Multicellular Tubes Research Articles

Crash resistance analysis and optimization of sponge like thin-walled pipes under multiple working conditions

The crashworthiness of bionic thin-walled structures has been the subject of considerable research interest. In this article, we emulate the bi-diagonal skeletal structure of deep-sea glass sponges and construct sponge-like multicellular thin-walled tubes (SLMTT) with a parameterized ratio of the number of two distinct single-celled organisms (CSS I and CSS II). Thin-walled sponge-like tubes of varying dimensions were manufactured using selective laser melting (SLM) technology. The crashworthiness of these structures was evaluated under axial compression, transverse compression, and three-point bending conditions through experimental and computational approaches, including parametric analyses of the inner and outer wall thicknesses. The results show that SLMTT I has better crashworthiness under the three working conditions, and the SEA of BLMESI is 40.9 and 26.13% higher than that of BLMESII. under transverse compression and three-point bending conditions, respectively. Finally, a multi-objective optimization design of SLMTT I under multiple operating conditions is carried out by the second generation of Non-dominated Sorting Genetic Algorithm (NSGA-II) with the aim of obtaining the ideal structure with maximum specific energy absorption and minimum initial peak crushing force. This study offers novel insights into the design of bionic energy-absorbing structures under diverse operational scenarios.

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.

A study of crashworthiness performance in thin‐walled multi‐cell tubes 3D‐printed from different polymers

AbstractMulticellular, thin‐walled impact tubes have been intensely studied and used in various engineering fields in recent years due to their lightweight, high performance, ease of application, superior energy absorption, and stable deformation characteristics. In this study, energy absorption, crashworthiness performances, and deformation properties of thin‐walled structures manufactured from polylactic acid (PLA+) and acrylonitrile butadiene styrene (ABS) using fused deposition modeling (FDM) technology were compared under quasi‐static axial compression. Thin‐walled structures consist of multicellular tubes connected by concentric corner‐edge connections with square and hexagonal cross‐sections. Experimental testing outcomes indicate that the energy absorption capacity increases with increasing the number of corners in multicellular structures. The tubes with square wall‐to‐wall (S‐WW) and hexagonal wall‐to‐wall (H‐WW) cross‐sections exhibit superior crashworthiness performance compared to other cross‐sections. Based on the experimental results, the absorbed energy by WW patterned PLA+ square tubes are 19%, 7%, and 46% more than that of wall‐to‐corner (WC), corner‐to‐wall (CW), and corner‐to‐corner (CC) patterned tubes, respectively, while it is 11%, 19%, and 80% more in hexagonal cross‐section tubes, respectively. This study provides an informative reference for easier applicability of multicellular energy‐absorbing structures with 3D‐print and the design of corner‐edge connections of internal connections in multicellular structures.

Sensitivity and Optimization Analysis of Torsional Behavior in Multicellular Thin-Walled Tubes

Multicellular thin-walled tubes are widely used due to their lightweight, economical design, and superior shear and torsional performance. Their design is sometimes governed by the available materials and the required dimensions. The current study uses advanced sensitivity analysis with meta-modeling tools to understand how different geometric and mechanical factors affect the torsional performance of multicellular thin-walled tubes. The geometric factors include the length, thickness, and width of the beams, while the mechanical properties involve the shear modulus. Variance-based sensitivity analysis is used to assess how variations in these factors impact the rate of twist, torsional stiffness, and shear stress. The interconnected relations between input parameters are exploited for optimal design and superior performance. The results revealed that for a three-celled tube, thick horizontal interior elements with thin deep vertical elements and thin exterior elements provide an optimal design when the cross-sectional area is constrained. This finding, combined with varying the geometrical and material properties, results in an optimal design using CFRP composites when constrained by minimizing the total weight and superior torsional performance. The analysis can be extended to include other constraint(s), but changing the design constraints might change the optimal design. Doi: 10.28991/CEJ-2024-010-09-09 Full Text: PDF

Crashworthiness analysis of bio-inspired hierarchical multi-cell circular tubes under axial crushing

