Hierarchical Tubes Research Articles

Design and study of crashworthiness for square vicsek fractal hierarchical multicellular tubes under axial compression

Through extensive examination of thin-walled structures, the efficacy of enhancing the crashworthiness of thin-walled tubes via layered structures has been confirmed. In this study, we introduce a novel design called the square Vicsek fractal hierarchical multicellular tube (SVFHMT), which integrates principles from fractal science, specifically Vicsek fractals. Unlike conventional layered structures that align along a single direction, our design incorporates layers evenly distributed at five positions throughout the structure, resulting in a more uniform material distribution compared to traditional layering methods. In this paper, the verified finite element model is used to analyze the crashworthiness of the structure, and the effects of levels, wall thickness, wall thickness ratio of different levels and height to diameter ratio on the crashworthiness of the structure are discussed. The mean crushing force (MCF) of SVFHMT is predicted by Simplified Super Folding Element theory. Our findings highlight the significant influence of layering, wall thickness, and ratios of wall thickness between layers on the crashworthiness of the structure. Specifically, for structures of equal mass, the energy absorption of second-order SVFHMTs and third-order SVFHMTs demonstrates substantial improvements compared to square nine-cell tubes, with increases of 51.05% and 91.70%, respectively. Moreover, when maintaining equal mass for second-order SVFHMTs with differing ratios of wall thickness between layers, specific energy absorption ranges from 15.69 kJ/kg to 21.29 kJ/kg. Notably, the maximum error between theoretical and simulated values of the mean crushing force for each order of SVFHMT is only 7.34%. This underscores the effectiveness of our novel layer design strategy, which diverges significantly from conventional approaches and offers valuable insights for advancing layered structures further.

Oxygen vacancy-enriched WO3 hierarchical tubes inherited from pine needle for the enhanced detection to ppb-level hydrazine at near room temperature

It is of great importance to develop low-temperature gas sensors for monitoring hydrazine (N2H4) with high toxicity and easy explosion. However, how to highly sense its ppb-level concentration remains challenging. For this purpose, biomorphic WO3 structure replicated by small-size nanoparticles was simply prepared though air calcinations of tungsten salt-immersed pine needle (PN) template. The mesoporous WO3-PN tubes with pore volume of 0.096 cc·g−1 had relatively large specific surface area (38 m2·g−1) for exposing more active sites, as well as rich oxygen vacancies (g = 2.005) and small band gap for promoting electron migration. With the assistance of W6+ Lewis acid catalytic sites, such unique multilevel structure facilitated the rapid transport and adsorption of basic N2H4 molecules, as well as their chemical reactions with high content of oxygen species (37.4 %) in sensing layer, thus first achieving the highly sensitive detection of ppb-level N2H4 gas at near room temperature. At 50 °C, WO3-PN sensor exhibited ultra-high response (S = 307), fast response time (Tres = 16 s) for 1 ppm N2H4, and low actual detection concentration (5 ppb). These key indicators were remarkably superior to reported semiconductor gas sensors. In addition, the enhanced low-temperature sensing mechanism of WO3-PN sensor was explored by means of analytical tests and DFT calculations.

Crashworthiness of hierarchical multi-cell square tubes under axial and oblique crushing

Hierarchical tubes have been proved to be excellent energy absorbers under axial compression. However, there are limited studies exploring their oblique crushing performance. Therefore, the oblique crushing characteristics of hierarchical tubes, bio-inspired hierarchical multi-cell square tubes (BHMS), hierarchical multi-cell square tubes (HMSA and HMSB), have been numerically studied. The influencing factors of loading angle and hierarchical order on deformation modes, force-displacement curves, and energy absorption (EA) behaviors were explored. It is found that BHMS tubes present the superior crushing performance among these hierarchical square tubes. Moreover, BHMS tubes display the excellent crushing characteristics in comparison with single square tubes. Specifically, the specific EA of BHMS-3 tubes is 213%, 212%, 66%, and 42% greater than that of single square tubes at loading angles of 0°, 10°, 20°, and 30°. The findings demonstrate the priority of hierarchical square tubes under oblique crushing, and provide the reference and insight for the design of energy absorbers.

