Energy-absorbing mechanisms and crashworthiness design of CFRP multi-cell structures

Composite Structures xxx (xxxx) xxxx

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Energy-absorbing mechanisms and crashworthiness design of CFRP multicell structures ⁎

Guohua Zhu, Qiang Yu, Xuan Zhao , Lulu Wei, Hao Chen School of Automobile, Chang’an University, Xi'an 710064, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Multi-cell structures CFRP Energy-absorbing mechanisms Crashworthiness design

This study aims to investigate crashworthiness and energy-absorbing capacity of CFRP multi-cell structures under the quasi-static axial loading. In the present study, CFRP single-cell and multi-cell tubes are manufactured, and the same overall dimensions and mass for all specimens are guaranteed through allocating different thickness of each side. The crushing process and energy-absorbing capacity of all specimens are experimentally investigated under the quasi-static axial crushing load. According to the experimental results, it is known that the single-cell tube develops unstable local buckling mode, and the multi-cell tubes with two configurations crush progressively. Total energy absorption of the multi-cell tubes are almost 69% higher than that of the single-cell tube. Subsequently, numerical simulations are further conducted to provide additional insights into the underlying energy-absorbing mechanisms of the multi-cell tubes. The numerical results indicate that intralaminar energy is the primary energy-absorbing mechanism for all configurations, and the energy absorbed by each part in the multi-cell tubes are much higher than the corresponding part in the single-cell tube. Based on the validated numerical models, the influences of wall thickness and cells number (n) on crashworthiness characteristics of multi-cell tubes are further investigated by performing a comparative analysis. It is found that the energy-absorbing capacity is slightly increased with raising cells number, and energy-absorbing capacity gradually increases with increasing layer number of inner cross beam. Finally, the CFRP multi-cell tube with n = 3 is further optimized, and as a result SEA is improved by 4.68% from the initial design. This study is expected to provide guideline for crashworthiness design of CFRP multi-cell structures.

1. Introduction In the past few decades, structural crashworthiness has been identified as the crucial link in design and development of vehicles as it is closely correlated to occupant fatalities. Accordingly, numerous research studies have been performed to enhance structural crashworthiness of vehicles so as to reduce passenger injury and the fatality rate. Metal thin-walled structures have been extensively applied in crashworthy component for vehicles by virtue of the outstanding energy-absorbing capacity and easy fabrication. The investigations on structural crashworthiness of metal thin-walled structures started in 1960s, when Alexander [1] carried out axial crushing tests on steel circular tubes and then proposed the theoretical formula to predict the mean crushing load. Afterwards, Wierzbicki et al. [2] and Abramowicz et al. [3] further investigated structural crashworthiness of metal square tubes, and meanwhile theoretically predicted their mean crushing force. With increasing demand for structural crashworthiness, the development of novel metal thin-walled structures (such as tailor-

⁎

welded blank structure [4,5], tailor rolled blank structures [6–8], foam filled structures [9,10] and functionally graded structures [11,12]) has seen a mushroom growth. In recent years, there are increasing concerns related to oil shortage and exhaust gas emissions among automotive industry. These concerns stimulate the idea of weight reduction in automotive industry, as lightweight design has been described as an effective method to enhance fuel economy and reduce exhaust gas emissions [13]. It has been proven that the replacement of metallic materials by lightweight materials is one of the most effective approaches to dramatically reduce the vehicle weight [14]. Alternatively, carbon fibre reinforced plastics (CFRP) composite materials have the features of lightweight, superior mechanical strength/mass ratio and specific energy-absorbing capacity, and consequently they are well-suited for the crashworthy components where outstanding mechanical properties are necessary in combination with weight savings [15–17]. For example, Mamalis et al. [18,19] explored energy absorption and structural crashworthiness of CFRP thinwalled columns with square profile by experimental approach, and the

Corresponding author. E-mail address: [email protected] (X. Zhao).

https://doi.org/10.1016/j.compstruct.2019.111631 Received 30 August 2019; Received in revised form 23 October 2019; Accepted 30 October 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Guohua Zhu, et al., Composite Structures, https://doi.org/10.1016/j.compstruct.2019.111631

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Fig. 1. A scheme for all specimens in experimental study: (a) M-1; (b) M-2; (c) S-1.

