Re-entrant Honeycomb Structure Research Articles

Auxetic hybrid metamaterial with tunable elastic wave bandgap

Abstract Auxetic metamaterials have shown good stability and uniform deformation capabilities against influences (vibration, temperature change, load change), making them significant in maintaining and adjusting the bandgap of phonon crystals. The low-frequency and broadband are the important goals of phonon crystals. For most traditional re-entrant honeycomb structures (T-RHS), the bandgap range is narrow and tunability is poor. Here, an auxetic hybrid structure with tunable acoustic bandgap (AHS-T) consisting of periodic mass inclusions integrated with traditional re-entrant honeycomb and chiral hybrid is proposed. Aiming at investigating the tunability of the bandgap in the low-frequency range. Compared with T-RHS, the bandgap real-time adjustment and wider bandwidth of the AHS-T be realized during compression and tension. The numerical results show that the bandgap of the AHS-T can be flexibly tailored by reasonably adjusting the strain and geometrical configurations of AHS-T. The bandwidth of AHS-T can be increased to 87.1% when the bottom diameter and column height H of the scatterer are changed reasonably. Moreover, the deformation behavior of auxetic material has an auxiliary effect on expanding the bandwidth. Compared with the structure which is not subjected to load, the adjustable amplitude of the bandgap is 41%. The findings of this work provide a design idea for manipulating elastic waves in dynamic environment.

Non local analytical and numerical modelling of re-entrant auxetic honeycomb

Auxetic materials, characterized by their negative Poisson’s ratio, have been extensively studied for applications in energy absorption and mechanical reinforcement. Re-entrant honeycomb structures, a subtype of auxetic materials, have demonstrated superior mechanical characteristics. However, understanding the mechanical behavior of these structures at the nanoscale remained a significant challenge. To address this gap, the authors explored the influence of size on the deflection behavior of re-entrant auxetic honeycomb structures through non-local continuum mechanics. Their analytical model, incorporating the Euler-Bernoulli beam model and considering four non-dimensional geometrical parameters, was validated through numerical simulations and a comprehensive review of existing literature. The study aimed to provide valuable insights into the design and engineering of re-entrant auxetic honeycomb structures across diverse applications, contributing to the advancement of non-local elasticity theory and deepening the understanding of the mechanical behavior of auxetic structures at the nanoscale. The research laid a foundation for further exploration and optimization of re-entrant honeycomb structures, facilitating their effective utilization in fields such as MEMS/NEMS by leveraging the dimensionless parameters identified in the study.

Biaxial porosity gradient and cell size adjustment improve energy absorption in rigid and flexible 3D-printed reentrant honeycomb auxetic structures

This paper compares different uniaxial and biaxial graded designs of auxetic reentrant honeycomb structures to enhance their mechanical properties, especially the specific energy absorption under compressive load. The lattice structures were 3D printed using the vat photopolymerization masked-stereolithography technique from two different materials – tough (OR) and flexible (FR). The results were evaluated from a material and structural point of view, investigating the effect of porosity, cell number, size, graded design, and fracture mode. The universally best energy-absorbing performance was found in a biaxially graded structure with a center-wise location of the highest local porosity. Depending on the used resin, its energy absorption capacity was up to 2–3 times enhanced compared to a reference uniform-porosity auxetic design. The presented data constitutes a fundamental understanding of auxetic structures and identifies practical approaches for tuning the auxetic structures’ performance regarding their mechanical response. Finally, this study demonstrates the potential of shape versatility offered by 3D printing and other additive manufacturing techniques.

