pre-buckled beams that snapping through from one pre-buckled mode to another buckled mode, when subjected to transverse loads, displaying negative stiffness, and dissipating a significant portion of the input energy. This paper presents finite element models (FEMs) developed to investigate the performance of negative stiffness pre-buckled beams and honeycombs. The FEMs were validated using experimental results of single pre-buckled beams and honeycomb structures. The experimental testing of the pre-buckled beams was presented in the current study while the results of the honeycomb were available in the literature. The FEMs have the ability to capture the transition of the elements from one mode of buckling to another mode as well as the force thresholds, energy dissipation values, and residual displacements. The FEMs were extended to investigate the effect of different parameters such as boundary condition, apex height-to-beam thickness ratio, and constraining the second mode of buckling on the behavior of negative stiffness honeycombs.

Mechanical Response of Applying Different Parameters On Negative Stiffness Honeycomb Structure

It has become apparent that negative stiffness behavior may have potential applications in vibration isolation mechanisms, vibro-acoustic dampening materials, and mechanical switches. Unlike traditional honeycombs, due to these properties, a negative honeycomb can absorb substantial amounts of mechanical energy whilst maintaining a stable stress. The force threshold under displacement loading was investigated of three variables applied on different models of negative-stiffness honeycomb (NSH) structures. The three variables are material applied, honeycomb unit cell, and beam thickness of the negative honeycomb structure. Accordingly, nine models were developed, and the three varied materials were assigned repeatably to each model and then force threshold were studied after validating the model. The Finite element analysis (FEA) for formed model was validated and shows force value of 289 N with an error of 5% compared to the referenced model. In the 4- unit cell model, the highest force threshold of approximately 240 N was noticed during loading phase at the beam thickness of 19.05 mm for both nylon 11 and 12 material. Finally, the force threshold of 550 N during loading and unloading phases was observed for nylon 6/6 material at beam thickness of 19.05 mm. The results obtained confirm the negative stiffness behavior on the models and shows that the force threshold applied is reduced comparing to forces required in the conventional honeycombs models.

Digital Twin Data-Driven Multi-Disciplinary and Multi-Objective Optimization Framework for Automatic Design of Negative Stiffness Honeycomb

Digital Twin Data-Driven Multi-Disciplinary and Multi-Objective Optimization Framework for Automatic Design of Negative Stiffness Honeycomb

Impact response of negative stiffness curved-beam-architected metastructures

Mechanical metamaterials and metastructures exhibit superior effective mechanical properties, such as enhanced energy dissipation and resistance against impact loads, beyond those of natural materials. Metastructures with the ability to manipulate wave propagation are particularly desirable in numerous applications, such as actuators, dampers, and lightweight impact resistant systems with structural tunability and recoverability. Specifically, multi-stable structural forms have attracted considerable attention in the design of architected multi-materials, metamaterials, and morphing structures. To design such systems, a recently developed mechanical metamaterial/metastructure known as negative stiffness honeycomb, composed of arrays of curved double-beams (CDBs), is proposed. Here, we develop an analytical model to predict the dynamic response of the CDB metastructures, architected with a periodic array of the CDBs, and subjected to impact by a striker. The analytical model is developed using the Euler-Lagrange theorem and the snap-buckling phenomena in the honeycomb have been examined. The derived closed-form solutions were in good agreement with those of the numerical finite element model at different bistability ratios, defined as the ratio of beam apex height to its thickness. The findings demonstrated that the bistability ratio had a noticeable influence on the buckling response of the metastructure and the desired negativity in the stiffness matrix, while the snap-back buckling phenomena may be realised at high bistability ratios.

Numerical and experimental study of viscoelastic properties and energy absorption of functionally graded negative stiffness honeycomb made of Polyamide 12

ABSTRACT This study investigated the effect of a functionally graded negative stiffness (FGNS) honeycomb made from polyamide 12 (PA12) on increasing energy absorption. In addition, the viscoelastic model of PA12 was implemented in the finite element (FE) model to demonstrate the recoverability of these structures. First, a quasi-static compression test was performed on constant thickness negative stiffness (CTNS) honeycomb and FGNS honeycomb. Then, these two structures’ FE models were simulated. The stress relaxation test was utilised to derive Prony series coefficients for PA12 viscoelastic properties. The results of viscoelastic simulation for CTNS and FGNS honeycombs were then compared with experimental results. The comparison demonstrated a good agreement in both the loading and unloading stages. Furthermore, the critical parameters for evaluating the structural energy absorption of the FGNS honeycomb and the conventional ones were used in this study. According to the results, the FGNS honeycomb outperformed the CTNS experimentally and numerically.

