Hierarchical Honeycomb Research Articles

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.

Stabilized and efficient multi-crushing properties via face-centered hierarchical honeycomb

The undesirable resistance to multi-crushing loads limits the development of regular honeycomb structures in advanced engineering fields. Therefore, a novel hierarchical strategy, namely face-centered hierarchical strategy, is proposed to improve the multi-crushing properties of honeycombs. The honeycombs with the face-centered hierarchical network are manufactured by selective laser melting to test their energy absorption mechanism against the oblique crushing load. The multi-crushing properties of face-centered hierarchical honeycomb (FCHH) are explored by a numerical investigation. The carrying capacity and energy absorption of the FCHH decrease with the increasing crushing angle. The parameter configuration design indicates that the hierarchy order has a positive effect on the multi-crushing resistance of the FCHH. The face-centered hierarchical network not only provides the strong lateral support, improving the collapse of the honeycomb, but also reduces the folding wavelength, improving its material utilization. Specifically, the specific energy absorption and crushing force efficiency of the FCHH improve by 27.65 % and 30.83 % respectively as the hierarchy order increases from 1 to 3 at the crushing angle of 30°. Furthermore, when the thickness gradient factor is close to 1, the FCHH obtains a more reasonable material distribution to resist the oblique crushing load. Compared with other hierarchical honeycombs for the oblique crushing resistance, the FCHH demonstrates a more stable carrying process and more efficient energy absorption. This research expects to propose a promising reinforcement strategy to guide the design of multi-crushing properties for honeycombs.

Study on re-entrant hierarchical honeycombs in-plane impact

The introduction of hierarchical structure in cell materials can further improve their energy absorption effect, and negative Poisson's ratio materials have excellent energy absorption capacity and special deformation mode. In this paper, augmented double arrow honeycomb structures is introduced into the re-entrant honeycomb with negative Poisson's ratio as a substructure (RHA) to improve the mechanical properties of the first-order re-entrant honeycomb and enhance the energy absorption effect of the structure. The analytical formula of the collapse stress of honeycomb under quasi-static compression was derived by the two-scale method. The failure stress of RHA under different relative densities and impact velocities is discussed, and the analytical formula of RHA stress in dynamic crushing is derived by combining momentum conservation. Due to the special substructure, the secondary honeycomb discussed in this paper has two plateau periods. In this paper, the second plateau stress of the honeycomb structure is calculated innovatively. The numerical simulation results show that the collapse stress of RHA in the first plateau period is similar to that of the first-order re-entrant honeycomb, and the collapse stress in the second plateau period is increased by 332%. The research in this paper shows that the honeycomb with the second plateau period has a better energy absorption effect, which is an effective strategy for improving the energy absorption effect of the honeycomb. It can be further explored to improve the impact resistance of the honeycomb.

Effective elastic properties of sandwich-structured hierarchical honeycombs: An analytical solution

Sandwich-structured honeycombs (SSHCs) are hierarchical structures comprising sandwiched cell walls and are known to exhibit enhanced mass-specific properties. Here, we present an analytical model capable of predicting the effective elastic properties of hexagonal SSHCs, employing a sandwich beam theory that accounts for the effect of thick faces and regards the core as structurally weak. The analytical solutions of the nine elastic constants are compared with the numerical predictions obtained from a finite element-based homogenization technique, and an excellent agreement is reported for a wide range of architectural parameters such as the beam size, core thickness, and angle. Overall, it is found that SSHCs outperform conventional (monolithic) honeycombs in terms of their in-plane elastic and shear moduli, reporting values up to 20 times the monolithic counterparts of identical mass. In contrast, the out-of-plane shear moduli of the SSHCs showed reductions of at least 10% as compared to the traditional monolithic honeycomb structures.

Hierarchical porous honeycomb NiCo/C catalyst for decarboxylation of fatty acids and upgrading of sludge bio-crude

Honeycomb NiCo/C-Na catalyst featured with a micro-meso-macroporous structure is fabricated and shows a significantly higher catalytic activity for decarboxylation of fatty acid compared to a series of other carbon-based catalysts. A 100 % conversion of stearic acid and a C15-18 alkane total yield of 70 % is achieved at 280 °C for 3 h under 1 MPa H2 with heptadecane as the main product. NiCo/C-Na also achieves a complete conversion of monoglyceride into heptadecane when using edible oil as reactant. The catalyst is further evaluated for upgrading of sludge HTL bio-crude and proves to be highly efficient. The obtained upgraded biofuel exhibits a decreased viscosity and an increased density. Specifically, the higher heating value (HHV) increases to 47.32 MJ/kg. This result is attributed to the easier desorption of CO2, better H2 activation capacity and the unique hierarchical pore structure of the catalyst, which allows faster mass transfer and reaction rate.