The dynamic response of composite auxetic re-entrant honeycomb structure subjected to underwater impulsive loading

The researches on dynamic responses of underwater impulsive loading have been conducted. However, the previous study mainly concentrated on metal sandwich structure and fixed supported boundary. The relative research on composite auxetic re-entrant honeycomb structure and simply supported boundary are rarely. In this paper, the effect of the gradient form and relative density on impact resistance performance of composite auxetic re-entrant honeycomb structure was experimentally and numerically investigated. The one-stage light gas gun was applied to provide initial kinetic energy of the fly plate, and the diffuser-type shock tube was utilized to generate and propagate exponential decaying shock wave. The pressure–time curve was respectively amplified and recorded by the charge amplifier and oscilloscope. The response speed, final deflection of rear panel and failure mode of cores and panels were used to evaluate impact resistance of composite auxetic re-entrant honeycomb structures. Moreover, acoustic-structure interaction algorithm was applied to simulate impact course of specimens in Abaqus/Explicit. The results between experiment and numerical simulation exhibited good consistency. The results indicated that the positive gradient form could excessively slow down response speed of rear panel by dissipating energy of shock wave, and the average gradient demonstrated smaller final displacement of rear panel and less failure compared with graded structures.

Experimental and simulation study on effects of material and loading direction on the quasi-static compression behavior of re-entrant honeycomb structure

The re-entrant honeycomb structure has a strong energy absorption capacity because of its auxetic characteristics. The energy absorption capacity of the re-entrant honeycomb structure is closely related to the material and loading direction. In this paper, the Selective Laser Sintering(SLS) 3D printing technology was used to print the re-entrant honeycomb structure with commonly used FS3300PA and Glass Fiber reinforced FS3300PA. A quasi-static compression finite element model was developed for the re-entrant honeycomb structure printed with two materials when loaded along three directions. The influence of material and loading direction on the quasi-static compression performance of re-entrant honeycomb structures was systematically studied through simulation and experiments. The deformation mode and energy absorption index of the simulation results are in good agreement with the experimental results, verifying the effectiveness of the finite element model. The results show that the deformation mode and energy absorption performance of the structure are affected by the material and loading direction. The quasi-static compression performance in the Y direction is optimal for both materials. However, when loading along the Y direction, the specific energy absorption of FS3300PA printed re-entrant honeycomb structure is 18.3 % higher than that of FS3300PA + 30 % Glass Fiber printed re-entrant honeycomb structure, ηCFEis 83.3 % higher. Therefore, when the re-entrant honeycomb structure of the two materials is loaded in different directions, the structure printed with FS3300PA has the best quasi-static compression performance when loaded in the Y direction.

VAM-based equivalent-homogenization model for 3D re-entrant auxetic honeycomb structures

The integration of two vertically crossed re-entrant honeycombs gives rise to a 3D re-entrant honeycomb (3D-RH), which displays intricate three-dimensional auxeticity. To simplify the modeling complexity, this study employs asymptotic analysis of the energy functional stored in the unit cell of the 3D-RH to develop unified constitutive models for 3D structures and panels with multiple length scales. Based on this, an equivalent 3D Cauchy continuum model is established for multi-layer 3D-RH, while a 2D equivalent plate model is developed for sandwich panel with single-layer 3D-RH (SP-3D-RH). The accuracy and effectiveness of these equivalent models are subsequently confirmed through investigations of the X-shaped compressive deformation of multi-layer 3D-RH, as well as the in-plane auxetic deformation and out-of-plane dome-shaped deformation of single-layer 3D-RH. Compared to traditional hexagonal and re-entrant honeycomb sandwich panels, the SP-3D-RH exhibited enhanced equivalent tensile stiffness while effectively mitigating maximum deformation and strain energy under bending and tension conditions. However, due to its relatively low equivalent shear stiffness, the SP-3D-RH exhibited significant deformation and strain energy when subjected to torsional loads, resulting in local stress concentration in the connect region between adjacent facesheets. Parameter analysis shows that the facesheet-to-strut thickness ratio had a substantial impact on the equivalent stiffness and in-plane behavior of the SP-3D-RH, while adjusting the horizontal strut length, strut depth, and re-entrant angle of the 3D-RH can improve the out-of-plane behavior.