Compressive strength and energy absorption characteristics of the negative stiffness honeycomb cell structure

Combining the performance advantages of chopped carbon fiber-reinforced nylon composites (MarkForged Onyx) with the manufacturing advantages of 3D printing, the negative stiffness honeycomb cell structure (NSH-C) was fabricated using fused filament fabrication technology. The study examined how to build directions, fill patterns, and wall layers, affecting the compressive strength and energy absorption characteristics of NSH-C. The results show that the printing parameters of Flat direction, triangular fill pattern, and two wall layers are optimal for NSH-C, which makes NSH-C exhibit a strong negative stiffness phenomenon with energy absorption efficiency up to 70% and peak force of approximately 185 N. In addition, the effect of structural parameters on the compressive strength and energy absorption characteristics of the structure was numerically simulated. Simulation results suggest that appropriately increasing the initial apex height of the curved beam, increasing the in-plane thickness of the curved beam and reducing the span of the curved beam will all be expected to further improve the mechanical performance of NSH-C.

Negative stiffness honeycomb structure as automobile leaf spring: A numerical investigation

The leaf spring is one of the main components in an automobile which carries the weight of the vehicle and passenger as well as absorbs the vibration and shock produced due to road irregularities. The weight, natural frequency, stress developed, energy absorption, fatigue life, etc. are the key factors that need to be considered to design a leaf spring. Towards that, a novel design integrating a Negative Stiffness Honeycomb Structure (NSHS) in the leaf spring is proposed. The proposed design and the traditional leaf spring are analyzed using the commercially available Finite Element Method (FEM) software Abaqus. Both the traditional and NSHS models were created using Solidworks and modal, harmonic, structural, and transient analyses were performed. It is found that the natural frequency of the NSHS leaf spring is well above the frequency produced due to road irregularities although it is lower than the traditional spring. The total weight of the NSHS spring structure is reduced significantly by 30.73% compared to the traditional spring. Structural analysis shows a lower stress development and higher energy absorption capacity for the NSHS leaf spring. Transient analysis reveals lower mean stress in the proposed NSHS spring. The fatigue life is also found to be 82.78 % higher in the proposed design. The NSHS-incorporated novel leaf spring design may be an excellent alternative to the traditional leaf spring.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys

A novel gradient negative stiffness honeycomb for recoverable energy absorption

This paper designs a novel reusable gradient negative stiffness (GNS) honeycomb structure and focuses on investigating its energy absorption (EA). Contrary to classical normal negative stiffness (NNS) honeycomb structures, the GNS honeycomb is characterized in that its unit cells have regular geometric (stiffness) changes throughout the honeycomb panel. The quasi-static mechanical characteristics of the novel GNS honeycomb are investigated with a combination of experiments and simulations. The influence of the structural parameters on energy absorption is revealed using an experimentally verified numerical model. After that, the repeatability of this honeycomb is verified by cyclic compression. In addition, the vibration control effect of the honeycomb is studied through vibration isolation tests, and revealing that the presented GNS honeycomb has better vibration control performance than the NNS honeycomb. Finally, plate-impact experiments are also performed to investigate the cushion properties of NNS and GNS honeycombs. The test results show that the novel GNS honeycomb has better cushion performance than the NNS honeycomb by inhibiting the threshold of acceleration response amplitude, which again verifies the potential of the novel GNS honeycomb in the EA field.