great improvement in weight reduction and structural crashworthiness, if CFRP composites are applied to the multi-cell structures. Nevertheless, there are limited studies addressing crushing characteristics of the CFRP multi-cell structures. It could become questionable whether or not such CFRP multi-cell structures can improve the structural crashworthiness like their metallic counterparts, as they have completely different deformation patterns and energy-absorbing mechanisms. Liu et al. [34] experimentally explore the crushing behavior of CFRP multi-cell tubes, which were manufactured by several singlecell tubes through bonding the adjacent tubal walls. They found that the CFRP multi-cell tubes have advantage in SEA over their single-cell counterpart. Nevertheless, the multi-cell tubes considered in Ref. [34] have different overall dimensions and mass. If the comparative analysis between single-cell and multi-cell tubes is guaranteed under the condition of the same overall dimensions and mass, the crashworthiness and energy-absorbing characteristics of the CFRP multi-cell structure could be well explored. To address this issue, we innovatively manufacture several CFRP single-cell and multi-cell tubes, which have the same overall dimensions and mass through allocating different thickness for each side. The crushing behavior of CFRP multi-cell tubes are experimentally investigated by comparing with their single-cell counterpart. The finite element (FE) models are developed to study in detail the energy-absorbing mechanisms of the tubes. Subsequently, the influences of tubal wall thickness and cells number (n) on crashworthiness characteristics of CFRP multi-cell tube are further numerically investigated by performing a systematically comparative analysis. In addition, based on the comparative analysis, the multi-cell tube is optimized to enhance its energy-absorbing capacity. This study is expected to explore energyabsorbing mechanisms and structural crashworthiness of CFRP multicell tubes and also to provide design guidance for these structures.

stable progressive crushing pattern and the unstable deformation pattern were observed in the tests, respectively. Liu et al. systematically investigated deformation modes and energy-absorbing capacity of CFRP thin-walled columns with various configurations (square profile [20], double hat shaped profile [21] and circular profile [22]). They found that the layer number played a critical role in total energy absorption. Zhu et al. [23–26] experimentally and numerically studied crushing behavior of CFRP tubes with circular and square cross-sectional profiles under multiple loading cases. It is indicated that the developed finite element models were capable to replicate the crushing behavior observed in the tests. On the other hand, creatures in nature, possessing almost perfect structures and functions adapting well to natural environment after millions of years of evolution, have been providing some design inspiration for researchers and engineers to develop the thin-walled structures with better structural crashworthiness [27]. Among these bio-inspired structures, multi-cell structures exhibit superior energyabsorbing efficiency and excellent structural crashworthiness, and consequently have become a research hotspot. For example, Kim et al. [28] creatively presented the novel multi-cell columns, and superior structural crashworthiness was observed in this new design. Zhang et al. performed a series of researches on structural crashworthiness and energy-absorbing mechanisms of multi-cell structures with different configurations [29–31]. Sun et al. [32] performed a design optimization for multi-cell columns under multiple loading cases to obtain an optimal cross-sectional configuration. Huang et al. [33] carried out an investigation of axial crushing of aluminum/CFRP hybrid multi-cell tubes under different loading rates. It is indicated that the increasing aluminum tubal wall thickness and cells number were capable to enhance the energy-absorbing capacity of the tubes. In general, the abovementioned investigations indicated that the energy-absorbing efficiency of multi-cell structures is considerably higher than that of single-cell structures under axial loading condition. It is noted that almost all of the multi-cell structures considered in the previous studies are made of metallic materials. There will be a

2. Experimental study To obtain the crushing process, force-displacement responses and 2

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Fig. 2. The fabrication process of the multi-cell tube.

crashworthiness indicators, the quasi-static axial crushing tests are performed. The details of specimen preparation, experimental setup and test results are presented in this section.

Table 1 Summary of all the test specimen dimensions.