Impact resistance of a double re-entrant negative poisson’s ratio honeycomb structure

Auxetic metamaterials, usually consisting of cellular solids or honeycombs, exhibit the advantages of high designability and tunability. In particular, the negative Poisson’s ratio (NPR) property endows them with innovative mechanical properties and makes them promising for a wide range of applications. This paper proposes a modified double re-entrant honeycomb (MDRH) structure and explores its Young’s modulus and Poisson’s ratio through theoretical derivation and finite element analysis. Additionally, it discusses the relationship between these parameters and the concave angle. Furthermore, the deformation mode, nominal stress–strain curve, and specific energy absorption of this MDRH are investigated for different impact velocities and compared with traditional re-entrant honeycomb (TRH) materials. The results show that the MDRH honeycomb structure greatly widens the range of effective modulus and NPR values. At different impact velocities, the MDRH exhibits high plateau stress and specific energy absorption, indicating good impact resistance. These results provide a theoretical foundation for the design and implementation of new energy-absorbing structures.

Composite curved hourglass cellular structures: Design optimization for stiffness response and crashworthiness performance

Auxetic lattice structures are known for their superior stiffness-to-density and strength-to-density ratios. Re-entrant hourglass exhibits an acceptable equivalent elastic modulus and remarkable energy absorption capacity among various auxetic configurations due to their flexibility and hinge deflecting during crushing loads. This study introduces a curved hourglass honeycomb which can be produced using 3D printing with pure or reinforced filaments incorporating continuous fibers. New closed-form formulations are analytically derived using an energy method by considering an extracted unit cell to predict the equivalent in-plane mechanical properties for the first time. The plateau stress of the proposed honeycomb is evaluated at the densification state of a unit cell using the energy conservation theory, equating external work with plastic energy dissipation. The accuracy of these extended relations is validated against experimental outcomes, demonstrating good agreement between analytical and experimental results. Additionally, robust linear and nonlinear finite element analyses are conducted to assess the accuracy of the obtained relations, including the equivalent stiffness and plateau stress for structures produced with reinforced filaments. The nonlinear finite element code employs appropriate subroutines to model plasticity/damage events. Based on the established analytical relations for stiffness and plateau stress, multi-objective optimization using Genetic Algorithm is applied to define optimum values for the Pareto front chart's objective functions of stiffness and plateau stress. The optimization process involves exploring the design space and defining the values of geometrical parameters to achieve the desired objectives. In conclusion, this study presents a novel approach to developing curved re-entrant honeycomb structures, with analytical formulations validated against experimental and numerical results. Optimization helps to identify optimal configurations concerning stiffness and plateau stress, offering potential applications in lightweight and high-strength materials design. According to the obtained results, for selection of the best value for curved strut angle which results in the optimum value of stiffness and plateau stress, a range between 10°-34° can be considered depending on the volume fraction of fibers.

The fluid-structure interaction response of composite auxetic re-entrant honeycomb structures to underwater impact

In this paper, the effects of the gradient form, peak pressure and decaying time on the fluid-structure interaction of composite auxetic re-entrant honeycomb structures was experimentally and numerically investigated. The specimens for this experiment were manufactured by hot-press molding method. The acrylic transparent tube was utilized to accommodate water medium, pistons and specimen during experiment. The exponential decaying shock wave was simulated by accelerating the fly plate to impact the piston based on the one-stage light gas gun system. The incident velocity of the fly plate and process of the fluid-structure interaction response were monitored by high frame rate camera. In addition, the velocity of the shock wave in water was measured by transducers installed at different measuring points. The voltage signal of the dynamic overpressure collected by transducers was amplified by the charge amplifier and recorded by the oscilloscope. On the other hand, finite element software Abaqus/Explicit was applied to simulate the cavitation process of water domain and dynamic response of specimens. The experimental results and numerical results were in good agreement. The results indicated that the increase of the thickness of the fly plate had a certain effect on the propagation velocity of the shock wave, and the increase of the peak pressure would make the cavitation generation position close to the fluid-structure interface and make the cavitation duration longer. And the average structure which has a minimum transformation of 8.12 mm shows better underwater impact resistance than the gradient structure.