Crashworthiness study of double square gradient hierarchical tubes

A new type of bi-double square gradient hierarchical tube (DSGHT) is proposed, and its crashworthiness under consistent wall thickness is analyzed. The results show that the energy absorption (EA), specific energy absorption (SEA), and crush force efficiency (CFE) of DSGHT3 are increased by 1305.14%, 430.14%, and 469.50%, respectively, compared to DSGHT0. The combination of double square tubes and gradient laminar design effectively enhances the crashworthiness of the structure. A parametric study indicates that increasing wall thickness significantly improves crashworthiness, with EA, SEA, and CFE improvements of 805.75%, 125.83%, and 126.83%, respectively, at a wall thickness of 0.8 mm compared to 0.2 mm. However, the effect of wall thickness gradient distribution on structural crashworthiness is minimal. Conversely, the ratio of the inner to outer square tube edge length (δ) significantly impacts crashworthiness; SEA and CFE increase by 37.77% and 37.35%, respectively, when δ is 6/12 compared to 8/12. Finally, DSGHT3 was compared to other hierarchical, tree-shaped fractal structures, and it demonstrated superior crashworthiness. Specifically, DSGHT3 has 35.32% and 34.29% higher SEA and CFE, respectively, compared with MSTL2-2.

Crashworthiness analysis of novel bidirectional gradient hierarchical double tubes inspired by the leaf tissue

Inspired by the cross-sectional view of leaf tissue, a bidirectional gradient hierarchical double tube (BGHDT) was proposed and its crashworthiness performance was investigated by finite element simulation. The results indicate that the proposed BGHDT has better energy absorption capacity than the conventional hexagon tube under the same mass condition. The folding wavelength of BGHDT is shorter than that of conventional hexagonal tubes, resulting in a larger number of folds. Compared with conventional hexagon tubes, the energy absorption of BGHDT with 3rd hierarchical level increases by 139.39% and its peak crush force (PCF) decreases by 16.29% at the same mass. Finally, the effects of wall thickness and the number of connecting units on the crashworthiness performance of BGHDT are systematically studied.

Biotemplate synthesis of graphitic carbon-doped ZnO tube bundles rich in oxygen vacancies for dual-sensing of NO2/H2S at different temperatures

How to fabricate one chemiresistive sensor for highly dual-selective detection of hazardous NO2 and H2S gases is a challenge owing to the fact that the great majority of gas sensors were designed to monitor only a given harmful gas. For the aim of portable practicality and internet of things, based on green and sustainable concept, natural poplar branches were utilized as template and simply soaked in zinc nitrate solution. Subsequently, the immersed biotemplates underwent air calcination to controllably reproduce two biomorphic ZnO-based materials. Among, the hierarchical tubes (GC/ZnO) prepared by calcination at 450 °C are interconnected by 5.68 wt% in-situ graphitic carbon (GC) and uniform nanoparticles, which possess small mesopores, large specific surface area and massive oxygen vacancies. Such distinctive microstructure not only facilitates rapid gas diffusion into sensing layer and modulates the state of adsorbed oxygen species, but also exposes more active sensing units and promotes surface chemical reactions, thus realizing a portable gas sensor for highly sensing and dual-selective detection of NO2 and H2S. At lower 92 °C or 133 °C, the GC/ZnO sensor exhibits response values of 203 and 65.5 for 10 ppm NO2 or H2S gases, respectively. Meanwhile, it possesses reversible response-recovery, low detection limit, good moisture tolerance and stability during 60 days. In addition, the temperature-controlled dual-response mechanism is also analyzed.

Crashworthiness Analysis of Self-Similar Nested Hierarchical Hexagonal Tubes

To enhance the crashworthiness of thin-walled structures, this study proposes a self-similar nested hierarchical hexagonal tube. This innovative design incorporates the hierarchical technique into the structural configuration of hexagonal thin-walled tubes. Numerical analysis, conducted using a validated finite element model, reveals that the proposed self-similar nested hierarchical hexagonal tube (SNHHT) significantly enhances energy absorption compared to traditional hexagonal tubes, maintaining consistent wall thickness and mass conditions. Particularly noteworthy is the improvement in energy absorption indexes under the same mass condition, with SNHHT-4 demonstrating enhancements of up to 76.45% and 86.84% in energy absorption and crushing force efficiency, respectively, while concurrently achieving a 4.11% reduction in initial peak crash force. Subsequently, a parametric study exploring wall thickness, shape factor, and various rib thicknesses was performed to investigate structural crashworthiness. Finally, employing the simplified super-folded element method, the theoretical formulation of mean crushing force was derived, and its accuracy was validated through numerical simulations.