2.1. Specimens preparation For experimental study, two configurational schemes of multi-cell tubes (M-1 and M-2) are considered here, and their crashworthiness characteristics are evaluated by comparing with their single-cell counterpart (S-1), as shown in Fig. 1. By allocating different thickness for each side of the tube, all specimens almost have the same mass. Specifically, the single-cell tube is of 6 CFRP layers in thickness. As for M-1, both the thickness of inner cross beam and outer tubal wall are made as constant of 4 CFRP layers. As for M-2, the inner cross beam is manufactured with 8 CFRP layers, and the outer tubal wall has 2 CFRP layers in thickness. The fabrication process of the multi-cell tube is shown in Fig. 2. Firstly, a layer of polyimide film and plain woven CFRP prepregs are successively wrapped onto a metal mandrel, and then assemble these four mandrels together. Subsequently, the outer CFRP prepregs are wrapped onto the assembled mandrels. The pre-formed specimen is fixed by four clamp platens, which are connected to the mandrels through bolts; and then they are cured in an oven by applying the recommended curing cycle. Finally, the mandrels are carefully taken out from the cured specimen. All specimens considered in the tests are shown in Fig. 3, and the useful geometric dimensions are listed in Table 1. In order to obtain a relatively stable crushing pattern and also to avoid an overrange condition, a singly-sided chamfer is machined for all tubes.

Specimens No.

a (mm)

b (mm)

c (mm)

h (mm)

Mass (g)

M-1 M-2 S-1

55.29 55.33 55.89

0.94 (4 layers) 1.88 (8 layers) /

0.94 (4 layers) 0.47 (2 layers) 1.41 (6 layers)

100 100 100

44.9 44.2 43.6

with an ultimate bearing capacity of 50 kN. Fig. 4 depicts the experimental setup. The crushing test is conducted at a loading rate of 4 mm/ min, and the final crushing displacement is set to 70 mm (70% length of the specimen). In addition, the details of the crushing process are recorded by a digital camera. 2.3. Crashworthiness indicators As for crashworthiness design, several indicators are generally used to assess the crashworthiness of the structures [35]. In the present study, three typical indicators are adopted and compared to qualitatively explore the crashworthiness for all specimens, and they are total energy absorption (EA), specific energy absorption (SEA) and peak crash force (PCF), respectively. The EA denotes total energy absorption during the crushing process, and it can be calculated as: d

EA = ∫ F (x )dx 0

(1)

where d is the total crushing displacement, and F(x) is the instantaneous crushing force at the crushing displacement x. The SEA is utilized to evaluate the energy-absorbing efficiency of the crashworthy structure, and can be defined as:

2.2. Experimental setup To explore crushing process and crashworthiness, the quasi-static axial crushing tests are conducted by using a standard testing machine

SEA =

EA m

Fig. 3. Specimens considered in the tests. 3

(2)

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Fig. 4. Schematic of experimental setup.

axially loaded square CFRP tube can be classified into three categories: progressive failure pattern, unstable local buckling and mid-length collapse mode. In this study, the unstable local buckling mode is observed in the CFRP single-cell tube, as shown in Fig. 6(a). In the elastic stage of S-1, the tube develops the elastic deformation, and meanwhile presents a linear-relationship between crushing force and displacement. In the crushing stage, the tube develops unstable local buckling mode with formation of relatively large fragments, which leads to several corresponding oscillations of its force-displacement curve, as shown in Fig. 7. Based on the force-displacement curve of S-1, it is indicated that the unstable local buckling mode leads to a relatively lower load carrying capacity. Besides, it is worth noting that this unstable local buckling mode agrees well with the results presented in Ref. [33], which demonstrates the validity of the present experimental results from another perspective. The crushing process of M-1 is illustrated in Fig. 6(b), in which progressive crushing mode of the tube is observed. At the beginning of the crushing stage, the progressive failure is initiated at the top side of M-1 with propagation of intra/inter-laminar cracks. With the increasing crushing displacement, the cracks further propagate with formation of considerable curled fronds. According to Fig. 7, it is indicated that the progressive failure pattern of M-1 develops a stable force-displacement curve. Clearly, the load carrying capacity of M-1 is much higher than that of S-1, indicating superior load carrying capacity of M-1. The crushing process of M-2 is presented in Fig. 6(c). Since the outer tubal wall thickness is excessively thin, the outer tubal wall develops progressive failure coupled with unstable local buckling mode during the crushing stage. On the other hand, the inner cross beam of M-2 develop progressive failure pattern with formation of considerable externally/internally curled fronds. According to Fig. 7, the load carrying capacity of M-2 is very close to that of M-1, which indicates that the two configurational CFRP multi-cell tubes are of great advantage in load carrying capacity over their single-cell counterpart.