Manufacturing of stretchable substrate with biaxial strain control for highly-efficient stretchable solar cells and displays

There has been significant research focused on the development of stretchable materials that can provide a large area with minimal material usage for use in solar cells and displays. However, most materials exhibit perpendicular shrinkage when stretched, which is particularly problematic for polymer-based substrates commonly used in stretchable devices. To address this issue, biaxial strain-controlled substrates have been proposed as a solution to increase device efficiency and conserve material resources. In this study, we present the design and fabrication of a biaxial strain-controlled substrate with a re-entrant honeycomb structure and a negative Poisson’s ratio. Using a precisely machined mold with a shape error of less than 0.15%, we successfully fabricated polydimethylsiloxane substrates with a 500 μm thick re-entrant honeycomb structure, resulting in a 19.1% reduction in perpendicular shrinkage. This improvement translates to a potential increase in device efficiency by 9.44% and an 8.60% reduction in material usage for substrate fabrication. We demonstrate that this design and manufacturing method can be applied to the fabrication of efficient stretchable devices, such as solar cells and displays.

Advanced Design and Fabrication of Dual-Material Honeycombs for Improved Stiffness and Resilience.

Auxetic re-entrant honeycomb (AREH) structures, consisting of a single soft or tough material, have long faced the challenge of balancing stiffness and rebound resilience. To achieve this balance, dual-material printing technology is employed to enhance shock absorption by combining layers of soft and tough materials. Additionally, a novel structure called the curved re-entrant honeycomb (CREH) structure has been introduced to improve stiffness. The selected materials for processing the composite structures of AREH and CREH are the rigid thermoplastic polymer polylactic acid (PLA) and the soft rubber material thermoplastic polyurethane (TPU), created utilizing fused deposition modeling (FDM) 3D printing technology. The influence of the material system and structure type on stress distribution and mechanical response was subsequently investigated. The results revealed that the dual-material printed structures demonstrated later entry into the densification phase compared to the single-material printed structures. Moreover, the soft material in the interlayer offered exceptional protection, thereby ensuring the overall integrity of the structure. These findings effectively serve as a reference for the design of dual-material re-entrant honeycombs.

Experimental investigation on 4D printed intelligent assembly cushion with adjustable pre-tightening force

In order to design an intelligent assembly cushion with an adjustable pre-tightening force, a reentrant honeycomb structure was printed by additive manufacturing to realize the active and intelligent assembly process of filling gaps. The thermo-mechanical deformation experiments of the reentrant honeycomb structure were conducted at different pre-compressions, constrained displacements, and recovery temperatures. The recovery force and the force recovery ratio under semi-constrained conditions are explored emphatically. The results show that pre-compression, constrained displacement, and recovery temperature affect the recovery force and force recovery ratio under semi-constrained conditions. The recovery force and force recovery ratio increase with pre-compression, decrease with constrained displacement, and increase with recovery temperature below the glass transition temperature. Based on these results, the adjustability of the recovery force of a reentrant honeycomb cushion can be controlled by changing the thermo-mechanical deformation processes. Finally, the reentrant honeycomb cushion is applied to the mimetic assembly environment for corresponding testing, achieving the design of an active and intelligent assembly cushion with an adjustable pre-tightening force.

Integrating experiments, finite element analysis, and interpretable machine learning to evaluate the auxetic response of 3D printed re-entrant metamaterials

Metamaterials have received extensive attention in fundamental and applied research over the past two decades due to their unique mechanical behavior. This paper presents an interpretable machine learning (ML) approach for efficient response prediction of three-dimensional (3D)-printed metamaterials. However, developing such an ML-based model requires a large consistent, representative, balanced, and complete dataset. To this extent, an experimentally validated finite element analysis (FEA) approach is implemented to generate 8096 non-self-intersecting re-entrant honeycomb structures by varying the mesoscale geometrical features to obtain the corresponding Poisson's ratios. This dataset is leveraged to develop a feed-forward multilayer perceptron-based predictive model. The developed ML model shows excellent predictive efficacy on the unseen test dataset. Shapely additive explanation (SHAP) is then used for model interpretation. SHAP results show that the slant cell length is the dominant input feature dictating the model output whereas cell angle and vertical cell length show mixed trends signifying that other input features influence their effect on the model output. Moreover, cell thickness does not significantly influence the model output when compared to other input features. Overall, the integrated numerical simulation-experiment-interpretable ML-based predictive approach presented here can be leveraged to design and develop metamaterials for a wide range of engineering applications.

