Mean Crush Force Research Articles

Breaking mechanical performance trade-off in 3D-printed complex lattice-inspired multi-cell tubes under axial compression

It is a long-standing challenge to balance the structural load capacity and toughness in the design of lightweight multi-cell tubes. To tackle this challenge, we provide two kinds of complex lattice-inspired composite multi-cell tubes. The composite multi-cell tubes consist of inner polylactic acid (PLA) complex lattice-inspired multi-cell tubes and outside aluminum tubes. The energy absorption capacity of these multi-cell tubes was evaluated under quasi-static axial compression. The effect of cross-sectional topology and thermal exposure were considered in the experiment. The results show that the integration of PLA tubes within aluminum tubes significantly enhances their energy absorption performance, effectively addressing the limitations posed by the low fracture strain of PLA. The synergistic effect between the aluminum and PLA tubes mitigates the fracture instability and distributes the load more evenly, resulting in improved specific energy absorption (SEA) and mean crushing force (MCF) up to 103.32% and 184.38%, respectively. In these composite tubes, a global self-similar layout can markedly enhance its energy absorption. However, their mechanical properties decrease significantly at 323K compared to room temperature. Overall, this research provides a novel approach to enhancing the mechanical performance of PLA tubes, paving the way for their application in engineering fields requiring lightweight and high-strength structures.

Out-of-plane impact characteristics of missing rib-plate type anti-tri-chiral honeycomb

Chiral honeycomb structures, renowned for their superior mechanical properties, find extensive application in passive safety protection and beyond. However, existing research predominantly centers on chiral honeycomb structures, neglecting discussions on the energy absorption capabilities of anti-chiral honeycomb structures subjected to out-of-plane impacts. In view of this, an innovative design method is proposed in this paper to construct a series of anti-tri-chiral honeycomb structures (MATCH-θ) with missing rib-plate and excellent crashworthiness by skillfully designing and replacing the nodal elements of the anti-tri-chiral structures. Subsequently, the effects of the constitutive angle θ and the wall thickness t of the cellular elements were investigated using a validated finite element model, revealing the energy absorption mechanism of MATCH-θ. It is shown that this type of structure has better crashworthiness performance compared to the conventional anti-tri-chiral honeycomb structure ATCH-90°. In particular, the MATCH-110° structure with t = 0.1 mm showed a 36% increase in specific energy absorption, a 36% increase in mean crush force, and a 35% increase in crush force efficiency compared to the conventional anti-tri-chiral honeycomb structure ATCH-90° with the same mass. The completion of this study provides valuable insights into the design and optimization of future honeycomb structures for crashworthiness.

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.

Study on Crashworthiness of Shrink Tube Anti-Creep Device

Based on the requirements of the narrow installation space of a train end, compact energy-absorbing travel, and huge energy suck, a shrink tube anti-creep device was designed. The crashworthiness of different structures was studied by means of a material test, a trolley test, and numerical simulation. For every 1 mm increase in tube wall thickness, 1 mm increase in the axial length of the friction cone, and 0.01 increase in the friction coefficient, the mean crushing force (MCF) increased by 45.1 kN, 13.5 kN, and 30.5 kN, respectively. When the cone angle of the shrink tube increased from α = 5° to α = 25°, the increase in the MCF with different thicknesses was about 600%. The MCF was most affected by the cone angle, followed by the wall thickness, the friction coefficient, and the axial length of the friction cone. The change in the contact length of the friction cone of the shrink tube under different structural parameters was compared. The contact length decreased with the increase in tube wall thickness and increased with the increase in angle. The variation rule of MCF was obtained to provide a reference for the development of genealogical products.

Axial Impact Response of Carbon Fiber-Reinforced Polymer Structures in High-Speed Trains Based on Filament Winding Process.