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.

Hierarchical porous honeycomb microspheres assembled by MoS2 nanocrystals-embedded carbon nanosheets for high-performance lithium storage

Hierarchical porous honeycomb microspheres assembled by MoS2 nanocrystals-embedded carbon nanosheets are synthesized by constructing polystyrene (PS) sphere-embedded Mo-polydopamine organic/inorganic hybrid microspheres, followed by carbonization and sulfuration. The as-prepared composite is systematically studied by various material characterization techniques. It is found that the diameters of the microspheres and honeycomb pores are 3–5 μm and 200 nm. The specific surface area reaches 150.8 m2 g−1. MoS2@honeycomb carbon microsphere anode can achieve outstanding rate performance (237 mAh g−1 at 10 A g−1), high specific capacity and stable long-term cycling performance (reversible capacity of 1199 mAh g−1 at 0.1 A g−1 after 120 cycles, 599 mAh g−1 at 2 A g−1 after 300 cycles with capacity decay rate of 0.07 % per cycle, 495 mAh g−1 at 5 A g−1 after 500 cycles). The high reversible capacity is mainly derived from conversion reaction of MoS2 and lithiation reaction of S, as revealed by the analyses on the rate discharge curves. Kinetic measurements and ex-situ characterization further demonstrate the fast and stable Li+ diffusion, low impedance, strong capacitive effect and robust composite structure. The assembled full cell exhibits a reversible capacity of 209.7 mAh g−1 after 1880 cycles at 5 A g−1 and can power a red LED lamp. Overall, the excellent lithium storage performance manifests the significant potential of this MoS2 composite in high-performance lithium-ion batteries.

MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems

We report a flexible multi-modal mechanics language model, MeLM, applied to solve various nonlinear forward and inverse problems, that can deal with a set of instructions, numbers and microstructure data. The framework is applied to various examples including bio-inspired hierarchical honeycomb design, carbon nanotube mechanics, and protein unfolding. In spite of the adaptable nature of the model-which allows us to easily incorporate diverse materials, scales, and mechanical features-it performs well across disparate forward and inverse tasks. Based on an autoregressive attention-model, MeLM effectively represents a large multi-particle system consisting of hundreds of millions of neurons, where the interaction potentials are discovered through graph-forming self-attention mechanisms that are then used to identify relationships from emergent structures, while taking advantage of synergies discovered in the training data. We show that the model can solve complex degenerate mechanics design problems and determine novel material architectures across a range of hierarchical levels, providing an avenue for materials discovery and analysis. To illustrate the use case for broader possibilities, we outline a human-machine interactive MechGPT model, here trained on a set of 1,103 Wikipedia articles related to mechanics, showing how the general framework can be used not only to solve forward and inverse problems but in addition, for complex language tasks like summarization, generation of new research concepts, and knowledge extraction. Looking beyond the demonstrations reported in this paper, we discuss other opportunities in applied mechanics and general considerations about the use of large language models in modeling, design, and analysis that can span a broad spectrum of material properties from mechanical, thermal, optical, to electronic.

Energy-absorbing characteristics of hollow-cylindrical hierarchical honeycomb composite tubes under conditions of dynamic crushing

