Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption

The axial crushing of hollow multi-cell columns were studied analytically and numerically. A theoretical solution for the mean crushing force of multi-cell sections were derived, and the solution was shown to compare very well with the numerical predictions. Numerical studies were also carried out on foam-filled double-cell and triple-cell columns. Based upon the numerical results, closed-form solutions were derived to calculate the mean crushing strength of these sections. It was found that the interaction effects between the foam core and the column wall contribute to the total crushing resistance by the amounts equal to 140% and 180% of the direct foam resistance for double cell and triple cell respectively. Finally, the relative merits of single-cell, multi-cell and foam-filled sections were discussed.     

New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency

New types of trigger and multi-cell profiles with four square elements at the corner are developed. In terms of the crash energy absorption and weight efficiency, the new multi-cell structure shows dramatic improvements over the conventional square box column. The optimization process with the target of maximizing the specific energy absorption has been successfully carried out, and the example of design process is provided. In the optimization process, the problem of stable progressive folding is also addressed. The analytical solution for calculating the mean crushing force of new multi-cell profiles is derived showing good agreement with the numerical results. Finally, the advantage of the new design over the conventional single or multi-cell profiles is discussed.     

Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular,square, hexagonal and octagonal sections

Energy must dissipate during a collision to prevent damage and injury. To reduce loss from collision, energy absorbers are used that dissipate energy upon deformation and folding to prevent damage to critical parts of a structure. In this paper, simple and multi-cell thin-walled tubes made from aluminum with triangular, square, hexagonal and octagonal sections were subjected to quasi-static loading. The experimental results were then compared with numerical simulations. The results showed that the energy absorption capacity of multi-cell sections is greater than for that of simple sections. Also, hexagonal and octagonal sections in a multi-cell configuration absorbed the greatest amounts of energy per unit of mass.     

Crashworthiness optimization design for foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure and multi-cell thin-walled structure both have recently gained attentions for their excellent energy absorption capacity. As an integrator of the above two kinds of thin-walled structures, foam-filled multi-cell thin-walled structure (FMTS) may have extremely excellent energy absorption capacity. This paper firstly investigates the energy absorption characteristics of FMTSs by nonlinear finite element analysis through LS-DYNA. Based on the numerical results, it can be found that the FMTS with nine cells has the most excellent crashworthiness characteristics in our considered cases. Thus, the FMTSs with cell number n=9 are then optimized by adopting a multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). During the process of multi-objective optimization design (MOD), four kinds of commonly used metamodels, namely polynomial response surface (PRS), radial basis function (RBF), Kriging (KRG) and support vector regression (SVR) for SEA and PCF, are established to reduce the computational cost of crash simulations by the finite element method. In order to choose the best metamodel for optimization, the accuracies of these four kinds of metamodels are compared by employing the error evaluation indicators of the relative error (RE) and the root mean square error (RMSE). The optimal design of FMTSs with nine cells is an extremely excellent energy absorber and can be used in the future vehicle body.     

Multiobjective crashworthiness optimization of multi-cornered thin-walled sheet metal members

Plastic deformation of structures absorbs substantial kinetic energy when impact occurs. Therefore, energy-absorbing components have been extensively used in structural designs to intentionally absorb a large portion of crash energy. On the other hand, high peak crushing force, especially with regard to mean crushing force, may lead to a certain extent and indicate the risk of structural integrity. Thus, maximizing energy absorption and minimizing peak to mean force ratio by seeking for the optimal design of these components are of great significance. Along with this analysis, the collapse behavior of square, hexagonal, and octagonal cross-sections as the baseline for designing a newly introduced 12-edge section for stable collapse with high energy absorption capacity was characterized. Inherent dissipation of the energy from severe deformations at the corners of a section under axial collapse formed the basis of this study, in which multi-cornered thin-walled sections was focused on. Sampling designs of the sections using design of experiments (DOE) based on Taguchi method along with CAE simulations was performed to evaluate the responses over a range of steels grades starting from low end mild steels to high end strength. The optimization process with the target of maximizing both specific energy absorption (SEA) and crush force efficiency (CFE), as the ratio of mean crushing load to peak load, was carried out by nonlinear finite element analysis through LS-DYNA. Based on single-objective and multi-objective optimizations, it was found that octagonal and 12-edge sections had the best crashworthiness performance in terms of maximum SEA and CFE.     