The continuous increase in the operating speed of rail vehicles demands higher requirements for passive safety protection and lightweight design. This paper focuses on an energy-absorbing component (circular tubes) at the end of a train. Thin-walled carbon fiber-reinforced polymer (CFRP) tubes were prepared using the filament winding process. Through a combination of sled impact tests and finite element simulations, the effects of a chamfered trigger (Tube I) and embedded trigger (Tube II) on the impact response and crashworthiness of the structure were investigated. The results showed that both triggering methods led to the progressive end failure of the tubes. Tube I exhibited a mean crush force (MCF) of 891.89 kN and specific energy absorption (SEA) of 38.69 kJ/kg. In comparison, the MCF and SEA of Tube II decreased by 21.2% and 21.9%, respectively. The reason for this reduction is that the presence of the embedded trigger in Tube II restricts the expansion of the inner plies (plies 4 to 6), thereby affecting the overall energy absorption mechanism. Based on the validated finite element model, a modeling strategy study was conducted, including the failure parameters (DFAILT/DFAILC), the friction coefficient, and the interfacial strength. It was found that the prediction results are significantly influenced by modeling methods. Specifically, as the interfacial strength decreases, the tube wall is more prone to circumferential cracking or overall buckling under axial impact.

Energy absorption structure with negative stepped plateau force characteristics under quasi-static loads

The force-displacement curve is the key to determine the energy absorption performance. Customizing the force-displacement curve enables the design of more advanced and efficient energy absorption systems. In this paper, we introduce a negative stepped plateau force structure (NSPFS) design by combining crooked plate units with curved and straight combined cross-section (CSCC) units. First, the NSPFS is fabricated by using additive manufacturing technology, and a compression experiment is conducted to validate the design methodology. Then, a finite element model is developed and compared with the experimental results to verify its effectiveness. The peak force (PF) and mean crushing force (MCF) of the crooked plate unit are primarily controlled by wall thickness t1 and initial angle θ1. When θ1 = 1.146° and t1 = 1.0 mm of crooked plate unit, the lowest point of the plateau phase decreases by 84 % compared to the PF, and the ratio of PF to MCF is 4.9. When the PF of the crooked plate unit is greater than the PF of the CSCC unit, the structure has the characteristics of negative stepped plateau force. More phase plateau forces can be obtained when multiple NSPFS are compressed in series. When multiple NSPFS units are compressed in parallel, multi-phase continuous negative stepped plateau force can be achieved. Therefore, NSPFS allows for the customization of complex force-displacement curves through series and parallel design.

A machine learning-based crashworthiness optimization for a novel pine cone-inspired multi-cell tubes under bending

Bionic tubes are of interest in vehicle engineering due to their superior crashworthiness potential. This study proposes a crashworthiness response investigation and machine learning-based multi-objective optimization of pine cone-inspired muti-celled tubes (PCMTs). The base computer PCMT model was correlated using existing experiments, followed by a dynamic response evaluation of different PCMT geometrical and thickness configurations to assess their structural performance. Surrogate models of these PCMTs were then constructed using machine learning algorithms, and their main and interaction effects were analyzed. A non-dominated sorting genetic algorithm II (NSGA-II) approach was employed to perform a multi-objective optimization. The results demonstrate that thickness change had more effect on the initial peak force (IPF) and the mean crushing force (MCF) than the specific energy absorption (SEA). Besides, due to the coupling effect, IPF, MCF and SEA of the optimal design solution of the PCMTs could reach a 36.82 %, 61.66 % and 72.95 % increase than the sum case, suggesting that embedding inner tubes could significantly increase energy absorption with a relative minor IPF increase. Moreover, the MCF and SEA of optimal design gave an average difference of 18.01 % and 5.91 % from the original tubes. PCMTs, therefore, could be used as an ideal energy absorption structure in the vehicle body structures.

Experimental evaluation on the axial crushing performance of BFRP-bamboo winding composite hollow components

In order to study the quasi-static axial crushing performance of BFRP-bamboo winding composite hollow components, considering the cloth ratio of BFRP (0%~14.68%) the number of BFRP layers (0 layer~4 layers) as an influencing factor, 20 tube specimens were designed for quasi-static compression tests. In this paper, the failure modes of the specimens under quasi-static axial compressive load are presented with the relevant load-displacement curves. The deformation types were carefully studied to evaluate the compressive crushing indicators of the specimens. The test results showed that when the cloth ratio of BFRP increased from 0 to 14.68%, the specific energy absorption (SEA), the mean crushing force (MCF) and the crushing load efficiency (CFE) increased to some extent, whilst the initial peak crushing force (PCF) did not show any trend. When compared with those of the bamboo winding hollow components (BT), the SEA, MCF and CFE of BFRP-bamboo winding composite hollow components with four layers of BFRP winding outside of BT (BBT4) increased by 87.53%, 194.37% and 255.59% respectively. Compared with other composite hollow components such as composite wrapped hollow components (CWT) and carbon reinforced composite hollow components (CRCT), BFRP-bamboo winding composite hollow components (BBT) showed superior crushing resistance while offering the advantages of light weight.

