Hexagonal Honeycomb Research Articles

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.

Assembled mechanical metamaterials with transformable shape and auxeticity

Fabricating auxetic metamaterials via an assembling process is a novel and economic method. In this work, an assembled structure that could realize the conversion of positive and negative Poisson’s ratio by changing the length of the connection plates was proposed. Two different honeycomb structures of the assembled re-entrant honeycomb (ARH) and assembled hexagonal honeycomb (AHH) were designed, manufactured and studied numerically and experimentally. Dimensions of the two assembled honeycomb structures are consistent. The nominal stress–strain curves of the two assembled honeycombs have similar initial peak stresses, but the assembled re-entrant honeycomb has a higher bearing capacity and shorter stress plateau. Subsequently, the mechanical properties of ARH were studied by changing the three parameters of corrugated plates. Besides, the energy absorption and specific energy absorption of the assembled re-entrant honeycomb were investigated through the numerical method. Finally, the assembled honeycomb structure with the suitable parameter was determined. Tunable mechanical properties of the assembled auxetic structures can be obtained by varying the length of the connection plates. This strategy of assembly can reduce the costs of manufacturing and improve transportation efficiency. The proposed assembled structures are promising in civil and protective engineering.

Dynamic fracture toughness of cellular materials with different microstructures

Ultra-lightweight cellular materials have been widely utilized owing to their excellent specific stiffness, strength and fracture resistance ability. However, current understanding of the fracture resistance of cellular materials is mostly limited to quasi-static loading conditions, and their resistance to dynamic fracture is comparatively less understood. In this study, we investigate the dynamic fracture behaviors of the triangular, kagome, and hexagonal honeycomb cellular materials using numerical methods. Both single-edge notched bend and single-edge notched tension specimens under dynamic loading are considered, and the J values of dynamic fracture toughness of the three configurations are determined. Simulation results demonstrate that the fracture resistance of the triangular honeycomb increases with increasing loading velocity, whereas the fracture toughness of the two other structures exhibits slight variation with respect to the loading rates. After examining the fracture response by changing the strain-rate-dependence of the constituent material, we concluded that the microstructure has a more significant effect on the rate-dependence of fracture toughness than the constituent material. A mechanism based on crack deviation is proposed to account for the distinct rate-dependence of fracture toughness in specimens with different microstructures.

Microstructure and geometry effects on the compressive behavior of LPBF-manufactured inconel 718 honeycomb structures

This work discusses the combined effect of the microstructure and geometry on the deformation modes and energy-absorbing characteristics of laser powder bed fusion (LPBF)-manufactured Inconel 718 (IN718) hexagonal honeycomb structures tested under quasi-static compression. Three different geometries of the hexagonal cells, varying only in the cell wall thickness (0.4, 0.6 and 0.8 mm) were manufactured using LPBF. Electron backscatter diffraction (EBSD) imaging of the three studied geometries revealed three distinct zones of grain morphologies and textures across the 0.6 and 0.8 mm cell walls and only two zones and higher overall <001> texture across the 0.4 mm cell walls. Miniature tensile tests were performed on 0.4 and 0.8 mm thick tensile samples to evaluate the thickness and orientation effects on the parent material behavior. Each hexagonal geometry was loaded in three different directions resulting in nine study sets. Exhibiting monotonically increasing plateau stress and specific energy absorbed (SEA) in addition to the high SEA/plateau stress ratios, LPBF-manufactured IN718 hexagonal honeycomb structures were demonstrated to be a viable candidate for additively-manufactured (AMed) metallic lattice structures in energy absorption applications. The reduction in the cell wall thickness influenced the instability failure mechanism for the in-plane load direction X1 but no pronounced effect was observed for the in-plane direction X2. As a result of the coupled change of the material properties with the variation in the cell wall thickness, a non-normalized anisotropic form of the Gibson-Ashby model for stochastic foams was proposed to characterize the honeycomb-structure mechanical properties. The findings of this paper more generally provide useful insights into optimizing the design of metallic AMed lattice structures.