where m is the mass of the structure. Clearly, the higher SEA is, the better energy-absorbing efficiency is. In addition, the peak crash force (PCF) is the maximum value of crushing force during the crushing process. Generally, a higher value of PCF generally leads to a relatively higher vehicle deceleration, which increases the risk of injury/damage of occupants/goods during the crash accident. Thus, PCF has been widely adopted as one of the most critical crashworthiness indicators, and the lower PCF is, the better crashworthiness is. In order to better understand these indicators, a schematic of the crashworthiness indicators is illustrated in Fig. 5. The gray-shaded area represents EA during the crushing displacement of 80 mm (d = 80 mm). 2.4. Experimental results and discussion 2.4.1. Crushing process and force-displacement responses Figs. 6 and 7 show crushing process and corresponding force-displacement curves for all specimens, respectively. From the force-displacement curves shown in Fig. 7, it is found that the crushing process can be divided into two stages: the elastic deformation stage (the stage before the initial peak load) and the crushing stage (the stage after the initial peak load). According to Ref. [19] studied by Mamalis, the failure pattern of

2.4.2. Crashworthiness characteristics In this sub-section, the crashworthiness indicators are calculated based on Eqs. (1) and (2) by using a unified cutoff point (displacement of 70 mm). According to the comparison of the indicators shown in Table 2, the differences in PCF are not significant as the chamfer is machined for all specimens. Additionally, it is clearly that EA and SEA of M-1 and M-2 are almost 69% higher than those of S-1. This is due to the fact that the single-cell tube develops unstable local buckling mode, which leads to a lower energy-absorbing capacity [19]. As for the multi-

Fig. 5. Schematic of crashworthiness indicators. 4

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Fig. 6. Crushing process of all specimens: (a) S-1; (b) M-1; (c) M-2.

cell tubes, both tubes develop progressive crushing mode, which is an ideal energy-absorbing mechanisms [19]. Besides, Fig. 8 illustrates the final deformation modes of all specimens, and it can be seen that the damage degree of the multi-cell tubes is much higher than S-1. To sum up, in spite of the similar overall dimensions and the mass between the single-cell and multi-cell tubes, the topological configuration of multi-cell is more likely to develop the progressive failure pattern, and hence providing the superior energy-absorbing capacity. 3. Numerical modeling, validation and mechanisms analysis The experimental results allow to quantify the crashworthiness indicators for the structures; however, they may not be capable to explore the energy-absorbing mechanisms intuitively. Thus, to further investigate the energy-absorbing mechanisms of the multi-cell tube and provide some insights into the future design, a detailed numerical study is performed by using commercial finite element (FE) code ABAQUS in this section. Fig. 7. Force-displacement curves of all specimens.

3.1. Numerical modeling Table 2 Crashworthiness indicators for all specimens. Specimens No.

EA (J)

PCF (kN)

SEA (J/g)

M-1 M-2 S-1

1561 1563 930

28.86 31.81 25.29

34.76 35.36 21.33

The representative FE model for multi-cell tube (M-1) is shown in Fig. 9. The tube is compressed by the moving upper rigid platen, and the lower rigid platen is fixed. With consideration of the complex failure modes shown by CFRP composites, a multi-layer modeling approach is adopted here. All tubes are modeled by applying several layers of shell elements (S4R) with five integration points across the thickness, and each layer of shell elements denotes one CFRP layer. In addition, all layers are joined together by the cohesive zone elements (CZEs), as shown in Fig. 9(c). The CZEs share their nodes with one shell 5

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M-1

M-2

Top view

S-1

Fronds

Large

Fronds

fragments

M-1

M-2

ISO view

S-1

Fig. 8. Final deformation modes of all specimens.

general contact algorithm, and its friction coefficient is set to 0.3. The previous studies [37,38] have proven that there are two main categories of the failure pattern exhibited by CFRP laminates: intralaminar damage (fibre breakage, matrix cracking and in-plane shear plastic deformation) and inter-laminar damage (delamination), which need to be characterized by applying two individual failure models. In the present numerical study, the user-defined material subroutine VUMAT and the in-built cohesive zone elements (CZEs) are used to implement the intra-laminar and the inter-laminar failure models, respectively. The details of these failure models are given in the Ref. [38] and our previous studies [25,26], and are not repeated here for brevity. For completeness of this paper, Fig. 10 illustrates the flowchart of the subroutine VUMAT for the intra-laminar failure model. The maximum stress failure criterias are used to check the initiation of each failure mode (including tensile failure and compressive failure along the fibre direction, and in-plane shear failure). Once any failure criterion is