Cross-section parameterisation and optimisation of double-hat beams under dynamic three-point bending

Double-hat beam is a lightweight and high-performance bending-resistant structure. In this work, the impact performance of a double-hat beam under dynamic three-point bending load is verified by drop weight tests. Three geometric parameters and splines are applied to obtain many novel cross-section shapes to improve the crashworthiness of double-hat beams. Compared with double-hat beam, the mean crushing force (MCF) of DB42-51-6 is increased by 45.4%, and the specific mean crushing force (SMCF) of DB22-46-41 is increased by 15.3%. It is also found that quadrangular cross-sections outperform rectangular ones, rectangular cross-sections outperform cruciform ones, and elliptical cross-sections perform the worst. The impact performance of butterfly shaped cross-sections is better than that of rectangular and gourd-shaped ones, and convex corner is conducive to improving the bending resistance of double-hat beam compared with the concave corner. Three cross-sections are selected for multi-objective optimisation to improve their crashworthiness, and multiple sets of Pareto solutions are obtained and presented in supplementary file to provide a variety of feasible solutions. These results have important implications for the impact performance design of double-hat structures and vehicle bodies.

Design of hierarchical multi-cell double circular tubes thin-walled structures for energy absorption

This study aims to investigate the crashworthiness performance of a novel hierarchical multi-cell double circular tubes (HMDC) structure under axial impact. Various dual-tube structures of different cross-sections were designed. The effects of hierarchical order, peak number of the core column, and inner circle diameter on the structure were analyzed using Abaqus finite element analysis. The results indicate that in dual-tube structures, replacing the traditional multi-cell structure with a hierarchical multi-cell structure in the interlayer significantly improves energy absorption (EA) characteristics. With the inner circle diameter of the HMDC fixed at 20 mm, the ratio of mean crushing force (MCF) to peak crushing force at the third order increased by 70.70% and 35.68% compared to the first and second orders, respectively. Experimental results and finite element results show that the initial peak value differed by 1.47%, indicating a close match between the experimental and simulation results. The parametric study shows that the inner circle diameter and the peak number of the core column significantly affect EA. The findings of this study provide effective guidance for designing multi-cell dual circular tubes with high EA efficiency.

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.

Crashworthiness analysis and optimisation of a multi-level bionic multi-cell tube under axial dynamic impact

In this study, a multi-level bionic multi-cell tube (MBMT-n) is proposed, inspired by the horsetail’s cross-sectional structure, and the multi-cell tube shape and distribution characteristics of bamboo vascular bundles. A systematic crashworthiness analysis of MBMT-n under axial dynamic impact was conducted using LS-DYNA. The findings indicate that MBMT-n can enhance crashworthiness while maintaining the same mass. Additionally, the impact of wall thickness and bionic unit cell’s length–width ratio was investigated. Furthermore, a theoretical prediction model for mean crushing force (MCF) was established using the simplified super-folding unit theory. Lastly, to further enhance the structure’s crashworthiness, multi-objective optimisation of MBMT-3 was performed using the NSGA-II algorithm. The several optimal structures were subsequently identified under various peak crushing force (PCF). This study offers a novel approach to the design of energy-absorbing structures.