Computational Comparison of Performance of Different Steel Plate Shear Yielding Dampers

The computational modeling of hysteretic dampers is a powerful tool for design, allowing us to predict and optimize damper performance. In this research, a numerical model, based on Chaboche’s nonlinear kinematic hardening constitutive law, was implemented. The parameters of this law were identified and validated by inverse analysis, based on the macro-hysteretic response of the hexagonal honeycomb steel damper. The validated model was applied to simulate the cyclic loading behavior of five proposed steel plate shear yielding dampers (SPSYDs), which were then used to compare the hysteretic performance in terms of effective stiffness, effective damping, and energy dissipation capacity. The parametric analysis of design variables performed on the SPSYDs demonstrated that the plate depth does not modify the effective damping, and the thickness is the most significant factor affecting the maximum displacement, dissipation energy and endurance cycles. The comparison of the performance of the dampers allowed us to establish design guidelines for the SPSYDs, which allow the device to be adjusted with the requirements of the building in which it is installed.

A novel design of an actively deformable honeycomb structure with application to a variable thickness leading-edge wing

This work develops a novel design method for the actively deformable honeycomb structure to realize the variable thickness leading-edge wing. Firstly, the classical Gibson theory is extended to be applicable for the non-regular hexagonal honeycomb single-cell with the positive Poisson’s ratio and the concave hexagonal honeycomb single-cell with the negative Poisson’s ratio. The equivalent mechanical properties of the above two types of single-cells are deduced. Then, the concept of the deformation unit composed of positive and negative Poisson’s ratio honeycomb multi-cells is proposed. The shape memory alloy is assigned as an actuator to produce the in-plane incompatible deformation which excites the out-of-plane bending of the deformation unit. The relationship between the in-plane driving displacement and the bending angle of the deformation unit is investigated. The segmented two-layered honeycomb-core plate composed of positive and negative Poisson’s ratio honeycomb layers is constructed using deformation units. Finally, the initial configuration of the leading-edge is simulated by the segmented honeycomb-core plate. The driving displacements required to be imposed to each deformation unit are determined according to the target shape of the leading-edge. The proposed method is validated by changing the leading-edge from the blunt shape to the sharp shape, using finite element simulations.

In-plane shear stiffness of diversified hexagonal honeycombs: A simple energy-based approach

The conventional hexagonal honeycomb is widely used in various practical applications. The re-entrant and semi re-entrant hexagonal forms derived from the conventional one have gained large attention in recent years due to their unusual Poisson's ratio and superior mechanical performance. However, the in-plane shear behavior of the semi re-entrant hexagonal honeycomb has not been reported yet. Especially, a comparative study on the shear stiffness of the three hexagonal honeycombs is lacking. A simple energy-based approach was used in this paper to establish theoretical models for predicting the in-plane shear modulus of the hexagonal honeycombs, which were later verified by the numerical simulations. Good agreement between the theoretical and numerical results is observed. The effect of the geometrical parameters on the shear modulus and the specific shear modulus were further discussed. It is found that the conventional hexagonal honeycomb displays higher shear modulus and specific shear modulus than both the re-entrant and semi re-entrant ones, while the re-entrant hexagonal honeycomb demonstrates the lowest values of shear modulus and specific shear modulus.

Scale Effect Assessment of Innovative 3D-Printed Honeycomb under Quasi-Static Compression

Honeycomb cores are widely used in the aerospace and automotive fields as a part of protective structures. Unfortunately, standard prismatic honeycomb cores offer a limited amount of energy absorption under lateral loads and suffer from degradation of their impact-deadening properties when their dimensional scale is increased. In this work, a multiscale study on energy absorption under quasi-static load is carried out on 3D-printed honeycomb core samples constituted by a variable section and compared to the cases of standard hexagonal honeycomb samples having the same mass and external dimensions. When doubling the dimensional scale in the case of lateral loads, the novel core geometry showed a substantial absence of specific energy absorption degradation, whereas the hexagonal core suffered from a 12.2%-degradation. Furthermore, by increasing the dimensional scale, the novel core geometry shows a delay in the densification onset. The variable-core geometry showed an average increase, in terms of energy absorption under lateral loads, of 46.8% for the regular scale and 71.4% for the double scale. Under axial loads, a 12.4%-decrease in energy absorption was observed for the samples with novel geometry, which, nevertheless, showed a relatively constant profile of reaction force under compression: this property could potentially allow it to avoid pre-crushing.