layer on the one side and tie their nodes to another shell layer on the other side. According to a mesh convergence study and our previous studies [24,25], the shell element size of 1.0 mm (axial direction) × 1.5 mm (circumferential direction) is found to be sufficient to simulate crushing behavior for all tubes. In order to obtain an appropriate computational efficiency, a much higher loading rate and mass scaling are commonly used in FE models [25]. In the present numerical analysis, the constant loading rate of the moving upper platen is set to 2 m/s, and a mass scaling of 100 is applied uniformly to the elements set of the tube. According to Ref. [36], in order to minimize the influence of the kinetic energy on numerical results, the kinetic energy of whole model needs to be less than 10% of the total internal energy. The present numerical results show that the kinetic energy is less than 5% of the total internal energy for all FE models. In addition, the contacts between the tube and the rigid surfaces and also between different layers are modeled by applying the

Fig. 9. FE model of the multi-cell tube (M-1): (a) Boundary and loading conditions; (b) Cross-sectional view; (c) Zoom view. 6

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Fig. 10. Flowchart of the subroutine VUMAT embedded within ABAQUS/Explicit.

satisfied, the corresponding damage evolution will initiate according to the predefined damage evolution equations, which are concerned with the fracture energy of the materials [25,38]. The damaged elements will be deleted when their corresponding damage variables (dij) reach the predefined maximum value (dmax). Table 3 presents the elasticity constants, tensile and compression strengths, which are measured by uniaxial tensile and uniaxial compressive tests according to ASTM 3039 and ASTM D659 standards, respectively. Table 4 lists the in-plane shear response parameters, which are measured by in-plane shear test according to ASTM D3518 standard. Table 5 gives the critical fracture energy for intra-laminar damage evolution, and these parameters are obtained by performing compact tension (CT) and compact compression (CC) tests according to ASTM E339 and ASTM E1820 standards, respectively. In this study, all these parameters to establish the intra-laminar failure model are offered by

Table 4 The in-plane shear response parameters for CFRP.

Variable

Value

Elastic properties

E1 (GPa) E2 (GPa) ν12

57 57 0.067

Strength

X1+ X2+ X1− X2−

(MPa) (MPa) (MPa) (MPa)

Variable

Value

Shear modulus Initiation of matrix damage Initial effective shear yield stress

G12 (GPa) S0 (MPa) ̂ (MPa) σy0

8.4 71 115

Coefficient

β12 C P

0.154 3080 0.8106

Table 5 The critical fracture energy for intra-laminar damage evolution.

Table 3 Elasticity constants, tensile and compression strengths along fibre directions. Description

Description

G1fc+ (kJ/m2)

2 G1fc (kJ/m )

G2fc+ (kJ/m2)

2 G2fc (kJ/m )

155

255

155

255

Note that: superscripts 1 and 2 denote fibre directions, and superscripts + and − represent tensile and compressive loading conditions, respectively. Table 6 Material properties for the cohesive model [38].

679 679 512 512

Note that: subscripts 1 and 2 denote fibre directions, and subscripts + and – represent tensile and compressive loading conditions, respectively. 7

t 0n (MPa)

t s0 (MPa)

t t0 (MPa)

2 GC n (J/m )

2 GC s (J/m )

2 GC t (J/m )

η

54

70

70

504

1556

1556

2.284

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Fig. 11. Comparison between numerical results and experimental results for S-1: (a) Crushing process; (b) Force-displacement curves; (c) Final deformation pattern.

with good accuracy. In addition, Figs. 12(b) and 13(b) compare the force-displacement curves of the multi-cell tubes between simulations and tests, and a relatively high correlation can be found. The comparisons of the crashworthiness indicators between simulations and tests are tabulated in Table 7, where a high correlation can be observed. Thus, the developed numerical models are of sufficient simulation accuracy to carry out the subsequent numerical study.