Crashworthiness behavior of multi-cell structures reinforced with small tubes under axial and inclined loading

In this paper, a novel design for the cross-sectional shapes of square, hexagonal, octagonal, and decagonal structures has been proposed for the development of energy-absorbing devices. The deformation behavior of these structures, which contain multiple small tubes, was analyzed under axial and inclined loads (0°, 10°, 20°, and 30°) using a validated finite element model in LS-DYNA, supported by experimental and analytical data. Various crushing metrics such as specific energy absorption (SEA), peak crushing force (PCF), mean crushing force (MCF), crush force efficiency (CFE), and undulation of load-carrying capacity (ULC) were evaluated for the structures. The results indicated an optimal size for the small tubes that maximizes energy absorption capability. Through the TOPSIS method considering 12 criteria, the multi-cell octagonal structure O5, which includes the highest number of small tubes, was identified as the most effective energy absorber. It demonstrated significantly higher Specific Energy Absorption (SEA) values compared to simpler structures S1, H1, O1, and D1, with improvements of 89%, 65%, 53%, and 46%, respectively. Therefore, it could be utilized in automotive structures for crashworthiness applications.

Numerical and theoretical analysis of the out-of-plane crushing behavior of a sinusoidal-shaped honeycomb structure with tunable mechanical properties

Honeycomb structures are widely utilized for energy absorption in engineering, showing superior crushing strength and energy absorption in the vertical direction, yet their potential as energy absorbers is limited due to a high initial peak force (IPF) in that direction. In this study, a novel honeycomb structure with tunable out-of-plane mechanical properties is developed by incorporating sinusoidal-shaped features into traditional vertically straight-walled cells. Crushing behavior and energy absorption performance of sinusoidal-shaped honeycomb structure (SSHS) under quasi-static out-of-plane compression are investigated numerically and theoretically. Results demonstrate that the IPF and the fluctuation of crushing response of SSHS can be effectively reduced for the introduction of sinusoidal-curved configuration. The predictable collapse mode of SSHS could be achieved for the buckling-induced features of trough and peak of sinusoidal waves. Parametric analyses were carried out to explore the influence of the geometrical topology of sinusoidal waves, namely, wave amplitude (A = 0.6–1.6 mm), wave number (N = 1–6) and the relative density (ρ = 0.05–0.25) on the out-of-plane mechanical properties of SSHS, including IPF, mean crushing force (MCF), specific energy absorption (SEA) and crushing force efficiency (CFE). The results imply properly adjusting topology parameters can determine the collapse patterns and the stress distribution, thereby substantially improving the mechanical properties. Moreover, theoretical investigation was also performed based on the simplified super folding element theory. The calculation of MCF shows a good agreement between the theoretical predictions and the numerical results. The sinusoidally curved-walled topology design strategy provides insights into the development of lightweight structures with controllable and improved crushing performance.

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.

Energy absorption and topology optimization of self-similar inspired multi-cell square tubes

Due to their low cost and lightweight properties, multi-cell square tubes have been widely used in impact protection as energy absorbers. In this study, two kinds of multi-cell square tubes were constructed according to the local self-similar and global self-similar layout strategies. The experiments and numerical simulations were conducted to investigate their quasi-static compression deformation and energy absorption. The results demonstrated that self-similar layout strategies can significantly enhance the crashworthiness of multi-cell square tubes, and the global self-similar layout appears to be more effective at energy absorption. A simplified theoretical model for the mean crushing force (MCF) was developed for its constituent elements of the proposed square tubes. Furthermore, the COPRAS method and the non-dominated sorting genetic algorithm II (NSGA-II) were employed for optimal structure selection and multi-objective optimization. The results showed that the 2nd-order global self-similar multi-cell square tube (MSTG1-2) had prominent crashworthiness compared with some typical self-similar square tubes. The current optimization and topology design strategies can be used in other polygonal multi-cell tubes, which provides an effective guide for enhancing the crashworthiness of these multi-cell tubes.

Crashworthy optimization of skeleton-filled FRP tubes based on back propagation neural network

Lightweight composite tubes have been widely used in vehicle safety systems as energy absorbers. To improve the crashworthiness of tubes, composite skeletons with a variety of cross-sectional profiles were ingeniously designed as internal reinforcements. Herein, a novel composite skeleton comprising cross-ribs and an inner circle (OS-skeleton) was proposed and integrally fabricated through the special assembling molds. The novel OS-skeleton presented a steady progressive failure mode under dynamic impact loads, leading to remarkable material utilization and energy absorption characteristics. Subsequently, finite element analysis (FEA) models were developed. The predicted response curves and deformation modes were consistent with the experimental results. Finally, a multi-objective optimization utilizing the back propagation neural network (BPNN) was then conducted to further enhance the mean crushing force (MCF) and specific energy absorption (SEA) by adjusting several structural parameters. The results showed that MCF and SEA increased with the increasing thickness of the skeletons and the number of circumferential ribs. By comparison, the diameter of inner tube and the number of circumferential ribs showed a non-linear relationship with the energy absorption characteristics due to their combined effects. In sum, the proposed composite tubes filled with OS-skeletons could maximize certain aspects of crashworthiness performance through proper structural design, demonstrating great potential for lightweight energy absorbers.

