Regular Hexagonal Honeycomb Research Articles

Phase Diagrams for Anticlastic and Synclastic Bending Curvatures of Hexagonal and Re-entrant Honeycombs

Abstract Transformation between saddle- and dome-like bending shapes of regular and re-entrant hexagonal honeycomb panels are explored. An analytical model is proposed to uncover the underlying mechanisms and identify the controlling parameter when the cell walls are slender beams. Then, 3D finite element simulations are performed to examine the architecture dependence of bending shape and construct the phase diagrams of anticlastic and synclastic curvatures when the cell walls have a general geometry. The results are believed helpful to the design and application of related honeycomb structures.

Study on the Design and Mechanical Properties of a Novel Hexagonal Cell Body Topology.

The honeycomb structure is a topological structure with excellent performance that stems from the properties of the basic units of the structure. Different structural features of basic units may lead to different mechanical characteristics in the whole part. In this study, a novel hexagonal cell body topology structure (NH) was designed and manufactured by the fused deposition modeling (FDM) technique to explore the effects on mechanical properties. The tensile and impact performance of the NH structure were compared with the regular hexagonal honeycomb structure (HH), and the influence of different unit single-cell sizes on the impact performance of the NH structure was investigated. The force transmission of the basic units of the NH structure was revealed through finite element analysis. The results indicate that both the tensile and impact performances of the NH structure have been improved compared to the HH structure. The improvement is due to the better force transmission capability of the basic units of the NH structure, leading to a more uniform stress distribution. Moreover, excessively large or small single-cell sizes of the NH structure will reduce the overall structure's impact resistance. The overall structure achieves optimal impact resistance when the single-cell size is around 1.2 mm.

Honeycomb structure design of automotive crash box

The crash box can protect the safety of passengers when a car collides. Due to its excellent mechanical properties, honeycomb structure can be applied to automotive crash boxes. Two kinds of crash boxes made of regular hexagonal honeycomb structure and re-entrant hexagonal honeycomb are designed. The research results indicate that, compared to the crash box made of hexagonal honeycombs, the crash boxes made of re-entrant hexagonal honeycombs have superior energy absorption ability. Furthermore, the influence of different structural parameters on the energy absorption performance (EAP) of the crash box made of re-entrant hexagonal honeycombs is analyzed. It is found that the total energy absorption and peak force increase with the increase of thickness and concave angle. The research in this article provides certain reference significance for the design of honeycomb structure crash boxes.

In-plane and out-of-plane compressive properties of regular and graded cellular cores of sandwich panels fabricated by additive manufacturing

Cellular materials with a gradient of properties become appealing as cores of the sandwich panels due to the possibility of improving strength and absorbed energy in lightweight components. 2D cellular structures designated by honeycombs have an anisotropic behaviour when loaded under in- and out-plane. Thus, when proposing new designs, it is essential to analyse how the in-plane arrangement with a gradient in cell wall thickness affects in-plane and out-of-plane mechanical properties. This work aims to study graded cellular structures in comparison with regular hexagonal honeycombs. Structures were manufactured by laser powder bed fusion using an aluminium alloy. Regular arrangements were formed with cells with the same thickness, while graded structures possessed a radial gradient of cell thickness. Three types of innovative gradients, where cell length varies radially along concentric layers, were analysed. The compressive properties of regular and graded structures were evaluated when loaded both under in-plane and out-of-plane conditions. Compression behaviour was assessed, both experimentally and by numerical modelling. Even though there is a mismatch between numerical and experimental results, they exhibit the same trends. All graded samples showed an increased mechanical performance when loaded under out-of-plane conditions in comparison with the results from tests under in-plane loading with values, for example, of stiffness four hundred times larger, absorbed energy around thirty times higher and with yield stress four times larger. The results showed that the graded samples attain higher values of strength, stiffness and absorbed energy in comparison with regular hexagonal honeycombs, for the same relative density.