the material supplier. The parameters to establish the inter-laminar failure model are obtained from Ref. [38] (see Table 6), where the similar materials are used. 3.2. Validation of the numerical models The comparisons of force-displacement curves and crushing process between tests and simulations for S-1, M-1 and M-2 are illustrated in Figs. 11–13. Fig. 11(a) illustrates crushing process of S-1, and the details of the deformation pattern are shown in the zoom view. Based on the comparison of the force-displacement curves for S-1 (see Fig. 11(b)), it is found that the curve yielded from the simulation is not well correlated with the test during the later stage of crushing process. The difference in force-displacement response may be mainly caused by the discrepancy between input material parameters of FE model and real mechanical properties of CFRP. Nevertheless, the tendency of the predicted curve agrees well with that of the test curve. Besides, the FE model is capable to replicate the local buckling failure mode observed in the test, as shown in Fig. 11(c). According to abovementioned experimental results and other experimental investigations studied by Hussein et al. [39,40], delamination failure observed in the middle of the tubal walls. Thus, Fig. 12(a) and 13(a) present the zoom view of the crushing process to exhibit such delamination failure for M-1 and M-2 (see yellow-circled area in Figs. 12(a) and 13(a)). Figs. 12(c) and 13(c) show the comparison of final deformation modes between simulations and tests. It is indicated that the complex failure patterns of the crushed multi-cell tubes, such as the progressive failure pattern with formation of external and internal fronds (M-1 and M-2), unstable local buckling of the outer tubal wall (M-2) and the delamination failure, have been replicated numerically

3.3. Energy-absorbing mechanisms analysis Not like the experimental results, the numerical simulation is capable to quantify the energy absorbed by different parts during the crushing process, and they are mainly include kinetic energy, internal energy, frictional energy and artificial strain energy (hourglass energy) [41]. In the present quasi-static simulations, both kinetic energy and artificial strain energy are a very small fraction of total energy absorption, and thus the frictional energy and the internal energy have become the essential parts. Specifically, the frictional energy represents the energy absorbed by the mutual frictions between the rigid surfaces and the specimen and also between the inter-plies of the tube; and the internal energy denotes the energy dissipated by the failure and the deformation of the tube. Generally, the internal energy makes up the larger part compared with the frictional energy. According to different energy-absorbing mechanisms, the internal energy of the crushed CFRP tube can be further divided into two parts: (a) intra-laminar energy, denoting the energy dissipated by the fibre breakage, matrix cracking and shear plastic deformation; (b) inter-laminar energy, representing the energy dissipated by the delamination failure. In this sub-section, the energy-absorbing mechanisms and the quantification of energy absorbed by each part for S-1, M-1 and M-2 are explored by using the 8

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Fig. 12. Comparison between numerical results and experimental results for M-1: (a) Crushing process; (b) Force-displacement curves; (c) Final deformation pattern.

Fig. 15(a), it is indicated that progressive failure pattern is observed in all layers. By comparing with S-1, the damage level of layer 3 and layer 4 in M-1 is much higher than that of layer 5 and layer 6 in S-1, even though they have the same mass and dimensions. This is due to the fact that geometric configuration of multi-cell tube is more likely to generate the progressive failure pattern, which leads to the higher damage level of M-1. Fig. 15(b) illustrates the proportion of energy dissipated by different mechanisms on total energy absorption for M-1. It is clear that the largest amounts of energy absorption are made up of the intralaminar energy (53.9%), followed by frictional energy (34.3%) and inter-laminar energy (7.5%). Due to the higher damage level, the intralaminar energy of layer 3 and layer 4 in M-1 are over 50% higher than those of layer 5 and layer 6 in S-1, and the intra-laminar energy of layer 1 in M-1 is 58% higher than the summation of layer 1 and layer 2 in S-1. Additionally, frictional energy of M-1 is almost 90% higher than that of S-1; and inter-laminar energy of M-1 is almost 30% higher than that of S-1, as more delamination failure is observed in M-1. Therefore, it is indicated that the frictional energy and the internal energy of CFRP square tube are significantly improved by applying the topological configuration of multi-cell. In order to investigate the crushing process more profoundly and meticulously, M-2 is further divided into the internal part and external part, and the crushing process of each part is illustrated in Fig. 16(a). Note that the mass of the internal part in M-2 equals to the mass summation of layer 1, layer 2, layer 3, layer 4 and layer 5 in S-1; and the mass of external part in M-2 is of the same mass and dimensions with layer 6 in S-1. As shown in Fig. 16(a), the progressive failure pattern is observed in the internal part, leading to a relatively higher damage level. Besides, due to the thinner outer tubal wall thickness of