Structural Mechanics of Negative Stiffness Honeycomb Metamaterials

AbstractThe development of multi-stable structural forms has attracted considerable attention in the design of architected multi-materials, metamaterials, and morphing structures, as a result of some unusual properties such as negative stiffness and, possibly, negative Poisson's ratio. Multi-stability is achieved through a morphological change of shape upon loading, and in doing so multi-stable structures undergo transitions from one equilibrium state to another. This paper investigates the structural performance of the negative stiffness honeycomb (NSH) metamaterials made of double curved beams which are emerging in various applications such as sensors, actuators, and lightweight impact protective structures with structural tunability and recoverability. An analytical treatment is pursued using the Euler–Lagrange theorem and the stability of the honeycomb has been studied. Based on a static analysis of the nonlinear elastic system, the developed tangent stiffness matrix and ensuing deformation curve were assessed through multiple phases of deformation. The closed-form solution was in good agreement with the numerical finite element (FE) model at different bistability ratios. It was shown that the bistability ratio had a pronounced effect on the overall response of the honeycomb and the desired negativity in the stiffness matrix could be achieved with high bistability ratios.

Analytical modeling and design of negative stiffness honeycombs

Negative stiffness honeycombs (NSHs) have multiple advantages compared to traditional honeycomb structures. These advantages include recoverable elastic buckling, shock absorption, and vibration isolation. As a result, NSHs have great potential in applications such as acoustic wave guiding, shape morphing, design of impact-protection devices and robotic grippers. In this paper, we present a design methodology for metamaterial consisting of negative stiffness beams assembled in a honeycomb structure. Based on analytical results, our methodology allows designing NSH mesostructures with predetermined buckling sequence. An NSH prototype was designed based on our algorithm and fabricated using a 3D printer with a nylon filament. The validity of our approach was experimentally verified by performing displacement controlled compression force measurements. Our methodology gives the ability to design NSH mesostructures with desired force–displacement characteristics.

Dynamics of Tensegrity Robots With Negative Stiffness Elements

Tensegrity structures have unique features such as low mass to payload ratio, strength, and robustness. Therefore, they present great potential in robotics, aerospace, and civil engineering. The dynamics of tensegrity robots is highly nonlinear and constrained. As a result, their modeling, simulation, state estimation, and control are non-trivial. Strings in tensegrity structures are usually modeled as linear springs. Utilization of nonlinear elastic/damping elements in tensegrities would further enrich their dynamics and endow them with additional properties, such as multiple equilibrium configurations. In this paper, our preliminary work on the dynamics of actuated tensegrities with strings containing nonlinear elastic and/or damping elements is presented. At first, the formulation of tensegrity dynamics with general nonlinear elastic/damping elements is explored. Later dynamics of tensegrities with negative stiffness honeycombs incorporated into strings are considered. Simulations are performed on three tensegrity systems: two-bar, three-bar, and six-bar structures. Results demonstrate that negative stiffness honeycombs result in nonlinear steady-state response to constant external force, reduced force magnitudes in strings and bars, and increased range of motion.

Non-reciprocity in mechanically modulated elastic metamaterials with geometric asymmetry

Elastic metamaterials with time- and space-dependent effective material properties have received great attention as a means to generate non-reciprocal wave propagation in acoustic and elastic media. These materials have promise for applications such as acoustic communication devices with increased data throughput and improved vibration isolation components. One means to modulate the material properties of a heterogeneous medium is via nonlinear mechanical deformation on time scales that are slow compared to propagating waves. This approach has been explored by the authors using the finite element method (FEM) to demonstrate non-reciprocal elastic wave propagation in negative stiffness honeycombs with a time- and space-varying external pre-strain [Goldsberry et al., JASA 144, 1763 (2018)]. One benefit of FEM is that it can be used to study the degree of non-reciprocity when varying sub-wavelength geometry or geometric modulations that are difficult or impossible to represent using analytical models. The present work employs FEM to investigate non-reciprocity in elastic lattices consisting of unit cells with varied geometric asymmetry and more general forms of mechanical modulation. [Work supported by National Science Foundation EFRI under Award No. 1641078.]

Numerical investigation of non-reciprocal wave propagation in mechanically-modulated elastic metamaterials

Acoustic systems that break reciprocity have recently received great attention due to their potential to increase control over wave propagation and to have far-reaching impacts on engineering applications, including more efficient acoustic communication devices and vibration isolation. One means to break reciprocity is by spatiotemporal modulation of material properties, typically via electromagnetic actuation. In the present work, tunable mechanical metamaterials are investigated as a platform to achieve non-reciprocity, where effective dynamic property modulations are induced by an external pre-strain of a two-dimensional cellular material. These elastic metamaterials are studied using a nonlinear finite element model, which is suitable for unit cells having complex geometry and undergoing large deformation caused by the external pre-strain [Goldsberry et al., J. Appl. Phys., 123, 091711 (2018)]. A small-on-large approximation is used to analyze linear elastic, non-reciprocal wave propagation in the presence of a slowly-varying pre-strain. Results on non-reciprocal wave propagation in negative stiffness honeycombs, a structure exhibiting large stiffness modulations due to the presence of a mechanical instability [Correa et al., Rapid Prototyping J., 21(2), 193–200, (2015)], are shown as a case example. [Work supported by NSF.]