Predicting the post-bifurcated patterns of architectured materials using group-theoretic tools

Extensive studies on hexagonal honeycombs under in-plane compression have demonstrated that the structure’s symmetry plays a decisive part in the emergence of deformation patterns in post-bifurcated configurations. In this work, the aim is to take advantage of this property by presenting a new group-theoretic approach to list the various attainable post-bifurcated patterns of periodic architectured materials.As of today, some group-theoretic approaches have been elaborated for determining the post-bifurcated paths and thus patterns of a symmetric system submitted to specific loading conditions. However, the application of these approaches requires knowledge of the system’s governing equations. By making use of another group-theoretic tool, this work predicts the various possible post-bifurcated configurations of a periodic architectured material a priori of any non-linear computation by simply assessing the symmetry group of its undeformed configuration.This approach is applied, as an example, to the buckling of regular hexagonal honeycombs but can be easily transferred to any periodic architectured material. This work is a first step towards the elaboration of a more general process for the design of architectured materials when harnessing post-bifurcated behaviour is essential.

In-Plane Elastic Properties of 3D-Printed Graded Hierarchical Hexagonal Honeycombs.

In this study, the graded hierarchical hexagonal honeycomb (GHHH) integrating gradient design and hierarchical design was fabricated using the 3D-printing technique, and its in-plane elastic properties were investigated theoretically, experimentally, and numerically. Theoretical solutions were developed based on the Euler beam theory to predict the effective elastic modulus and Poisson's ratio of GHHH, and theoretical values were in good agreement with the experimental and numerical results. The effect of gradient design and hierarchical design on the in-plane elastic properties of GHHH was also analyzed and compared. Results showed that the hierarchical design has a more significant effect on Poisson's ratio and adjusting the internal forces of GHHH compared with the gradient design. In addition, it was found that GHHH exhibited higher stiffness compared with regular hexagonal honeycomb (RHH), graded hexagonal honeycomb (GHH), and vertex-based hierarchical hexagonal honeycomb (VHHH) under the constraint of the same relative density, respectively. Specifically, the effective elastic modulus of GHHH can be enhanced by 119.82% compared to that of RHH. This research will help to reveal the effect of integrating hierarchical design and gradient design on the in-plane elastic properties of honeycombs.

Active vibration suppression of tetrachiral auxetic core sandwich panel with CFRP skin: An RVE homogenization-assisted finite element approach

Free vibration as well as the controlled dynamic response of moderately-thick smart sandwich panel are numerically explored considering the size effect of chiral unit cells at the microscopic level, with the help of RVE-assisted-finite element (FE) approach. In this scientific article, the authors have made a debut attempt to analyse the smart damping behaviour of a tetrachiral-type auxetic core sandwich panel (with carbon/epoxy skin) deploying a real-time based constant velocity feedback controller in a closed loop configuration. Effective anisotropic elastic properties as well as the reduced stiffness matrix of the cellular core layer have been determined by using RVE-FE based full-scale homogenization technique in ANSYS® platform. Dynamic equation of motion governing the plate structure, has been derived using an energy-based variational principle, and further solved with the help of a quadratic interpolation based finite element method. The mid-plane kinematics of the plate structure are assumed to follow first order shear deformation theory (FSDT). A number of numerical examples have been solved and compared with previously published literature to ensure the consistency of the present homogenization-cum-numerical approach. From the observation it is found that, the natural frequency and the controlled dynamic response of tetrachiral-type sandwich structure are very much sensitive towards the geometry (cell wall thickness, ligament length etc.) and architecture of the unit cell of the auxetic core. Also, a comparison study has been performed between tetrachiral auxetic smart sandwich and regular hexagonal honeycomb smart sandwich plate, which confirms about the mechanical advantage of the former over the later configuration, due to the existence of out-of-plane negative Poisson's ratio (NPR) and axial-shear coupling stiffness. Afterwards, a few additional numerical examples have been solved by changing different influencing parameters of the auxetic core sandwich plate and important results are reported in the article.