validated FE models. In the deformed FE models, the current damage state for intra-laminar failure pattern is characterized by applying the field variable. Specifically, the elements with red color represent the intra-laminar failure areas, and the elements with blue color denote the undamaged areas. Fig. 14(a) illustrates the crushing process of each CFRP layer for S-1 to explore its energy-absorbing mechanisms more clearly. At the early stage of the crushing process, S-1 exhibits progressive failure with formation of internal (see layers of 1, 2 and 3) and external (see layers of 4, 5 and 6) fronds. With increasing crushing displacement, all layers generate unstable local buckling mode, leading to a relatively lower damage level. Fig. 14(b) plots the proportion of energy dissipated by different mechanisms on total energy absorption for S-1. Clearly, the largest amounts of energy absorption are made up of the intra-laminar energy (55.6%), followed by frictional energy (29%) and inter-laminar energy (9.3%); and kinetic energy and artificial strain energy make up the smaller part, occupying less than 4% of total energy absorption, respectively. Therefore, it is shown that the fibre breakage, matrix cracking and shear plastic deformation are the primary energy-absorbing mechanisms for S-1. Besides, since each layer exhibits the similar failure pattern, the contribution of each CFRP layer on the intralaminar energy is almost the same, as shown in Fig. 14(b). Fig. 15(a) shows the crushing process of each layer for M-1. According to the cross-section of M-1 illustrated in Fig. 1, it is found that the mass of layer 1 in M-1 equals to the mass summation of layer 1 and layer 2 in S-1; and also the mass of layer 2 in M-1 equals to the mass summation of layer 3 and layer 4 in S-1. Additionally, layer 3 and layer 4 in M-1 are of the same mass and dimensions with layer 5 and layer 6 in S-1, respectively. From the crushing process of each layer shown in 9

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Fig. 13. Comparison between numerical results and experimental results for M-2: (a) Crushing process; (b) Force-displacement curves; (c) Final deformation pattern.

deformation, is the primary energy-absorbing mechanism for all specimens. Due to the higher damage level of multi-cell tubes, their intralaminar energy of each layer is much higher than that of the corresponding layer of single-cell tube. In addition to the intra-laminar energy, the frictional energy and the inter-laminar energy of the multi-cell tubes are much higher than those of the single-cell tube as well. As for the multi-cell tubes, it is found that varying thickness of outer tubal wall and inner cross beam has influence on intra-laminar energy of each layer.

Table 7 Comparison of crashworthiness indicators between tests and simulations. Specimens No.

Type

EA (J)

PCF (kN)

SEA (J/g)

Error for SEA (%)

M-1

Experiment Simulation

1561 1483

28.86 30.62

34.76 34.48

0.8

M-2

Experiment Simulation

1563 1611

31.81 32.83

35.36 37.43

−5.9

S-1

Experiment Simulation

930 924

25.29 31.09

21.33 21.50

−0.8

4. Numerical results and discussion M-2, the external part develops progressive failure coupled with unstable local buckling mode, which leads to a moderate damage level compared with M-1 and S-1. The proportion of energy dissipated by different mechanisms on total energy absorption for M-2 is plotted in Fig. 16(b). The largest amounts of energy absorption are made up of the intra-laminar energy (49.9%), followed by frictional energy (35.8%) and inter-laminar energy (9.9%). By comparing with S-1, the intra-laminar energy of internal part in M-2 is about 65% higher than the summation of layer 1, layer 2, layer3, layer 4 and layer 5 in S-1; and the intra-laminar energy of external part in M-2 is about 14% higher than that of layer 6 in S-1. By comparing with M-1, the intra-laminar energy of external part in M-2 is about 22% lower than that of layer 4 in M-1, while the total energy absorption of M-2 is slightly higher than that of M-1. According to the energy-absorbing mechanisms analysis for S-1, M-1 and M-2, it can be concluded that the intra-laminar energy, characterized by the fibre breakage, matrix cracking and shear plastic

4.1. Comparative analysis In this sub-section, several CFRP tubes with more configurations (including different combinations of cells number and tubal wall thickness) are considered here to comprehensively explore their effects on failure patterns, energy-absorbing mechanisms and crashworthiness indicators. For the purpose of comparison, the mass of all models is made as constant as the FE models in Section 3.2 (43 g) by allocating different thickness for each side, as shown in Table 8. In order to label specimens uniformly, the specimens of S-1, M-1, and M-2 in the experimental studies are re-labeled as M1-1, M2-2, and M2-4, respectively. The crushing process of all configurations is illustrated in Fig. 17. The multi-cell tubes with n = 2 and n = 3 exhibit progressive failure pattern, and the single-cell tube (n = 1) develops unstable local buckling mode. Due to the thinner wall thickness, the outer tubal wall of M25 and M3-4 exhibit unstable local buckling mode, as shown in Fig. 17(f) 10