Non-dimensional parameters governing the crashworthy performance of tubes with complex cross-sections

The crashworthiness of thin-walled tubes with various designs under axial compression has been extensively investigated. Despite this, the parameters that govern the performance of tubes and can be applied across different cross-sectional topologies have not hitherto been available. In this paper, twenty types of thin-walled tubes with different cross-sectional shapes (e.g., multi-celled, bi-tubular, and hierarchical square, hexagonal and circular tubes) have been numerically simulated and theoretically analysed. All the tubes are made from identical material and possess identical apparent cross-sectional area, height and mass. Six indicators are employed to characterise the crashworthiness performance of the tubes. Two novel non-dimensional indices, the geometric complexity index (RG) which is the ratio of the total length of solid segments in the cross-section of a tube to that of the square tube, and the topological index (RT) which is the non-dimensional coefficient in the expression of plastic energy dissipation closely related to the types and numbers of the wall junctions in cross-section, are identified for the first time. Both the indices RG and RT are used in a regression analysis of the indicators that characterise the crashworthiness of the tubes. The results reveal that the crashworthiness indicators of the tubes, the mean crushing force (MCF), the specific energy absorption (SEA) and the effectiveness of energy absorption (EEA) do not exclusively vary with RG. Instead, MCF, SEA and EEA are all properly fitted by linear relations with a single non-dimensional parameter ω, which is a simple function of RG and RT, i.e., ω=RT/RG. Increasing the magnitude of ω ultimately improves the crashworthiness of tubes, including enhanced specific energy absorption, effectiveness of energy absorption and crushing force efficiency, while reducing the force fluctuation during the crushing process. Of the tubes studied, the edge-based hierarchical circular tube (EH_C) has the highest SEA of 22.17 J/g, which is 133%, 60% and 41% larger than that of single-celled square, hexagonal and circular tubes, respectively.

Energy absorption characteristics of corrugated hexagonal gradient hierarchical tube

Energy absorption characteristics of corrugated hexagonal gradient hierarchical tube

Enhanced redox kinetics in hierarchical tubular FeSe2 by incorporating Se quantum dots towards high-performance sodium-ion batteries

Metal selenides have emerged as promising Na-storage anode materials owing to their substantial theoretical capacity and high cost-effectiveness. However, the application of metal selenides is hindered by inferior electronic conductivity, huge volume variation, and sluggish kinetics of ionic migration. In response to these challenges, herein, a hierarchical hollow tube consisting of FeSe2 nanosheets and Se quantum dots anchored within a carbon skeleton (HT-FeSe2/Se/C) is strategically engineered and synthesized. The most remarkable feature of HT-FeSe2/Se/C is the introduction of Se quantum dots, which could lead to high electron density near the Fermi level and significantly enhance the overall charge transfer capability of the electrode. Moreover, the distinctive hollow tubular structure enveloped by the carbon skeleton endows the HT-FeSe2/Se/C anode with robust structural stability and fast surface-controlled Na-storage kinetics. Consequently, the as-synthesized HT-FeSe2/Se/C demonstrates a reversible capacity of 253.5 mAh/g at a current density of 5 A/g and a high specific capacity of 343.9 mAh/g at 1 A/g after 100 cycles in sodium-ion batteries (SIBs). Furthermore, a full cell is assembled with HT-FeSe2/Se/C as the anode, and a vanadium-based cathode (Na3V2(PO4)2O2F), showcasing a high specific capacity of 118.1 mAh/g at 2 A/g. The excellent performance of HT-FeSe2/Se/C may hint at future material design strategies and advance the development and application of SIBs.

Energy Absorption Characteristic of Biomimetic Gradient Hierarchical Multicellular Tubes Under Axial Impact

This paper introduces a biomimetic gradient hierarchical multicellular structure consisting of two tree-like fractal variants: one based on vertex connections (HCV) and the other based on wall connections (HCW). We investigate their mechanical behavior and deformation through numerical simulations. Our findings reveal that, irrespective of whether they have the same wall thickness or mass, second-order and third-order structures exhibit superior energy absorption capacity (EA) and crushing force efficiency (CFE) compared to first-order structures, resulting in significantly enhanced crashworthiness performance. In the case of HCV structures with identical wall thickness, the third-order structure outperforms the first-order structure by 79.73% in specific energy absorption (SEA) and by 38.51% in CFE. Similarly, for HCW structures, the third-order variant surpasses the first-order one by 45.57% in SEA and 28.39% in CFE. We also conduct a parametric study, exploring the influence of inner circle diameter, fractal coefficient, and fractal angle on the crashworthiness of biomimetic gradient hierarchical multicellular structures. We identify the optimal fractal coefficient and inner diameter distribution range for HCV when the fractal angle is 60°. Lastly, we compare these structures with traditional multicellular tubes, demonstrating that biomimetic gradient hierarchical multicellular tubes achieve up to 50.34% higher SEA and 55.13% higher CFE. The results of this study offer valuable design insights for developing lightweight and efficient energy-absorbing structures.