Drawing inspiration from nature’s hierarchical organization, we propose a novel bio-inspired hierarchical multi-cellular circular tubes (BHMC) with a fractal structure. Using an experimentally validated LS-DYNA finite element model, we investigated the impact resistance of this structure under axial loading. Numerical analysis was conducted to explore the energy absorption performance of BHMC tubes with varying numbers of branches, fractal orders, and tube masses. The numerical findings indicate that specific energy absorption (SEA) increases with higher numbers of fractal orders. Specifically, the SEA of 2nd order BHMC tubes surpasses that of conventional multicellular circular and single-layer tubes by approximately 35.07% and 17.10%, respectively. Optimal performance is achieved with the proposed structure featuring tree branching (N = 6) and 2nd order fractal characteristics, yielding the highest specific absorption energy across different parameters. These results offer valuable insights for designing multicellular bilayer tubes with superior energy absorption efficiency, providing an effective guideline for structural optimization.

Mechanochemical patterning and wave propagation in multicellular tubes

Multicellular tubes are fundamental tissues for transporting and distributing liquids and gases in living organisms. Although the molecular, cellular and mechanical aspects in tube formation have been addressed experimentally, how these factors are coupled to control tube patterning and dynamics at the tissue level remains incompletely understood. Here, we propose a three-dimensional (3D) vertex model that incorporates a mechanochemical feedback loop correlating cell deformation and actomyosin signaling pathway to probe the morphodynamics of multicellular tubes. We show that diverse patterns, including ring, helix, double helix, and labyrinth, are generated in tubes through pitchfork bifurcation, where spatial fluctuations of both biochemical signaling and 3D cell deformation are remarkably involved. The mechanochemical feedback loop enables cell oscillations via Hopf bifurcation, which induces the mechanical and chemical patterns to propagate successively as either traveling or pulse waves while their spatial configurations are maintained, strikingly distinct from the classical Turing instability. Our simulations, together with stability analysis of a minimal model, uncover the essential role of mechanochemical principles in sculpting biological tubes.

Crashworthiness analysis of okra biomimetic corrugated multi-cellular structure

This study introduce an innovation okra biomimetic corrugated multi-cellular Taper tube (OBCMT) designed for the energy absorption, drawing inspiration from the okra, which comprises a Fourier curve wall and X-shaped ribs. Validation is accomplished through quasi-static crushing experiments, ensuring the accuracy of the finite element simulation model. Numerical simulations investigate the influence of critical interaction structural parameters on the performance of the OBCMT, and a theoretical model based on the super folding theory is deduced to predict the mean crushing force of the OBCMT. The result show that the specific energy absorption(SEA) exhibited the heightened sensitivity to the variation of C_height under the same C_R, approximately reached 8.36 kJ/kg which increased by 43.2 % compared to the minimum value in the identical group. Simultaneously, the structure parameters of height coefficient(C_height) and radiu coefficient(C_R) have the most significant impact on the deformation mode of OBCMT. Comparative analysis demonstrates that the OBCMT exhibits the extraordinal crashworthiness compared to the contemporary typical energy absorption structures under identical mass, with the SEA reaching 21.8 kJ/kg. This represents approximately 290.7 %, 205.7 %, 187.9 %, 189.6 %, and 174.4 % relative to the six-cell hexagonal tube (SHT), quadruple-cell circular tube (QCT), multi-cell bicircular tube (MBT), five-cell square tube (FST), and quadruple-cell square tube II (QST_Ⅱ), respectively. This research significantly advances the development of high-performance bionic energy-absorbing structures for crash applications and enhances our comprehension of the biomimetic engineering.

Bionic design of thin-walled bilinear tubes with excellent crashworthiness inspired by glass sponge structures