This paper presents an experimental and numerical study on the energy-absorbing characteristics of Biomimetic Multi-Cell Tubes (BMCTs), these being hollow-cylindrical-joint hierarchical honeycomb composite tubes inspired by the microstructural features of a beetle's forewing and geometrical features found in a spider's web. The BMCTs were fabricated using carbon fiber composites in optimized multi-tiered configurations. Low velocity crushing tests were conducted to characterize the load-displacement response, crashworthiness mechanisms, and energy absorption capacity of the BMCTs based on specific layer stacking sequences (LS). Additionally, the dynamic response of the BMCTs was modeled using the finite element analysis techniques.The predicted load-displacement relationships and failure modes show good agreement with the experimental results. Dynamic effects in the energy absorption characteristics of the tubes were evaluated. It is shown that the dynamic energy-absorbing capability of the BMCT-LS2 structure (Wall [±45/±30/±15]s Cylinder [±45/±30/±15/06]) is 6.5% higher than its quasi-static counterpart. In contrast, the SEA of BMCT-LS1 (Wall [+453/-453]s Cylinder [+453/-453/06]) is almost the same under both loading regimes. Finally, the quasi-static SEA of the plain circular tube is 13.8% lower than its dynamic counterpart. However, the SEA values of both BMCT-LS1 and BMCT-LS2 structures are 65% and 173% higher than the plain circular tubes, respectively.

Dynamic Characteristics and Effective Stiffness Properties of Sandwich Panels with Hierarchical Hexagonal Honeycomb.

The dynamic characteristics of sandwich panels with a hierarchical hexagonal honeycomb (SP-HHHs) show significant improvements due to their distinct hierarchy configurations. However, this also increases the complexity of structural analysis. To address this issue, the variational asymptotic method was utilized to homogenize the unit cell of the SP-HHH and obtain the equivalent stiffness, establishing a two-dimensional equivalent plate model (2D-EPM). The accuracy and effectiveness of the 2D-EPM were then verified through comparisons with the results from a detailed 3D FE model in terms of the free vibration and frequency- and time-domain forced vibration, as well as through local field recovery analysis at peak and trough times. Furthermore, the tailorability of the typical unit cell was utilized to perform a parametric analysis of the effects of the length and thickness ratios of the first-order hierarchy on the dynamic characteristics of the SP-HHH under periodic loading. The results reveal that the vertices serve as weak points in the SP-HHH, while the vertex cell pattern significantly influences the specific stiffness and stiffness characteristics of the panel. The SP-HHH with hexagonal vertex cells has superior specific stiffness compared to panels with circular and rectangular vertex cells, resulting in a more lightweight design and enhanced stiffness.

In‐Plane Crushing Behaviors of Hexagonal Honeycombs with Hollow‐Circle Joint under Different Compressive Velocities

The in‐plane crushing behaviors of hierarchical hexagonal honeycombs, structured by replacing every three‐wall vertex of both the conventional and reentrant hexagonal honeycombs with a small hollow‐circle, are investigated herein. The finite element (FE) models are first verified by an empirical formula from the literature and then further used to simulate the in‐plane crushing behaviors of the honeycombs under different compressive velocities. The deformation mode, plateau stress, and specific energy absorption (SEA) are studied based on the FE simulations. With respect to the conventional hierarchical honeycombs, the reentrant hierarchical honeycombs, in most instances, are found to exhibit higher plateau stress but lower SEA. It is remarkable that the hierarchical hexagonal honeycombs exhibit higher plateau stress and SEA than the basic hexagonal ones, which indicates that the hierarchical design is effective in improving both the impact resistance and energy absorption capabilities of the honeycombs.

High-Performance Li-S Batteries with a Minimum Shuttle Effect: Disproportionation of Dissolved Polysulfide to Elemental Sulfur Catalyzed by a Bifunctional Carbon Host.

A long cycle-life Li-S battery (both the coin cell and pouch cell) is reported with minimum shuttle effect. The performance was achieved with a bifunctional carbon material with three unique features. The carbon can catalyze the disproportionation of dissolved long-chain polysulfide ions to elemental sulfur; the carbon can ensure homogeneous precipitation of Li sulfide on the host carbon, and the carbon has a honeycomb porous structure, which can store sulfur better. All the features are demonstrated experimentally and reported in this paper. Few dissolved polysulfides are found by high-performance liquid chromatography in the electrolyte of the Li-S batteries during cycling, and only dissolved elemental sulfur is detected. The unique porous structure of the carbon made from raw silk is revealed by scanning electron microscopy. The N-containing functionalities that were introduced to carbon from the amino acids of raw silk can catalyze the disproportionation of the dissolved Sn2- to solid S8 at the cathode side, thereby mitigating the shuttle effect. In addition, the hierarchical honeycomb porous structures generated by a carbonization process can physically trap high-order lithium polysulfides and sustain the volume change of sulfur. With the synergistic effects of the unique structures and characteristics of the carbon prepared at 800 °C, the sulfur/carbon composite delivers a high reversible capacity of over 1000 mAh g-1 after 100 cycles with a sulfur content of 1.2 mg cm-2 in a pouch cell.