对钢管材料在液压膨胀试验中的应力—应变关系的测定

基于塑性膜理论和力平衡方程等,对试验数据进行曲线拟合,来确定在液压成形过程（THF）中薄壁管的应力一应变关系。由此提出一种简单实用的液压膨胀试验方法,并对不锈钢和低碳钢管进行自由膨胀试验,以得到所需的试验变形数据。而自由膨胀的有限元模拟同时也验证了该方法的有效性。结果表明：目前的做法是正确的,可用于对钢管材料的应力一应变性能进行界定,此外,由此法也可得到扩展的大应变流动应力曲线。     

Quasi-static axial and lateral crushing of radial corrugated composite tubes

This paper presents the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tube. Experimental investigations were carried out on three geometrical different types of composite tubes subjected to axial and lateral compressive loadings. On the addition to a radial corrugated composite tube, cylindrical composite tube, and corrugated surrounded by cylindrical tube were fabricated and tested under the same condition in order to know the effect of corrugation geometry. The results showed that the loading carrying capability is significantly influenced by corrugation geometry in axial crushing. However, no affect of corrugation geometry was observed for lateral crushing. Load–displacement curve was plotted for all conducted tests, thus clear comparison between different specimen's geometry was achieved. It is also found that radial corrugation could significantly applicable as a stable and effective energy absorber.     

Energy absorption of axially compressed thin-walled square tubes with patterns

The paper suggests the introduction of patterns to the surface of conventional thin-walled square tubes to improve the energy absorption capacity under axial compressive loads. A quasi-static axial crushing analysis has been conducted numerically by the nonlinear explicit finite element code LS-DYNA. Two types of patterns constructed using the basic pyramid elements were introduced. Type A pattern was aimed at triggering the extensional mode for relatively thin square tubes whereas type B pattern was intended to develop new collapse mode capable of absorbing more energy during collapse. A total of 30 tubes with a length of 120 mm, thickness 1.2 mm and widths of 40 or 60 mm were simulated. Numerical results showed that all tubes with type A patterns developed the extensional collapse mode instead of the symmetric collapse mode and absorbed about 15–32.5% more energy than conventional thin-walled square tubes with a mass increase less than 5%. Meanwhile, a new collapse mode named octagonal collapse mode was observed for tubes with type B pattern and the energy absorption of tubes developing this mode increased by 54–93% compared with the conventional tube. The influence of various configurations of the patterns on the deformation and energy absorption of the tubes was also discussed. The paper opens up a new avenue in design of high energy absorption components.     

Quasi-static axial compression behavior of constraint hexagonal and square-packed empty and aluminum foam-filled aluminum multi-tubes

The axial crushing behavior of empty and Al close-cell foam-filled single Al tubes and Al multi-tube designs (hexagonal and square) were investigated through quasi-static compression testing. The effects of foam filling on the deformation mode and the crushing and average crushing loads of single tubes and multi-tube designs were determined. The foam filling was found to shift the deformation mode of empty single tube and empty multi-tube designs from diamond into concertina. In multi-tube designs the constraint effects and the frictional forces were found to increase the average crushing loads over those of single tubes. It was also found that foam filling induced a higher strengthening coefficient in multi-tube than single tubes. Although foam filling increased the energy absorption in single tubes and multi-tube designs, it was not effective in increasing the specific absorbed energy over that of the empty tubes. However, multi-tube designs were found to be energetically more effective than single tubes at similar foam-filler densities, proving a higher interaction effect in multi-tube designs.     

Numerical studies on STFD-HAT sections under axial dynamic impact

A new type of spot-weld double-hat section with symmetrically distributed tilt flanges (STFD-HAT) is introduced in this paper to improve the crushing performance, especially crushing stability. LS-DYNA code has been employed here to analyze the effect of several parameters on the collapse modes of STFD-HAT sections under axial dynamic impact loading condition. Some variables, such as tilt angle, size of core cross-section and thickness of sheet shell, have been proved to be effective in controlling the collapse mode and crushing performance of STFD-HAT sections by analysis on energy absorption and RSS of result curves. Compared with traditional double-hat sections, the STFD-HAT sections with reasonable designed profiles can effectively improve the crushing resistances and stabilities, especially, the bending mode.     