Multiobjective optimization of dimension and position of elliptical crush initiator on crashworthiness performance of square tube using response surface methodology

In this study, the crashworthiness performance of a thin-walled square steel-tube structure with an elliptical crush initiator under impact loading was investigated. The effect of the height, width, and distance of the crush initiator from the top of the tube on the crashworthiness performance was analyzed using several numerical simulations using ABAQUS Explicit. The response surface methodology was used to predict the crashworthiness performance indices, and optimization was performed to determine the optimal dimensions and position of the crush initiator. The optimization was aimed at minimizing the peak force (PF) while maximizing the mean crushing force (MCF), crush force efficiency (CFE), and specific energy absorption (SEA). The result was an elliptical crush initiator with a height of 15 mm, width of 24.784 mm, and distance of 15.08 mm. Validation was performed to verify these results. The optimal crush initiator effect resulted in a 10.12% decrease in the peak force, 13.67% increase in the crush force efficiency, and 2.23% increase in the mean crushing force. However, a slight decrease of 0.82% in specific energy absorption was observed.

Curved woven lattice truss sandwich panels strengthened by foams: Designing, manufacturing, and testing

AbstractThe woven lattice truss sandwich panels (WLTSPs) have been studied much, and this article proposes a new structure (curved woven lattice truss sandwich [CWLTS] panels). CWLTS were designed, made, and tested. The foam‐filling technique was applied to strengthen the CWLTS. Curving and foam‐filling effects to the deformation, damage, failure, and energy absorption under cylindrical and plated loadings were revealed by three‐point bending experiments. Under cylindrical loading, foam‐filling can effectively increase the load capacity, especially the CWLTS‐A. The load‐bearing capacity of the plated loading is greater than that of the cylindrical loading, and the phenomenon is significantly improved after foam filling, except for the central angle of 60° and the CWLTS‐A of 44.05°. Foam‐filling changes failure from core‐shearing to face fracture. For foam‐filled panels, the change in loading pattern results in energy absorption increase of 2.45 times for CWLTS‐B and 2.86 times for CWLTS‐A. Plated loading approximately doubles the peak load and energy absorption with two plastic hinges. The effect of foam filling on the mean crush force of the CWLTS plated loading is greater. The mechanical and energy absorption properties of the CWLTS can be improved by changing the loading mode and using foam filling, effectively increasing the applicability.Highlights Curved woven lattice truss sandwich panels were designed, made, and tested. Foam‐filling method greatly improves the bearing capacity of the CWLTS panels. Plated loading much increases the bearing capacity and energy absorption. The impact of curvature on mechanical performances is not immediately apparent.

Crash Performance of Inward-Inverting Composite Tubes Filled with Foam: Experimentation and Simulation.

This study presents a novel shock absorber with an inward-inverting composite foam-filled tube. Under the compression of a pressing cap and the action of an internal inversion cap, the composite tube inverted inward. During the crushing, the fronds of the composite tube compacted the foam, thereby enhancing the energy absorption. Three types of foams were applied to the absorber, and a drop-weight impact test was performed to obtain the assessment parameters. The foam increased the specific energy absorption (SEA) of the composite tube to 103 kJ/kg. Finite-element simulation based on the user-defined material subroutine was performed for the initial failure and stable stages of the crushing, and a foam model was identified through the experimental data. The mean crush force from the simulation agreed with the experimental data, and the SEA maximum error was <7%, thus validating the crush simulation of the proposed shock absorber. The development of the damage modes of the plies was analyzed based on the simulation results, showing a good energy absorption mechanism of this shock absorber.