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.

Carbon-Fiber- and Nanodiamond-Reinforced PLA Hierarchical 3D-Printed Core Sandwich Structures

The aim of the present paper is to investigate the mechanical behavior of FFF 3D-printed specimens of polylactic acid (PLA), PLA reinforced with nanodiamonds (PLA/uDiamond) and PLA reinforced with carbon fibers (PLA/CF) under various experimental tests such as compressive and cyclic compressive tests, nanoindentation tests, as well as scanning electron microscopy tests (SEM). Furthermore, the current work aims to design and fabricate hierarchical honeycombs of the zeroth, first and second order using materials under investigation, and perform examination tests of their dynamic behavior. The mechanical behavior of hierarchical sandwich structures was determined by conducting experimental bending tests along with finite element analysis (FEA) simulations. The results reveal that the incorporation of nanodiamonds into the PLA matrix enhanced the elastic modulus, strength and hardness of the 3D-printed specimens. In addition, the second order of the PLA/uD hierarchical sandwich structure presented increased strength, elastic and flexural modulus in comparison with the zeroth and first hierarchies. Regarding the dynamic behavior, the second order of the PLA/uD honeycomb structure revealed the biggest increase in stiffness as compared to PLA nanocomposite filaments.

Out-of-plane crashworthiness of hierarchical cellular topology with different wall thicknesses in hierarchies

Hierarchical honeycomb is a topology presenting better weight-efficiency than the conventional honeycomb. However, the existing research are mainly conducted based on an assumption of uniform in-plane wall thickness. Rare studies consider the effect of different wall thicknesses in hierarchies. This paper investigates the out-of-plane crashworthiness of vertex hexagonal-based hierarchical honeycombs with non-uniform wall thickness in distinct hierarchies experimentally and theoretically. The coupons with parent material of 316L steel are obtained using Selective Laser Melting fabricating technique. The experimental results indicate that the first order honeycombs with uniform wall thickness experience a failure mechanism transition from local elastic buckling to local plastic buckling of cell walls at the critical density of 0.0772. A progressive folding wave can be identified when relative density is lower than 0.0386. At any edge length ratio, the plateau crushing stress increases monotonously as the increase of the wall thickness ratio, but not for the half wavelength. Both the half wavelength and maximum plateau crushing stresses are linearly related to relative density. For the first order honeycombs, the effect of edge length ratio is more considerable on the plateau crushing stress than the wall thickness ratio. The second order honeycombs exhibit higher half wavelengths and maximum plateau crushing stresses than the first order honeycombs owing to the more considerable cell wall constraint among the hierarchies. Compared to the hierarchical honeycombs with uniform wall thicknesses at relative densities of 0.005∼0.0386, the non-uniform wall thickness enhances the maximum plateau crushing stress significantly, especially at a low relative density, and the maximum improvements for first order and second order honeycombs are 71.5 and 48.6%, respectively. However, the absolute improvements are similar, averaging approximately 1.18 MPa. This work provides a foundation for developing ultralight hierarchical material candidates applied in passive protection equipment, such as aircrafts and vehicles.

Designing architected materials for mechanical compression via simulation, deep learning, and experimentation

Architected materials can achieve enhanced properties compared to their plain counterparts. Specific architecting serves as a powerful design lever to achieve targeted behavior without changing the base material. Thus, the connection between architected structure and resultant properties remains an open field of great interest to many fields, from aerospace to civil to automotive applications. Here, we focus on properties related to mechanical compression, and design hierarchical honeycomb structures to meet specific values of stiffness and compressive stress. To do so, we employ a combination of techniques in a singular workflow, starting with molecular dynamics simulation of the forward design problem, augmenting with data-driven artificial intelligence models to address the inverse design problem, and verifying the behavior of de novo structures with experimentation of additively manufactured samples. We thereby demonstrate an approach for architected design that is generalizable to multiple material properties and agnostic to the identity of the base material.

Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption.