Self-similar hierarchical honeycombs in two different fractal layouts: A comparative study of the in-plane crushing behaviors

This paper provides a new avenue for the development of cellular structures. By mimicking the chemical structural formula of the TpPB-Fe coordination polymer, a new self-similar hierarchical honeycomb was proposed. With respect to the existing self-similar hierarchical honeycomb in the literature which was constructed by replacing every three-edge vertex of the regular hexagonal honeycomb with a smaller hexagon, the new one is created by setting the fractal position at the midpoint of the cell walls of the regular hexagonal honeycomb. What I am really curious about is the difference in mechanical properties between the two self-similar hierarchical honeycombs. Finite element (FE) model was first built and validated by comparing against the existing theoretical data. Subsequently, the in-plane crushing behaviors of the honeycombs under different impact velocities were fully investigated by FE simulations. The deformation modes, plateau stress as well as the energy absorption capability of the honeycombs were studied. Different macroscopic and microscopic deformation patterns between the two hierarchical honeycombs were observed. The plateau stress of the new hierarchical honeycomb is higher than that of both the existing counterpart and the basic regular hexagonal one. Under low- and medium-velocity impact loading, the new honeycomb with low fractal ratio (α) has superior energy absorption capability with respect to the existing counterpart and the basic regular hexagonal one. However, the new honeycomb will lose its advantage in energy absorption when the fractal ratio or the impact velocity is large.

Symplectic stiffness method for the buckling analysis of hierarchical and chiral cellular honeycomb structures

Structure-function-material integration design based on the buckling instability of flexible cellular structures has attracted much attention. According to the reversible and repeatable characteristics of buckling deformation, phonon bandgap switches, the autonomous drive of soft robots, programmable logic controllers, and reusable spacecraft landing buffer devices can be designed. Based on the Hamiltonian variational principle and symplectic eigen expansion, a theoretical analysis model of the symplectic stiffness method is established, and analytical expressions for the stiffness of several typical buckling modes of elastically supported beams are obtained. The analytical closed-form expressions for the macroscopic buckling strength of honeycombs are obtained according to the bending moment equilibrium equation. The buckling modes of regular hexagonal, hierarchical hexagonal, and tri-chiral honeycombs are obtained by numerical simulation and experimental verification, and some novel higher-order modes are observed. Uniaxial compression experiments reveal that these higher-order buckling modes can be triggered by adjusting the geometric parameters of the unit cells. The high agreement between experimental, numerical, and existing literature results for the failure surfaces of cellular structures verifies the effectiveness of the proposed symplectic stiffness method. In a word, the buckling modes can be designed to meet different functional requirements by changing the initial configuration of flexible cellular structures. This provides a new idea and theoretical guidance for the development of metamaterials and structures with tailored properties.

Blast performance of 3D-printed auxetic honeycomb sandwich beams

Little research has been conducted on comparing the blasting characteristics between the regular hexagonal and auxetic honeycomb sandwich beams (RHSBs and AHSBs). To address this gap in knowledge, the study utilised both experimental and numerical analyses. The HSBs consisted of steel top and rear face sheets bonded to a stainless- steel honeycomb core. The parameters considered in this test included the core configuration (regular vs. auxetic hexagonal) and face-core bonding method (adhesive vs. integrated). Results revealed that at scaled distances of 0.8617 m/kg1/3 and 0.7971 m/kg1/3, the AHSB core exhibited a reduction in mid-span displacement of only 3.3 % and 3.7 %, respectively, compared to the RHSB core. However, the compression value of the AHSB core significantly exceeded that of the RHSB core by 171.5 % and 161.5 %, respectively. This finding indicates that auxetic honeycomb cores possess enhanced energy absorption capacity to withstand blast loading. In addition, using unbonded face sheets increases the range of local cell deformation and decreases the global flexural bending by 22.66 % and 24.14 % at scaled distances of 0.8617 m/kg1/3 and 0.7971 m/kg1/3, respectively, compared to the AHSBs with face sheet debonding. To further investigate the damage mechanism of HSBs subjected to blast loading, a well-validated finite element model was employed. Notably, parametric simulations demonstrated that the dynamic behaviour of AHSBs under blast loading is significantly influenced by cell wall thickness, face sheet thickness, and cell angle.