An improved nano-scale material model applied in axial-crushing analyses of square hollow section aluminium profiles

The behaviour of square hollow section AA6060 aluminium profiles subjected to quasi-static axial crushing was investigated experimentally and numerically. The profiles were artificially aged to three different tempers (under-aged, peak-aged and over-aged) using two different cooling rates (water quench or air cooling) after the solution treatment, thus obtaining six different materials. The materials’ microstructures were characterized by scanning and transmission electron microscopy and mechanical testing was used to determine the stress–strain curves in uniaxial tension. Axial crushing tests were carried out on profiles made of the six different materials to study the influence of the heat treatment on the energy-absorbing capability of the profile. The nanometre-scale material model NaMo was employed to predict the stress–strain curves of the three water-quenched materials based on the chemical composition and the thermal history. A new feature was introduced in NaMo in order to account for the incubation period, which cannot be ignored for low-alloy materials such as the AA6060 alloy. The stress–strain curves predicted using the improved nano-scale material model showed good agreement with the experimental curves for the three tempers when the incubation period was considered. Using the predicted stress–strain curves in finite element simulations of axial crushing of the profiles, gave excellent predictions of the experimentally obtained force–deformation curves and thus the energy absorption. The results indicate that two-scale simulation based only on chemical composition and thermal history is now possible in designing AA6xxx structural components for safety applications.     

Energy absorption capability of fibreglass composite square frusta subjected to static and dynamic axial collapse

The crashworthy behaviour of square frusta of fibreglass composite material subjected to axial compression at various strain rates is reported. The effect of specimen geometry and the loading rate on the energy absorbing capability was experimentally studied. The mechanics of the axial crumbling process from macroscopic and microscopic points of view were also investigated theoretically and experimentally. The collapse modes at macroscopic and microscopic scale during the failure process were observed and analysed. A theoretical analysis of the observed stable collapse mechanism of the components crushed under axial compression, for calculating crushing loads and energy absorbed during collapse, is proposed. A good agreement between theoretical and experimental results was obtained indicating the efficiency of the theoretical model in predicting the energy absorbing capacity of the collapsed shell.     

Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such as the peak load, fold lengths, axial compression and energy absorption are studied. An examination is also made of the influence of filtering on the accuracy of data obtained usually in dynamic tests.     

Effects of hinges and deployment angle on the energy absorption characteristics of a single cell in a deployable energy absorber

Numerical simulation is carried out to investigate the crushing characteristics of a single cell in a fan-shaped deployable energy absorber (FDEA) under quasi-static axial loading. FDEA can effectively improve the crashworthiness behavior of aircrafts with the advantages of saving space and deploying actively. Hinges are added to the single cell to meet the need of fan-shaped deployment. The finite element model is established to study the effects of hinge׳s parameters, including material properties such as Young׳s modulus, yield strength and the tube thickness, on the single cell׳s energy absorption characteristics. The relationship between the deployment angle and the specific energy absorption (SEA) of the single cell is also studied. The numerical results indicate that the energy absorption increases rapidly as yield strength and the hinge׳s thickness increase, while it only has minor correlation with Young׳s modulus of the material. Three different modes of the cell appear during its axial crushing as the deployment angle increases. Besides, experiments were conducted to observe the crushing mode of the straight single cell, and the results are compared with the numerical simulation results. Finally, a theoretical model of a straight single cell with hinges is proposed to predict the mean crushing force, which is in good agreement with the numerical simulation.     

Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries

In this paper, deformations and energy absorption capacity of thin walled tubes with various section shapes (circular, square, rectangular, hexagonal, triangular, pyramidal and conical) are investigated both experimentally and numerically. The tubes have the same volume, height, average section area, thickness and material and are subjected under axial quasi static loading. The results of simulations are in good agreement with the experimental data and show that the section geometry has considerable effect on the energy absorption. The circular tube has the most energy absorption capacity and the most average force among all investigated sections. Since the maximum force is concerned in impact events, pyramidal and conical tubes are recommended, due to their uniform load–displacement curves and therefore, less difference between the maximum and the average forces.     

Energy absorption properties of non-convex multi-corner thin-walled columns

In this paper, we proposed a strategy to improve energy absorption efficiency of thin-walled columns by introducing extra non-convex corners in the cross section. Several profiles of non-convex multi-corner thin-walled columns obtained through this strategy are presented and their energy absorption capacities under axial crush are investigated analytically and numerically. Explicit formulations for predicting the mean crushing force of non-convex multi-corner thin-walled columns are derived based on the theory of Super Folding Element method, and the predicting results of these formulations have good agreement with the numerical simulation performed by explicit non-linear finite element method. The comparisons of the non-convex columns with square column show that the non-convex multi-corner thin-walled columns have higher energy absorption capacity.     