Out-of-plane energy absorption and crashing behavior of arc-curved hexagonal honeycomb structure

To enhance the out-of-plane mechanical performance, a novel honeycomb with arc-curved edge is proposed. The numerical model is built based on the elastoplastic failure criterion. The impact performance of proposed honeycomb is investigated and revealed. The influence of central angle and thickness on the crashworthiness is researched. The results show that the numerical result is in agreement with that of experimental test. The central angle has great influence on the deformation mode. The global buckling of edge tube is exhibited for the small central angle, and the consistent deformation mode is demonstrated for the central area. With the increasing of central angle, the energy absorption ability is enhanced for the plastic hinge could absorb more impact energy. The more stable deformation mode is exhibited for the larger central angle. The honeycomb with relatively large central angle has the best crashworthiness performance for the balance of energy absorption and structural mass. Compared with traditional honeycomb, the proposed honeycomb could improve the out-of-plane energy absorption characteristics.

Mechanical characteristics and foam filling enhancement mechanism of polymeric periodic hybrid structures under uniaxial compression

In this study, two types of polymeric periodic hybrid (PPH) structures with hexagonal and re-entrant cells were proposed and manufactured by 3D printing using polylactic acid (PLA). PVC foam was adopted as filler material. The mechanical characteristics of PPH structures under uniaxial compression were experimentally and numerically investigated. Experimental results show that PPH structures with foam filling in re-entrant cells exhibit higher elastic modulus and peak stress than those with foam filling in hexagonal cells, which is due to the bi-directional compression of the foam filler in re-entrant cells. Moreover, their deformation processes are more stable, benefiting from compatible deformation between hexagonal and re-entrant cells. With the increase in foam filling volume fraction, the plateau stress and specific energy absorption of PPH structures increase. Numerical results reveal that the enhancement efficiency of foam filling gets improved by suitably increasing the cell wall thickness. The fully foam-filled PPH structures exhibit significantly higher yield strength than the fully foam-filled hexagonal honeycomb structures, and also possess excellent stable deformation characteristics compared with fully foam-filled re-entrant honeycomb structures. The PPH structures proposed in this study show superior comprehensive mechanical performance, thus offering potential application prospects in structural protection fields.

Energy Absorption of 3D Printed ABS and TPU Multimaterial Honeycomb Structures.

Advances in multimaterial 3D printing are enabling the construction of advantageous engineering structures that benefit from material synergies. Cellular structures, such as honeycombs, provide high-energy absorption to weight ratios that could benefit from multimaterial strategies to improve the safety and performance of engineered systems. In this study, we investigate the energy absorption for honeycombs with square and hexagonal unit cells constructed from acrylonitrile butadiene styrene (ABS) and thermoplastic polyurethane (TPU). Honeycombs were fabricated and tested for out-of-plane and in-plane compression using ABS, TPU, and a combination of ABS with a central TPU band of tunable height. Out-of-plane energy absorption for square honeycombs increased from 2.2 kN·mm for TPU samples to 11.5 kN·mm for ABS samples and energy absorption of hexagonal honeycombs increased from 2.9 to 15.1 kN·mm as proportions of TPU/ABS were altered. In-plane loading demonstrated a sequential collapse of unit cell rows in square honeycombs with energy absorption of 0.1 to 2.6 kN·mm and a gradual failure of hexagonal honeycombs with energy absorption of 0.6 to 2.0 kN·mm. These results demonstrate how multimaterial combinations affect honeycomb compressive response by highlighting their benefits for controlled energy absorption and deformation for tunable performance in diverse engineering applications.

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.