Mechanical properties of horsetail bio-inspired honeycombs under quasi-static axial load

The bionic strategy is regarded as a highly effective design approach for honeycomb structures. To improve the crushing resistance of the honeycombs, some novel bio-honeycombs are proposed by introducing the microstructure of horsetail stems into regular hexagonal honeycomb (RH) cells in this study. Two types of developed bio-honeycombs are considered, including MP type and CC type. A circular honeycomb compression test is carried out to validate the finite element (FE) model. Subsequently, FE models of bio-honeycombs are established to investigate their out-of-plane crashworthiness. The results suggest that the introduced bionic units and the RH frame component will produce a significant interaction effect, where more severe plastic deformation will be formed at their intersections and more folding lobes are formed on the cell walls. Furthermore, the effect of geometric parameters on crashworthiness of MP_6 (MP type with six ribs) bio-honeycombs is discussed. It demonstrates that the smaller cell size of bio-honeycomb is beneficial for improving the utilization efficiency of materials. The deformation modes of MP_6 bio-honeycombs are determined by the ratio of cell wall thickness to cell length (t/l), and the global bending occurs when t/l exceeds 0.0625. In addition, a theoretical model for estimating the mean crushing force of MP_6 bio-honeycombs is derived, and the error with the FE results is within 7%, confirming that the theoretical solution is in good agreement with the simulation.

Dynamic Compressive and Flexural Behaviour of Re-Entrant Auxetics: A Numerical Study.

Re-entrant auxetics offer the potential to address lightweight challenges while exhibiting superior impact resistance, energy absorption capacity, and a synclastic curvature deformation mechanism for a wide range of engineering applications. This paper presents a systematic numerical study on the compressive and flexural behaviour of re-entrant honeycomb and 3D re-entrant lattice using the finite element method implemented with ABAQUS/Explicit, in comparison with that of regular hexagonal honeycomb. The finite element model was validated with experimental data obtained from the literature, followed by a mesh size sensitivity analysis performed to determine the optimal element size. A series of simulations was then conducted to investigate the failure mechanisms and effects of different factors including strain rate, relative density, unit cell number, and material property on the dynamic response of re-entrant auxetics subjected to axial and flexural loading. The simulation results indicate that 3D re-entrant lattice is superior to hexagonal honeycomb and re-entrant honeycomb in energy dissipation, which is insensitive to unit cell number. Replacing re-entrant honeycomb with 3D re-entrant lattice leads to an 884% increase in plastic energy dissipation and a 694% rise in initial peak stress. Under flexural loading, the re-entrant honeycomb shows a small flexural modulus, but maintains the elastic deformation regime over a large range of strain. In all cases, the compressive and flexural dynamic response of re-entrant auxetics exhibits a strong dependence on strain rate, relative density, and material property. This study provides intuitive insight into the compressive and flexural performance of re-entrant auxetics, which can facilitate the optimal design of auxetic composites.

On the out-of-plane crashworthiness of incorporating hierarchy and gradient into hexagonal honeycomb

Hierarchical design and gradient design have proven to be effective in improving the crashworthiness of honeycombs. In this study, a novel graded hierarchical hexagonal honeycomb (GHHH) is proposed by introducing wall thickness variation into the vertex-based hierarchical hexagonal honeycomb (VHHH). The VHHH is obtained by replacing every vertex of the regular hexagonal honeycomb (RHH) with a smaller hexagon. Numerical simulations and theoretical analysis are performed to study the crashworthiness performance of GHHH under the out-of-plane impact. The numerical results show that the specific energy absorption (SEA) of GHHH can be 146.09%, 39.01%, and 50.23% higher than that of RHH, VHHH, and graded hexagonal honeycomb (GHH), respectively, while their peak stresses are nearly the same. In addition, a theoretical model for the plateau stress of GHHH is developed, and the theoretical values show good consistency with numerical results of GHHH with in-extensional mode. The findings of this study provide an effective guideline for the design of honeycombs with enhanced crashworthiness.