Crashworthiness properties of square hierarchical multicellular tube under axial impact

A new square hierarchical multicellular tube design is introduced, and the crashworthiness of various square hierarchical multicellular tubes with identical wall thickness and mass is systematically analyzed using validated numerical models. The study explores the impact of parameters such as layer level, wall thickness, and impact load angle on the structure’s impact resistance. Additionally, the impact resistance of square hierarchical multicellular tubes is compared to that of conventional square multicellular tubes with the same wall thickness. The findings reveal that the proposed square hierarchical multicellular tube effectively mitigates peak crushing forces and enhances crushing force efficiency under the same mass. Specifically, the third-order square hierarchical multicellular (SHMT-3) tube exhibits a 48.23% increase in specific energy absorption and a 75.14% improvement in crushing force efficiency. Notably, the peak crushing force decreases by 15.40% compared to that of the square tube. Under identical wall thickness, the crush force efficiency of SHMT-3 reaches 89.51%, marking a 125.21% improvement compared to square tube. Overall, the comprehensive crashworthiness of square hierarchical multicellular tubes surpasses that of traditional square multicellular tubes. These results contribute valuable insights for innovatively designing new hierarchical multicellular tube structures.

Axial crushing and energy absorption of graded hierarchical hexagonal tubes

The concept of both hierarchy and gradient are incorporated into thin-walled hexagonal tubes for a configuration with optimum crashworthiness and energy absorption. Graded hierarchical hexagonal (GHH) tubes are developed by replacing the corners of an original hexagonal tube with a series of micro hexagonal cells. The total net cross-sectional area as well as the mass are kept the same for all the GHH tubes. The axial crushing behavior of the GHH tubes is investigated in terms of deformation modes, crushing forces and energy absorption. Theoretical solutions are also derived to predict the mean crushing forces (MCFs) of the GHH tubes. Two deformation modes have been identified, a locally layer-by-layer folding deformation (Mode-L) and a globally buckling-like deformation (Mode-G). The hierarchical and graded parameters have significant but quite different influences on the crushing behavior of GHH tubes. The MCF and the specific energy absorption (SEA) can be significantly improved with reasonably hierarchical and graded arrangements, while the initial peak force (PF) remains almost constant.

Energy absorption characteristics of a novel hierarchical cross tube under axial impact loading

Energy absorption characteristics of a novel hierarchical cross tube under axial impact loading

Crushing analysis of square gradient hierarchical multicellular tubes

Inspired by tree fractals, a novel square gradient hierarchical multicellular tube (SGHMT) is proposed, and a finite element (FE) model of the structure is constructed using Abaqus/Explicit. The accuracy of the FE numerical model was verified using experiments, and the energy absorption characteristics of the structure under axial impact were analyzed. The results show that the high-level SGHMTs have higher energy absorption capacity and impact force efficiency (CFE) compared with the low-level SGHMTs for both the same wall thickness and the same mass, and crashworthiness is greatly improved. The energy absorption (EA) and CFE of SGHMT-3 are 11.39 and 4.47 times higher than those of SGHMT-0 under the same wall thickness condition, respectively. The EA and CFE of SGHMT-3 are 2.15 and 2.28 times higher than those of SGHMT-0, respectively, under the same mass condition. On this basis, further geometrical parameter analysis was carried out, and it was found that the structural parameters (wall thickness, hierarchy, and shape scale factor γ 1 , γ 2 ) had a significant effect on the crashworthiness of the square gradient hierarchical multicellular tubes. Finally, a comparative study with other multicellular tubes was carried out to demonstrate the superiority of the proposed square gradient hierarchical multicellular tubes compared with other multicellular tubes.

Crashworthiness of multicellular tubes with tree-like fractal hierarchical structure under axial impact

A new type of tree-like fractal hierarchical multicellular tubes (TFHMTs) is proposed, and the crashworthiness of the structure under axial impact is studied by using a verified Abaqus/Explicit finite element model. The research results show that the TFHMTs have better energy absorption capacity than single-cell tubes of the same thickness and mass under the same conditions. The wrinkle wavelength of the third-order TFHMTs is significantly shorter than that of the single-cell tubes, resulting in more folds. For the same mass, the proposed third-order TFHMTs has a lower peak crush force than a single-cell tube. Moreover, the specific energy absorption is up to 49.40% greater than that of the single-cell tube, and the crush force efficiency is up to 66.18%. Subsequent parameterization research on the layer ratio coefficient and wall thickness on TFHMTs was systematically conducted. Finally, a comparative analysis with typical hierarchical multicellular tubes was performed.