Crashworthiness optimization of crash box with 3D-printed lattice structures

Crash boxes are important energy-absorbing components to ensure the passive safety of automobile vehicles during crashworthiness. The current study presents an investigation of a novel crash box, which consists of Al shell and 3D-printed lattice core. In view of obtaining a good lightweight and energy absorption, the lattice structures are fabricated by fused filament fabrication (FFF) technology using carbon fiber reinforced polyamide 6 (PA6/CF) composites. First, the correlations between fiber content and elastic modulus, maximum tensile stress are established by a least squares method. Four different lattice structures including hexagonal, kagome, re-entrant and triangular honeycombs are additive-manufactured. The results reveal that the experimental data from compression test is in good agreement with the simulation analysis, and the kagome achieves the maximum specific energy absorption (SEA) values through numerical analysis. Then, an integrated “material-structure” model is constructed in an Isight environment to analyze the sensitivity of the material property (elastic modulus (E), tensile strength (σ) and fracture strain (ε)) and geometric parameters (thickness (t) and unit size (r) on the crashworthiness performance. A multi-objective optimization strategy with maximum SEA and minimum mass as objectives for the novel crash box is established using response surface model approach and optimal Latin hypercube. Simulation results show that the crash box optimized by non-dominated sorting genetic algorithm (NSGA-II) algorithm can improve the energy absorption with mass reduction, which provides some reference for the structural design and optimization of the crash box.

Nonlinear vibrations of all-composite sandwich plates with a hexagon honeycomb core: Theoretical and experimental investigations

Nonlinear vibrations of all-composite sandwich plates with a hexagon honeycomb core: Theoretical and experimental investigations

Three-point bending characteristics of all-composite sandwich panels with different core configurations

With cores of the hexagonal honeycomb (HH), staggered corrugated lattice (SCL), bidirectional corrugated lattice (BCL), reinforced hexagonal honeycomb (RHH), and reinforced staggered corrugated lattice (RSCL) made by cutting, bonding, arranging and weaving the trapezoidal corrugation (TC) formed by mold hot pressing, six types of composite sandwich panels of the same macro size were proposed. The failure processes of the six sandwich panels in three-point bending experiments were compared and analyzed, and the effects of core configuration and reinforced stiffener on the bending response were evaluated. A general analytical model was established to predict the bending stiffness and failure mode of six sandwich panels, which was also visually presented by a three-dimensional numerical model. The numerical and experimental results validated the effectiveness of the analytical model. The effects of ply parameters and corrugated sizes on bending responses were studied by a combing application of experiment, analytical and numerical models. The three-dimensional failure mechanism maps were displayed to evaluate the failure mode and failure load. The longitudinal discontinuity of the bonding zone of the core could significantly weaken the bending performance and bonding strength of BCL, SCL, RSCL, and HH. The peak load of SCL and HH was enhanced by 45.97% and 60.29%, respectively, by setting stiffeners. Both RHH and TC could achieve bending stiffness of more than 3.5 kN·mm−1, while the failure load of the latter could be up to 25 kN. The design parameter space of bending stiffness, failure load with respect to ply orientation angle, core wall thickness, corrugated web angle, and horizontal segment length was provided intuitively.

Graphene Nanocomposite Membranes: Fabrication and Water Treatment Applications.

Graphene, a two-dimensional hexagonal honeycomb carbon structure, is widely used in membrane technologies thanks to its unique optical, electrical, mechanical, thermal, chemical and photoelectric properties. The light weight, mechanical strength, anti-bacterial effect, and pollution-adsorption properties of graphene membranes are valuable in water treatment studies. Incorporation of nanoparticles like carbon nanotubes (CNTs) and metal oxide into the graphene filtering nanocomposite membrane structure can provide an improved photocatalysis process in a water treatment system. With the rapid development of graphene nanocomposites and graphene nanocomposite membrane-based acoustically supported filtering systems, including CNTs and visible-light active metal oxide photocatalyst, it is necessary to develop the researches of sustainable and environmentally friendly applications that can lead to new and groundbreaking water treatment systems. In this review, characteristic properties of graphene and graphene nanocomposites are examined, various methods for the synthesis and dispersion processes of graphene, CNTs, metal oxide and polymer nanocomposites and membrane fabrication and characterization techniques are discussed in details with using literature reports and our laboratory experimental results. Recent membrane developments in water treatment applications and graphene-based membranes are reviewed, and the current challenges and future prospects of membrane technology are discussed.