Experimental characterization of the mechanical properties of 3D printed TPU auxetic cellular materials under cyclic compressive loadings

PurposeFused filament fabrication (FFF) is a popular technique in rapid prototyping capable of building complex structures with high porosity such as cellular solids. The study of cellular solids is relevant by virtue of their enormous potential to exhibit non-traditional deformation mechanisms. The purpose of this study is to exploit the benefits of the FFF technology to fabricate re-entrant honeycomb structures using thermoplastic polyurethane (TPU) to characterize their mechanical response when subjected to cyclic compressive loadings.Design/methodology/approachSpecimens with different volume fraction were designed, three-dimensionally printed and tested in uniaxial cyclic compressions up until densification strain. The deformation mechanism and apparent elastic moduli variation throughout five loading/unloading cycles in two different loading orientations were studied experimentally.FindingsExperimental results demonstrated a nonlinear relationship between volume fraction and apparent elastic modulus. The amount of energy absorbed per loading cycle was computed, exhibiting reductions in energy absorbed of 12%–19% in original orientation and 15%–24% when the unit cells were rotated 90°. A softening phenomenon in the specimens was identified after the first compression when compared to second compression, with reduction in apparent elastic modulus of 23.87% and 28.70% for selected samples V3 and H3, respectively. Global buckling in half of the samples was observed, so further work must include redesign in the size of the samples.OriginalityThe results of this study served to understand the mechanical response of TPU re-entrant honeycombs and their energy absorption ability when compressed in two orientations. This study helps to determine the feasibility of using FFF as manufacturing method and TPU to construct resilient structures that can be integrated into engineering applications as crash energy absorbers. Based on the results, authors suggest structure’s design optimization to reduce weight, higher number of loading cycles (n > 100) and crushing velocities (v > 1 m/s) in compression testing to study the dynamic mechanical response of the re-entrant honeycomb structures and their ability to withstand multiple compressions.

Auxetic behavior of 3D-printed structure made in acrylonitrile butadiene styrene and carbon fiber-reinforced polyamide

AbstractParts with an auxetic structure, which exhibit negative Poisson’s ratio, can be associated with a novel class of smart materials. Such interesting property has been widely explored, over the time, for different applications, i.e., medical, automotive, robotic and aeronautic field. However, the research about the design and analysis of auxetic behavior is still on the way. In this paper, a 2D re-entrant honeycomb structure was realized using material extrusion additive manufacturing technology. Two different materials, acrylonitrile butadiene styrene and carbon fiber-reinforced polyamide were adopted. The technique of digital image correlation was implemented during the tensile test to evaluate over the time and in different areas of specimens the strain behavior of the auxetic structure for both investigated materials. The measured negative Poisson’s ratio confirmed the auxetic behavior of the designed structure. The comparison between the two investigated materials showed a different trend of negative Poisson’s ratio.

The Exact Solution of the Bending Moment in the Folding Process of Negative Poisson’s Ratio Honeycomb Tape Spring and Multi-Objective Optimization Design