Self-sacrifice-template epitaxial growth of hierarchical MnO2@NiCo2O4 heterojunction electrode for high-performance asymmetric supercapacitor

Constructing three-dimensional (3D) hierarchical bimetallic pseudocapacitive materials with abundant opening channel and heterojunction structures is rather promising but still challenging for high-performance supercapacitors. Herein, a self-sacrifice-template epitaxial growth strategy was proposed for the first time to construct 3D hierarchical bimetallic pseudocapacitive material. By using this strategy, NiCo2O4 nanowires (NiCo2O4NW) arrayed randomly to form a porous shell via in-situ epitaxial growth fully enclosing a MnO2 tube core, forming multiple transport channels and nano-heterojunctions between MnO2 and NiCo2O4NW, which facilitates electron transfer, i.e. exhibiting high electronic conductivity than any single component. As a result of the self-sacrifice-template epitaxial growth method, special hollow tectorum-like 3D hierarchical structure with considerable inter-nanowire space and hollow interior space enables easy access of electrolyte to NiCo2O4NW surface and MnO2 core, thereby resulting in highly exposed redox active sites of MnO2 core and NiCo2O4NW shell for energy storage. Comprehensive evaluations confirmed MnO2@NiCo2O4NW was a supercapacitor electrode candidate, delivering a superior energy density of 106.37 Wh kg−1. Such performance can be ascribed to the synergistic coupling effect of 3D hierarchical tube and nano-heterojunction structures. The proposed self-sacrifice-template epitaxial growth strategy provides important guidance for designing high-performance energy storage materials.

Crashworthiness analysis of hexagonal hierarchical gradient tubes with axial variable thickness inspired by tree fractal structure

Inspired by the tree fractal structure, a novel hexagonal hierarchical gradient tube with axial variable thickness (HHGAVT) is proposed and its crashworthiness performances are systematically investigated. Results show that when the axial variation coefficient of wall thickness k > 0, the peak crushing force (PCF) of HHGAVT will significantly decrease meanwhile the energy absorption maintains at a high level compared with the referenced structures under the same mass. When k > 0, the PCF and CFE of HHGAVT have absolute advantage compared with the uniform wall thickness tube. The crashworthiness performance can further increase by rational designing the distance factor δ.

Axial compression of multi-cell hexagonal tubes with novel hierarchical architectures: Numerical and theoretical analyses

The architecture of hierarchy is extensively used in the construction of energy absorbers due to its super mechanical performance. Two new types of hierarchical multi-cell hexagonal tubes were constructed in this study based on different hierarchical architectures. Numerical models of both two types of tubes were developed and employed to study their crashworthiness under axial compression. It is found that the peak crushing force (PCF) of the proposed tubes is smaller than that of single hexagonal tubes with the same mass, demonstrating the merit of hierarchical tubes to minimize sudden injury. The mean crushing force (MCF), energy absorption (EA) and specific energy absorption (SEA) of the proposed tubes increase with the increase of wall thickness and hierarchical order. The SEA of the 3rd order is up to over 200% that of single hexagonal tubes with the same mass. In addition, the second type of proposed hierarchical tubes with hierarchical cells relatively uniformly distributed in the tubes display slightly greater SEA than the first type of proposed hierarchical tubes with hierarchical cells along the edges. Theoretical model for the first type of hierarchical tubes was further developed and verified. The theoretical analysis and numerical simulation agree well.

Biotemplate-assisted synthesis of CuO hierarchical tubes for highly chemiresistive detection of dimethylamine at room temperature

The fabrication of low-temperature metal oxide-based sensors with highly sensitive to carcinogenic organic-amines remains challenging. Herein, a biomorphic CuO-5 material was synthesized by simply immersing mulberry twig slices in copper nitrate solution and calcining the precursors in air at 500 ℃. Its multistage tubes are assembled from well-crystallized nanoparticles, and possess uniform mesopores and abundant oxygen vacancies. These microstructural factors facilitate the rapid diffusion of gas molecules to sensing layer, and improve the conductivity of CuO material, as well as the content of active sites and surface adsorbed oxygen species. In particular, under the synergy of adsorption and catalysis of the suspended bonds for surface Cu2+ ions, this material achieves the high sensing and selective detection of trace dimethylamine (DMA) at room temperature for the first time. At 25 °C, CuO-5 sensor reaches a response value of 35.9–50 ppm DMA, which is 8.3 times larger than that of template-free CuO-0 sample. Meanwhile, the sensor also has good response-recovery reproducibility, low detection limit, and satisfactory moisture resistance and stability. In addition, the mechanism for enhanced sensing of DMA at room temperature is discussed in detail.