Impact behavior of negative stiffness honeycomb materials

Abstract

Negative stiffness honeycombs as tunable elastic metamaterials

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Numerical investigation of metafluid behavior in pre-strained negative stiffness honeycombs

Negative stiffness honeycombs (NSH) are doubly periodic arrays of curved beams that have recently been shown to exhibit a reversible pseudo-plastic large deformation response and are therefore interesting candidates for impact isolation applications. The authors previously used finite element analysis to show that NSH exhibit three types of propagating modes described by (i) longitudinal, (ii) transverse, and (iii) rotational displacements with respect to the propagation direction. The phase and group velocities of each mode can be significantly altered by applying a uniaxial pre-strain imposed on the top and bottom boundaries of the NSH. The present work will show that the transverse and rotational mode phase speeds are significantly more sensitive to strain than the longitudinal modes for small but finite pre-strain levels. Consequently, for some pre-strain levels there exists a large frequency band where only longitudinal waves propagate. The pre-strained NSH therefore behaves as a pentamode metamaterial, or metafluid, and may represent a new type of structure to realize devices designed using transformation acoustics. The effect of the geometry and pre-strain on the existence and frequency range of unimodal propagation in pre-strained NSH will be investigated. [Work supported by NSF.]

Elastic wave dispersion in pre-strained negative stiffness honeycombs

A doubly periodic array of curved beams, known as a negative stiffness (NS) honeycomb, has recently been shown to exhibit tunable impact isolation by exploiting nonlinear mechanical behavior [Correa et al., Rapid Prototyping J., 21 (2), 2015]. The primary benefit of NS honeycombs over standard honeycomb materials lies in their ability to return to their original shape after experiencing an impact. The recoverable nature of their response is a result of the curved beam structure which has a single stable configuration but experiences one or more buckling events when loaded. The complex nonlinear elastic response of NS honeycombs lead to large variations in mechanical stiffness, which makes these materials compelling candidates for tunable control of elastic waves. The present work investigates linear elastic wave propagation of a representative NS honeycomb lattice at varying levels of pre-strain. Eigenfrequency finite element analysis is performed on the unit cell subjected to finite uniaxial deformation. The longitudinal and transverse phase speeds are shown to be anisotropic and highly dependent on uniaxial pre-strain. This is especially true near points of instability, where one observes very different functional dependence of longitudinal and transverse wave motion on pre-strain.

Mechanical design of negative stiffness honeycomb materials

AbstractA mechanical system exhibits negative stiffness when it requires a decrease in applied force to generate an increase in displacement. Negative stiffness behavior has been of interest for use in vibro-acoustic damping materials, vibration isolation mechanisms, and mechanical switches. This non-intuitive mechanical response can be elicited by transversely loading a curved beam structure of appropriate geometry, which can be designed to exhibit either one or two stable positions. The current work investigates honeycomb structures whose unit cells are created from curved beam structures that are designed to provide negative stiffness behavior and a single stable position. These characteristics allow the honeycomb to absorb large amounts of mechanical energy at a stable plateau stress, much like traditional honeycombs. Unlike traditional honeycombs, however, the mechanism underlying energy-absorbing behavior is elastic buckling rather than plastic deformation, which allows the negative stiffness honeycombs to recover from large deformations. Accordingly, they are compelling candidates for applications that require dissipation of multiple impacts. A detailed exploration of the unit cell design shows that negative stiffness honeycombs can be designed to dissipate mechanical energy in quantities that are comparable to traditional honeycomb structures at low relative densities. Furthermore, their unique cell geometry allows the designer to perform trade-offs between density, stress thresholds, and energy absorption capabilities. This paper describes these trade-offs and the underlying analysis.