A novel energy-absorbing structure, the Koch hierarchical honeycomb, which combines the Koch geometry with a conventional honeycomb structure, is proposed in this work. Adopting a hierarchical design concept using Koch has improved the novel structure more than the honeycomb. The mechanical properties of this novel structure under impact loading are studied by finite element simulation and compared with the conventional honeycomb structure. To effectively verify the reliability of the simulation analysis, quasi-static compression experiments were conducted on 3D-printed specimens. The results of the study showed that the first-order Koch hierarchical honeycomb structure increased the specific energy absorption by 27.52% compared to the conventional honeycomb structure. Furthermore, the highest specific energy absorption can be obtained by increasing the hierarchical order to 2. Moreover, the energy absorption of triangular and square hierarchies can be significantly increased. All achievements in this study provide significant guidelines in the reinforcement design of lightweight structures.

Effect of Hierarchical Geometries Matching on the Crashworthiness of Honeycomb

Structural hierarchy has become a popular technique to improve the crashworthiness of engineering structures. A study is conducted to explore the interaction between hierarchical geometries and determine the optimum honeycomb configuration that improves crashworthiness. Nine distinct second‐order vertex‐based hierarchical honeycombs are constructed by iteratively replacing the vertices of a square‐based honeycomb with squares, circles, and octagons. Validated finite element models are then established to investigate the out‐of‐plane crashworthiness performance. Subsequently, the effect of the hierarchical geometry combinations and cell length ratios on the crashworthiness performance of the nine honeycombs is studied. The study showed that the second‐order hierarchical honeycomb exhibited superior crashworthiness performance under the same relative density compared to the regular and first‐order hierarchical square honeycombs. The study determined that the circle is a suitable matching geometry in the first‐ and second‐order hierarchies for improving the crashworthiness of a square‐based honeycomb. Using Complex Proportional Assessment, the Square‐Circle‐Circle ranked as the optimum structure for crashworthiness application.

Hierarchical re-entrant honeycomb metamaterial for energy absorption and vibration insulation

A novel hierarchical re-entrant honeycomb metamaterial is proposed by integrating the re-entrant honeycomb (RH) with square unit cell and named as square re-entrant honeycomb (SRH). The novel hierarchical re-entrant honeycomb can not only improve energy absorption capacity but also present better vibration insulation compared with traditional RH structure. Dynamic crushing behaviors of the SRH structures are investigated theoretically and numerically. The theoretical plateau stress is in good agreement with the numerical plateau stress. Meanwhile, the deformation modes and energy absorption capacity of RH and square re-entrant honeycombs (SRHs) are compared under different impact velocities. The results show that the plateau stress and the specific energy absorption (SEA) of SRHs is higher than RH. Moreover, the vibration isolation capability of the SRHs is studied using finite element analysis. In particular, the introduction of square unit cells expand the band gap, especially in the low frequency range. By adjusting the size of oscillators, the starting and stopping frequencies of band gaps are lower effectively and the number of band gaps is increased. The results indicate that the introduction of the mass inclusions can improve the band gap characteristics of the SRH, which produce local resonance effect and the local resonance type band gap. It also appears multiple band gaps at the same time. In addition, the introduction of the mass inclusions also improves the SEA of the SRH under high-velocity crushing. This work may benefit structural vibration isolation and protection design, which provides a new thought for design and development of advanced multi-functional composite structures and materials in the engineering.

Fabrication, design, and optimization of hierarchical composite Kagome honeycomb sandwich structure under uniaxial compression

Abstract In this study, a hierarchical composite Kagome honeycomb sandwich (HCKHS) structure was manufactured based on the interlocking method, and its uniaxial compression performance was explored. Through experiments, the compressive strength, stiffness, energy absorption, and failure process of HCKHS specimens of seven different sizes were determined and compared. Mechanical analytical models were established, and the variation trend in the specific strength was predicted and compared with those of other advanced sandwich structures. The size effect of the HCKHS specimens was analyzed. The influence of a single variable on the core modulus, failure strength, and failure modes was discussed, and failure mechanism maps were drawn. The structure was optimized based on the maximum specific strength and engineering application, and the optimal size design ratio was obtained. The results showed that the HCKHS specimens exhibited excellent compressive properties with a convenient manufacturing process, making them suitable for lightweight applications in engineering. The optimization ideas presented herein are also applicable to other two-dimensional hierarchical or normal composite honeycomb sandwich structures with diamond, triangular, and hexagonal shapes.