Numerical simulation of the axial collapse of thin-walled polygonal section tubes

This paper deals with the post-buckling deformation characteristics of aluminum alloy extruded polygonal section tubes subjected to dynamic axial impacts. The explicit finite element code LS-DYNA is the primary analytical tool used in this investigation. The study focuses on investigating a post-buckling deformation phenomenon that is primarily manifested by an axial crumpling action that generates material folds as the impact energy is dissipated. The research is conducted in two phases. The first phase consists of validating the LS-DYNA model parameters and numerical results pertaining to thin-walled aluminum extruded square tubes with actual published experimental data. The post-buckling deformation characteristics of the specimens such as the overall final configuration and the various folding deformation modes (extensional, symmetric and asymmetric) resulting from the axial collapse of the member is also investigated in a subsequent phase. Based on the numerical simulation results, it is apparent that the increase in the number of walls (flanges) has a direct impact on the mean axial crushing force and permanent displacement parameters. In particular, the adoption of a hexagonal tube section as an axially loaded energy absorbing column yields an average increase of 11% in the mean axial crushing force and an average decrease of 10% in the permanent displacement. The greatest benefits are obtained in the specimens with the thinnest nominal wall thickness, where the upper bound results show an average increase of 27% in the mean axial crushing force and average decrease of 20% in the permanent displacement.     

准静态轴向和侧向挤压下对径向波纹管的分析

介绍了波纹几何形状对破坏性能、能量吸收、失效机理和玻璃纤维方格布／环氧复合材料管失效模式的影响。对承受轴向和侧向压力的3个具有不同几何形状的复合材料管进行试验研究。同时对相同受力条件下的径向波纹复合管、圆柱型复合管、圆柱管环绕的波纹管进行试验,以了解波纹几何形状的影响。结果表明,轴向挤压中波纹几何形状会显著影响管的承载能力。然而,侧向挤压中并没有发现波纹几何形状的影响。试验中绘制了荷载一位移曲线,因此可以对各种不同几何形状的构件进行清晰的对比。研究同时发现,径向波纹可以稳定并有效地吸收能量。     

Energy evaluation in reinforced concrete hollow circular sections under bending

Four specimens were tested for monotonically increasing bending. Another four identical specimens, except for possible variations in concrete strength, were tested for reversed cyclic bending. The hollow cylindrical specimens were 128 inches (3.25 m) long and 16 inches (406 mm) in outside diameter with wall thickness of two inches (50.8 mm) and reinforced by both longitudinal and circumferential steel.

Two parameters were varied, the axial load and the longitudinal steel ratio. The effects of the axial load and the longitudinal steel ratio on the specimens stiffness, curvature ductility and energy absorption were quite apparent.

The test results confirmed that the use of ductility factors in evaluating energy absorption or dissipation in reinforced concrete hollow circular sections under bending does not take into account the effect of the stiffness degradation or the pinching effects that are found in the hysteretic behaviour of sections subjected to cyclic bending coupled with high axial forces.     

Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure has recently gained attention due to its excellent crashworthiness. Based on the previous study, a new kind of foam-filled thin-walled structure called as functionally graded foam-filled thin-walled structure has more excellent crashworthiness than the traditional uniform foam-filled thin-walled structure. Moreover, as far as we know multi-cell thin-walled structure has more excellent crashworthiness than the traditional single-cell thin-walled structure. As an integrator of the above two kinds of excellent thin-walled structures, functionally graded foam-filled multi-cell thin-walled structure (FGFMTS) may has extremely excellent crashworthiness. Based on our study, the crashworthiness of the FGFMTSs is significantly affected by the design parameter of the graded functional parameter m. Thus, in order to obtain the optimal design parameters, the FGFMTSs with different cross sections and different wall materials are optimized using the multiobjective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). At the same time, the corresponding uniform foam-filled multi-cell thin-walled structures (UFMTS) which have the same weight as these FGFMTSs are also optimized in our study. In the multiobjective design optimization (MDO) process, polynomial functional metamodels of SEA and PCF of FGFMTSs are used to reduce the computational cost of crash simulations by finite element method. The MDO results show that the FGFMTS with PCF in the initial period of its crash not only has better crashworthiness than the traditional UFMTS with the same weight but also performs superior balance of crashing stability. Thus, the optimal design of the FGFMTS with PCF occurring in the initial crash is an extremely excellent energy absorber and can be used in the practical engineering.