The tape spring is a crucial component used in the deployment mechanism of spacecraft, and the lightweight design of the deployment mechanism is currently one of the critical issues that need to be addressed. This paper explores the substitution effect of two different negative Poisson’s ratio honeycomb-corrugated spring structures for use in space-deployable structures. Theoretical and finite element methods demonstrated that the negative Poisson’s ratio honeycomb structure could be equivalent to an orthotropic structure. The cylindrical shell bending theory was adopted, taking into account the nonlinearity of the geometric equation, the influence of cross-sectional deformation and cross-sectional position on the internal force expression, and the influence of the geometric equation to derive expressions for the bending moment and curvature radius during the folding and bending process. Numerical methods were used for comparative analysis. The NSGA-II algorithm optimized the geometric parameters of the negative Poisson’s ratio honeycomb, resulting in the optimal solution under given constraints. The results showed that the Auxetic re-entrant honeycomb structure performed better in bending moment capacity than the Star-shaped honeycomb, and the bending moment capacity of the Auxetic re-entrant honeycomb structure per unit mass was superior to that of the traditional tape spring.

In-plane elastic property prediction of straight-arc coupled auxetic structures

Auxetic metamaterials with two components exhibit a wide variety of potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to Castigliano’s second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson’s ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameter re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of SACS with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear model can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The SACS design can enhance the auxetic effect and structure Young’s moduli under the same dimension.

The arrangement patterns optimization of 3D honeycomb and 3D re-entrant honeycomb structures for energy absorption

In the design of lattice structures for energy absorption, arrangement pattern optimization has not been investigated in 3D space previously. In this work, a systematic method is proposed to optimize the arrangement pattern for 3D honeycomb and 3D re-entrant honeycomb structures. A new sample multiplication method is proposed as a supplement technique to gather sufficient training data while reducing time consumption by 93.75%. Simulations and experiments show that the ideal arrangement pattern proposed by this method increases the energy absorption capacity by 43% in equivalent lateral deformation. Further investigation demonstrates that the combination of different lattice structures in particular local arrangement pattern can alter their local mechanical behavior, thereby improving global performance. This optimization further unleashes the design potential of lattice structures and could provide some reference for future engineering application.

The compressive responses and failure behaviors of composite graded auxetic re-entrant honeycomb structure

This paper investigated the quasi-static compressive performances and failure behaviors of composite auxetic re-entrant honeycomb sandwich structure. Three types of auxetic re-entrant honeycomb structures with different gradient configurations were manufactured and tested. The carbon/epoxy prepreg was used to fabricated the auxetic re-entrant honeycomb sandwich structure. The reaction force and displacement of the test fixture were collected by the transducer of the universal testing machine. The compressive processes of specimens were recorded by high-resolution camera. Combined with the stress–strain curves and deformation processes of composite structures, the compressive responses and deformation mechanisms was analyzed. The Poisson’s ratio, energy efficiency and plateau stress of re-entrant honeycomb sandwich structures were defined and utilized to study the auxetic performance and energy absorption ability. Furthermore, a high-fidelity numerical model was established and finite element software ABAQUS was used to analyzed the compressive performances and failure behaviors of composite graded auxetic re-entrant honeycomb structure. The compressive failure modes of the numerical simulation results were compared with that of the experimental results, and the numerical simulation results agreed well with the experimental results. The results indicated that average structure exhibited best energy absorption performance and bidirectionally graded auxetic honeycomb structure had the best negative Poisson’s ratio performance.

Design, fabrication and mechanical properties of a 3D re-entrant metastructure

A 3D re-entrant honeycomb structure was designed in a simple configuration by introducing a spatial angular design parameter. Mechanical responses under uniaxial compression of it at constant spatial angle (α) and different re-entrant angles (θ) were investigated both experimentally and theoretically. Designed lattice auxetic structures with high shape fidelity were fabricated using selective laser sintering (SLS) of PA 2200 powder. The produced samples exhibited negative, zero, and positive Poisson's ratios depending on a selected θ value, and their mechanical properties varied over a wide range. Bend- and buckling-dominated deformation mechanisms of the struts have been observed under compression. Additionally, the analytical models of re-entrant honeycomb structures effectively illustrated the quantitative relationships between their mechanical properties (Young’s modulus (E) and Poisson’s ratio) and the design parameter θ. The results presented in this study would provide a reference to the customized design of the porous auxetic structures with unique mechanical properties.