In order to enhance energy absorption, this study draws inspiration from the diagonal bilinear robust square lattice structure found in deep-sea glass sponges, proposing a design for thin-walled structures with superior folding capabilities and high strength-to-weight ratio. Firstly, the crashworthiness of bionic glass sponge tube (BGSTO) is compared with that of equal-wall-thickness equal-mass four-X tube through both experiments and simulations, and it is obtained that the specific energy absorption of BGSTO is increased by 78.64%. And the crashworthiness of BGSTO is also most significant compared to that of multicellular tubes with the similar number of crystalline cells. Additionally, we found that the double-line spacing of the glass sponge can be freely adjusted without changing the material amount. Therefore, based on BGSTO, we designed two other double-line structures, BGSTA and BGSTB. Then with equal wall thickness and mass as a prerequisite, this study proceeds to design and compare the energy absorption properties of three bilinear thin-walled tubes in both axial and lateral cases. The deformation modes and crashworthiness of the three types of tubes with variable bilinear spacing (βO/A/B ) are comparatively analysed. The improved complex proportional assessment (COPRAS) synthesis decision is used to obtain that BGSTO exhibits superior crashworthiness over the remaining two kinds of tubes. Finally, a surrogate model is established to perform multi-objective optimization on the optimal bilinear configuration BGSTO selected by the COPRAS method.

On the crashworthiness of novel right-angle fractal gradient hierarchical multi-cell bi-tubular tubes under axial loading

To achieve a thin-walled structure with enhanced crashworthiness, inspired by tree fractals, a new right-angle fractal of gradient hierarchical multi-cellular square bi-tubular tube (RFGHMBT) was proposed. Its energy absorption characteristics under axial impact were systematically studied using numerical simulation methods. The results show that, for both the same wall thickness and the same mass, the high-level hierarchical multicellular bi-tubular tube has a higher energy absorption capacity and crushing force efficiency compared to the low-level hierarchical multicellular bi-tubular tube. This substantially improves crashworthiness performance. Under the condition of the same wall thickness, the specific energy absorption (SEA) and crushing force efficiency (CFE) of the third-order RFGHMBT improved by 270% and 244.13%, respectively, compared to the 0th-order. The energy absorption (EA) and CFE under the same mass condition are 1.96 times and 2.20 times higher than those of the 0th-order RFGHMBT, respectively. Further geometric parameter analysis revealed that structural parameters (inner measured square tube side length 2 l, shape scale factors γ1, γ2, wall thickness t) significantly affect the crashworthiness of the square gradient-layered multicellular bi-tubular tubes. Additionally, a comparative study with other multicellular tubes demonstrated the superiority of the proposed square gradient-layered multicellular bi-tubular tubes. The findings of this study offer an effective design concept for developing lightweight and efficient energy absorbers.

Crashworthiness Analysis of Bio-Inspired Fractal Plant Stems Multi-Cell Circular Tubes

A novel structure resembling plant stems, termed bio-inspired fractal plant stems multi-cellular circular tubes (BFPMC), was developed by incorporating fractal plant stem characteristics into smaller circular tubes within larger ones. The crashworthiness of this structure under axial impact was investigated using a validated LS-DYNA finite element model. The energy absorption performance of BFPMC tubes, varying in the number of branches, fractal orders, and inner circular diameters, was numerically studied. The numerical findings reveal a 19.27% increase in specific energy absorption (SEA) for BFPMC with [Formula: see text][Formula: see text]mm compared to [Formula: see text][Formula: see text]mm, indicating that filling a single circular tube can enhance the structure’s impact resistance. Subsequently, structural parameters conducive to excellent energy absorption characteristics were determined for various combinations of a number of branches, fractal order, and inner circle diameter parameters. These results offer valuable insights for designing multi-cellular double tubes with high energy absorption efficiency.

Energy absorption characteristics of asymmetric tree-like fractal gradient hierarchical structures

Bionic gradient hierarchy design as a design method that can effectively improve the structural crashworthiness, but its current research only focuses on the symmetric fractal method related to the discussion. In view of this, this article carries out the innovative design and research of asymmetric tree-like fractal gradient hierarchy structure (ATFGHS). The results show that the crashworthiness of the structure can be greatly improved by using the asymmetric tree-like fractal gradient hierarchy design method. Specifically, the ATFGHS-P3 showed a 98% increase in energy absorption (EA), a 98% increase in specific energy absorption (SEA), and an 84% increase in crush force efficiency (CFE) compared to a conventional hexagonal multicellular tube. The completion of this study provides valuable insights into the design and optimization of novel lightweight thin-walled energy-absorbing structures.

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.

Axial Crushing Theory and Optimization of Lattice-Filled Multicellular Square Tubes.