The interplay between constituent material and architectural disorder in bioinspired honeycomb structures

The advent of additive manufacturing has enabled the precise manufacturing of lattice materials at different length scales. While honeycombs are usually constructed from a tessellated array of identical unit cells, most structures in nature tend towards stochastic or disordered tessellation. In this work, we explore the effect of disorder properties of honeycombs, in particular, stiffness, strength, fracture toughness, and crack propagation paths using finite element models. The honeycombs are created using Voronoi tessellations with different levels of disorder measured by a regularity parameter δ, where δ=1 corresponds to a regular hexagonal honeycomb and decreasing values of δ correspond to increasing levels of disorder. We consider three constituent materials: very brittle, quasi-brittle, and very ductile (0.0007–0.25 in failure strain). The results show that pseudo-order realizations with 0.5≤δ≤0.8show the best strength-toughness trade-off. With increased plasticity, the improvement in fracture toughness compared to regular honeycombs can be as high as 50% at the expense of a 20% decrease in strength. This increase in fracture toughness is achieved both at crack initiation with crack blunting intrinsically and extrinsically during crack growth by a combination of crack deflection and crack bridging. Also, a single mathematical variable δ usually referred to as a “regularity parameter” to control cell stochasticity cannot account for the variability in tensile strength and fracture toughness parameters for brittle or quasi-brittle constituent materials and significantly more for a ductile constituent material. Thus, a local parameter for disorder is required to explain the large statistical variance seen in the mechanical properties of disordered honeycomb structures across the same irregularity value.

Simulation study on the anti-penetration performance and energy absorption characteristics of honeycomb aluminum sandwich structure

This work studied the anti-penetration performance and energy absorption characteristics of the honeycomb aluminum core structure. Tests of penetrating depth were conducted. The response and deformation resistance of the aluminum sandwich structure with a regular hexagonal honeycomb were studied through numerical simulation. The effect of the face/back plate thickness ratio and the shape of the core layer unit on the performance of the aluminum sandwich structure with a regular hexagonal honeycomb were compared and analyzed with a theoretical model of equivalent target calculation. Based on the results, the aluminum sandwich structure with a regular hexagonal honeycomb has the strongest anti-penetration capability when the thickness ratio of the face/back plate is set to 2.5:1. In terms of the energy consumption, the Arrow and concave hexagonal honeycomb aluminum sandwich structures are 14.7% and 25.9%, respectively, than the aluminum sandwich structure with a regular hexagonal honeycomb. The typical hierarchical honeycomb aluminum sandwich structure has better energy absorption characteristics than the aluminum sandwich structure with a regular hexagonal honeycomb. Therefore, the anti-penetration performance of the honeycomb aluminum sandwich structure can be improved by adjusting the thickness ratio of the face/back plate and changing the shape of the core layer. The research results are of great significance in guiding the design of the honeycomb aluminum sandwich structure.

Multi-scale characterization and in-plane crushing behavior of the elliptical anti-chiral honeycomb

Honeycombs with anti-chiral (AC) unit cells are found to have auxetic properties and enhanced energy absorption capacities than regular hexagonal honeycombs. To further improve the energy absorption capacity, by replacing the straight cell walls of the criss-cross anti-chiral (CAC) honeycomb with elliptical cell walls, a novel elliptical anti-chiral (EAC) honeycomb is proposed in this paper. The in-plane crushing response of the EAC honeycomb is investigated numerically under different impact velocities. The numerical modeling method in ABAQUS software is validated by the compression test data of 3D-printed EAC honeycomb specimens. Both experimental and numerical results reveal that the EAC honeycomb has a plateau stage and an enhancement stage in the stress–strain curve. The empirical formulas of critical impact velocity and plateau stress are further derived, which is in good agreement with the numerical simulation results. The parameter analysis further shows that the microstructural parameters have a great influence on the crushing strength of the EAC honeycomb. Under the same impact velocity, larger semi-axis length ratio results in larger plateau stress and densification strain, while smaller semi-axis length ratio means larger initial peak stress and plateau strain.

Anti-blast performance of 3D-printed sandwich panels with auxetic hexagonal and regular hexagonal honeycomb cores

3D-printed auxetic honeycomb sandwich panels (HSPs) have considerable potential for blast resistance enhancement. This study aims to bridge the gap with regard to the experimental data on the effect of 3D-printed auxetic hexagonal honeycomb cores on the blast response of HSPs. To this end, the blast resistance of HSPs developed using auxetic re-entrant and regular hexagonal honeycomb cores is investigated experimentally and numerically. First, six HSPs are tested under close-in blast loadings. The HSPs comprise Q345 steel top and bottom sheets as well as a honeycomb aluminum alloy core with two configurations (regular hexagonal and auxetic re-entrant). According to the results, the former configuration enhances the HSP blast resistance by not only decreasing the deformation of the HSPs but also improving their damage tolerance. In addition, the responses of the HSPs are numerically studied via finite element analysis. The numerical method using the finite element program LS-DYNA achieves reasonable accuracy. Finally, a parametric study is conducted to investigate the effects of the honeycomb type, cell angle, debonding effects, and core material on the blast resistance of the HSPs. The results demonstrate that employing auxetic hexagonal honeycomb core, smaller cell angle, and ductile core material can improve the blast resistance of HSPs.