Finite element analysis on yield surface evolution of cellular materials

The yield surface is the boundary of elastic region in the theory of plasticity, therefore the area and the shape of the yield surface can represent the capability of cellular materials in the stress space. The yield point and the yield surface of one kind of 2D cellular materials, hexagonal honeycombs, is investigated in this study via the finite element analysis with a representative block approach. All components of requisites to computationally investigate yield surface evolution of 2D cellular materials are prepared. A proper determination of yield point for the honeycombs is proposed for the detection of initial and subsequent yield surfaces in the axial-shear stress space and the yield point determination is validated by the comparison between experimental result and finite element analysis. Taking into account a wide range of relative density for honeycombs, the mesh size as well as the pattern and the size of the representative block in finite element is investigated and selected based on the analysis of the mesh convergence analysis, the boundary effect, and the size effect. After probing paths and preloading paths are designed, the initial and subsequent yield surfaces of the honeycombs with different relative density are detected and the influence of relative density on the yield surface evolution is investigated. The investigation shows a shear preloading path followed by an axial preloading path strengthens the capability of honeycombs and the honeycomb with lower relative density may exhibit different behavior of yield surface evolution than those with higher relative density. Further, phenomena of cellular materials including the Bauschinger effect and the hardening behavior (isotropic, kinematic, rotation, distortional) are observed from the yield surface evolution of honeycombs.

Experimental and finite element analyses of a 3D printed sandwich with an auxetic or non-auxetic core

This work presents the results of experimental and numerical analyses of the static properties of architectural cores and the dynamic behavior of sandwich structures made with an auxetic or non-auxetic core. Three architectural cores have been studied which are re-entrant, rectangular and hexagonal honeycombs. Each configuration was produced with four relative densities depending on the number of cells in the width of the specimens. The specimens were made with additive manufacturing technology. The material used to make the specimens was polylactic acid with flax fibers. Several tensile tests were carried out on the architectural cores to analyze and understand the influence of the topology and the density of the core on the Poisson’s ratio and the Young’s modulus of these architectural structures. Then, vibration tests were carried out on the cores and the sandwich structures. The objective was to study the influence of these structures and their densities on the dynamic properties of sandwiches. The structural Poisson’s ratio shows a sensitive behavior to the core topology and density.

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States

Based on the negative Poisson’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties.

Bio-inspired hierarchical honeycomb metastructures with superior mechanical properties

• A new honeycomb metastructure design methodology is inspired by the hierarchical idea found in nature. • The principles of conformal, hierarchy, number and size design are deduced. • A novel hierarchical honeycomb metastructure can improve energy absorption with other performances unchange. Inspired by the hierarchical macro and microstructures widely found in nature, this study proposes a novel hierarchical honeycomb design methodology. The aim is to overcome the shortcoming of conventional honeycomb structures that have poor energy absorption properties due to damage after loading. Thereby, a new honeycomb structure with several superior mechanical properties is obtained. Firstly, triangular, square, and circular holes are used at the third microstructure level. Moreover, their filling types, filling principles, and dimensional design basis are thoroughly investigated. And a hierarchical honeycomb is generated by arranging them on the cell walls of a conventional honeycomb according to the conformal design guidelines. Finally, the performance of the designed hierarchical honeycomb metastructure is analyzed and compared by simulation and experiment. It is found that the hierarchical honeycomb metastructures exhibit significantly improved overall mechanical properties compared with the conventional honeycomb structures. The hierarchical honeycomb metastructures with different holes have different performance enhancement effects on the conventional honeycomb structure. Among them, the hierarchical honeycomb metastructures with circular holes have the best performance improvement compared to conventional honeycomb structures. The hierarchical square honeycomb with circular holes has 0.84% stiffness loss, 19.38% strength loss, and 199.67% energy absorption performance improvement. However, the hierarchical hexagon honeycomb with circular holes has 1.06% stiffness improvement, 5.55% strength loss, and 345.24% energy absorption performance improvement. Additionally, the reliability of the novel honeycomb metastructure is verified to be better than the conventional honeycomb structure with the spacecraft return capsule shell.