A lattice-filled multicellular square tube features a regular cross-sectional shape, good energy consumption, and good crashworthiness, which is suitable for the design of energy absorbers in various protection fields such as automobiles, aerospace, bridges, etc. Based on the super folding theory, two reference planes are set to refine the energy consumption zone of the super folding element in this study. The energy consumption calculation of convex panel stretching is involved, and the critical crushing force formula is introduced in this study. Meanwhile, the calculation method from a single-cell square tube to a multicellular thin-walled square tube is extended and the structural optimization is investigated, in which the NSGAII algorithm is used to obtain the Pareto front (PF) of the crashworthiness performance index of the square multicellular tubes, the Normal Boundary Intersection (NBI) method is adopted to select knee points, and the influence of different cross-sectional widths on the number, as well as the thickness, of cells are discussed. This study's results indicate that the theoretical value is consistent with that obtained from the numerical simulation, meaning that the improved theoretical model can be applied to predict the crashworthiness of multicellular square cross-sectional tubes. Also, the optimization method and study results proposed in this study can provide a reference for the design of square lattice multicellular tubes.

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.

Seismic behavior and shear capacity prediction of coupled concrete‐filled multicellular steel tube composite shear walls

AbstractIn this paper, a coupled concrete‐filled multicellular steel tube composite shear walls structure (CCSSW) is proposed. A finite element model (FEM) is developed to investigate the seismic behavior of CCSSW, and the model was validated by the tests. The effects of four parameters including axial compression ratio (ACR) on the hysteretic behavior of the CCSSW were studied. Then, a theoretical model for predicting the ultimate shear capacity (USC) of CCSSW was established. The results show that the failure mode of coupled walls exchanged from flexural failure to flexural‐shear failure with increasing the ACR, and it is recommended that the ACR should less than 0.6 to ensure the ductility requirement. To better realize the function of the first line of defense of steel coupling beam (SCB), following recommendations are concluded: the span‐to‐depth ratio range of SCB is 4.0–6.0, the wall stiffness ratio is 2.4–4.7, and low yield strength material should be used for SCB. The maximum error on USC between FEM results and theoretical results is 12.8%, and most of them are less than 10%, indicating the effectiveness of the proposed theoretical model.

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.

New design and energy absorption characteristic study of bionic beetle's elytra under axial compression

Inspired by the microstructure of the beetle's elytra, a new bionic polycellular tube protective structure based on the fractal principle was proposed in this paper, and its energy absorption characteristics were studied. Firstly, the typical microstructures of two-branch structure (type A), three-branch structure (type B) and mixed-branch structure (type C) of the beetle's elytra were extracted. Based on that, three types of the bionic multicellular thin-walled circular tube (BMTC) were designed, and the reliability of finite element models was verified by experiments. Secondly, the energy absorption characteristics and crushing mechanism of three groups of BMTCs were compared and analyzed by LS-DYNA software, and the analytical expression of mean crushing force (Fm) for BMTCs was established. The results show that the energy absorption structures of type B have better comprehensive energy absorption characteristics. Compared with the traditional ribbed structure, specific energy absorption (SEA) of BMTCs is increased by 36.75 %. In addition, when the central column is connected to the three ribs, the central column has the best deformation resistance. Moreover, the theoretical solutions matched well with the results of numerical simulation. Consequently, the research results provide inspiration for the design of energy absorption protection devices, and theoretical guidance for the analysis of energy absorption characteristics.

Crashworthiness analysis of double-corrugated multicellular tubes under axial impact

Crashworthiness analysis of double-corrugated multicellular tubes under axial impact

Effect of cross-sectional shape evolvement on the energy absorption performances of multicellular square tube

This study systematically investigated the effect of position evolvement of four ribs in multicellular square tube on its crashworthiness performance. Results show that the multicellular square tubes with the shape factors of k = 0.25 and k = 0.75 have better energy absorption performances than other multicellular square tubes under the same wall thickness or the same mass. The mean crush force is derived through the simplified super folding element theory. Moreover, multi-objective optimization of multicellular square tube is carried out and the optimal result is validated by the finite element model.

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.