Bionic inspired honeycomb structures and multi-objective optimization for variable graded layers

Bionic and gradient designs offer promising applications in honeycomb structures. The intersection unit of the beetle elytra is extracted as to enhance regular hexagonal honeycomb (RHH), and several bionic honeycombs are proposed. Finite element (FE) modeling approach is verified through formulae and experiments. Curves of force and displacement of bionic honeycombs present two prominent stages under medium- and low-speed impacts in plateau stage, and several bionic honeycombs exhibit a zero or negative Poisson’s ratio. The specific energy absorption (SEA) of INT_6, whose crashworthiness is best in bionic honeycombs. A gradient design of INT_6 is implemented to further increase its crashworthiness. Multi-objective optimization design (MOD), which aims to simultaneously increase the SEA and reduce the peak crushing force, is adopted to determine the optimal parameters of each layer of graded INT_6. The SEA of the optimized graded INT_6 increase 142%, and its peak crushing force decrease by 25.4% compared with those of the INT_6.

In-plane dynamic crashing behavior and energy absorption of novel bionic honeycomb structures

A series of novel bionic honeycombs (bio-honeycombs) are proposed by incorporating the microstructure of the beetle elytra intersection unit into the regular hexagonal honeycomb (Hex) cell. To explore the in-plane mechanical properties and energy absorption performance of bio-honeycombs under different impact speeds, finite element (FE) models are established and verified by empirical formulas and current experiments. The results indicate that the bio-honeycombs outperform the Hex in terms of energy absorption capacity, and the nominal stress–strain curves of the bio-honeycombs show two prominent stages (stage Ⅰ and stage Ⅱ) under quasi-static and mid-impact. Bionic units also undergo two evident deformation stages: preliminary collapse and further crushing. The bending and traction of bionic units make more adjacent cells added to the collapse earlier, forming a global crushed trend, leading to an interesting phenomenon that the localized band of bio-honeycombs are always wider than that of Hex. Also, negative Poisson’s ratio is observed in stage Ⅱ from several bio-honeycombs under quasi-static and mid-speed due to bionic units' bending and traction in the further crushing stage. Besides, the number and distribution of ribs have a considerable impact on the crashworthiness of bio-honeycombs. Compared with the Hex, the incorporated bionic units reduce the peak crushing force (PCF) while improving the crashworthiness of bio-honeycomb in the case of the same relative density, which provides a promising potential solution to strengthen the energy absorption performance of honeycomb structures.

Dynamic Crushing Analysis of Hexagonal-Kagome Combined Honeycomb with Negative Poisson’s Ratio

To enhance the mechanical performances of traditional honeycombs, a novel combined honeycomb (HKH) was proposed based on the regular hexagonal honeycomb (RHH) and Kagome honeycomb (KH). A systematic investigation of the in-plane dynamic crushing behaviors of the honeycombs was conducted via the finite element method, and the crashworthiness characteristics of the three honeycombs were examined. Using one-dimensional shock wave theory and least squares fitting, a fitting formula of the plateau stress was obtained, and the deformation mechanism of the HKH was determined based on the elastic buckling of the cell wall. The results showed that the HKH exhibited a higher plateau stress than the RHH for any velocity impact, while the negative Poisson’s ratio effect was more significant than that of the KH for low-velocity impacts (the peak Poisson’s ratios of the HKH and KH were −0.312 and −0.286, respectively). Furthermore, the effects of the impact velocity and relative density on the energy absorption and auxetic performances were explored. In this study, a novel design was proposed by combining various cell elements to obtain better crashworthiness, providing a new concept to promote the development of lightweight materials.