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Fig. 14. Energy-absorbing mechanisms analysis for S-1: (a) Crushing process of each layer; (b) Proportion of energy dissipated by different mechanisms on total energy absorption.

energy-absorbing characteristics of multi-cell tubes. Thus, in this subsection, the tubal wall thickness for each side are optimized to further enhance the energy-absorbing capacity for the multi-cell tube with n = 3.

and (j). Fig. 18 compares the force-displacement curves among different configurations with n = 1, n = 2 and n = 3. Clearly, the multi-cell tubes with n = 2 and n = 3 are of higher load carrying capacity compared with the single-cell tube (n = 1), while PCF of all specimens have no obvious difference. In addition, the energy-displacement curves for all specimens are plotted in Fig. 19. The multi-cell tubes with n = 2 and n = 3 are of higher energy-absorbing capacity compared with the single-cell tube (n = 1). As for the multi-cell tubes with n = 2, their energy absorption gradually increase with increasing thickness of inner cross beam and decreasing thickness of outer tubal wall, as shown in Fig. 19(a). Besides, the multi-cell tubes with n = 3 exhibit slight advantage in energy absorption over the tubes with n = 2. This is due to the fact that the tubes with n = 3 provide higher intra-laminar energy and frictional energy, as shown in Fig. 20. In addition, Table 9 presents all crashworthiness indicators for all configurations, and M3-4 is of superior energy-absorbing efficiency. It is concluded that CFRP multi-cell tubes exhibit superior energyabsorbing capacity, which can be slightly improved by raising cells number (n). Additionally, it is indicated that varying layer number of inner cross beam and outer tubal wall is capable to affect the energyabsorbing capacity of the multi-cell tubes.

4.2.1. Discrete optimization model With consideration of the discreteness of the CFRP layer number (design variables), a discrete optimization method based on orthogonal arrays is adopted to determine the optimal layer number of each side for the multi-cell tube. The details of the optimization method are available in Ref. [42]; and a summary of corresponding steps is presented as follows: Defining the optimization problem; Firstly, it is critical to establish a mathematical model to describe the optimization problem, which includes objective function (F), discrete design variables and constraints. To take into account constraints, the objective function (F) is coupled with constraints by using a penalty function (φ (x ) ), developing a new objective function (F′) (Eqs. (3) and (4)):

F′ = F+ φ (x )

(3)

4.2. Discrete optimization for multi-cell tube with n = 3 n

φ (x) = p ∗

Based on the above comparative analysis, it is known that superior energy absorption is observed in the multi-cell tubes with n = 3; and additionally tubal wall thickness would be of noticeable impact on the

∑ max(0,Vi ) i=1

(4)

where Vi is the maximum violation corresponding to the ith constraints; 11

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Fig. 15. Energy-absorbing mechanisms analysis for M-1: (a) Crushing process of each layer; (b) Proportion of energy dissipated by different mechanisms on total energy absorption.

and p represents scaling factor to emphasize the constraint violation for the penalty function.

Based on the design variables and levels defined in Step 1, a suitable orthogonal array is established. For example, an orthogonal array involving 4 design variables (x1, x2, x3 and x4), 3 design levels (1, 2 and 3) and 9 tests can be labeled as L9(34), as shown in Table 10.

Selecting an orthogonal array based on the defined optimization problem;

Fig. 16. Energy-absorbing mechanisms analysis for M-2: (a) Crushing process of each part; (b) Proportion of energy dissipated by different mechanisms on total energy absorption. 12

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Table 8 The dimensions of CFRP multi-cell tubes with different configurations. Specimens No.

Number of cells (n)

M1-1 (S-1)

Cross-section

a (mm)

b (mm)

c (mm)

1 × 1 (n = 1)

55.73

\

1.4136 (6 layers)

M2-1 M2-2 (M-1) M2-3 M2-4 (M-2) M2-5

2×2 2×2 2×2 2×2 2×2

(n = 2) (n = 2) (n = 2) (n = 2) (n = 2)

55.73 55.73 55.73 55.73 55.73

0.4712 (2 0.9424 (4 1.4136 (6 1.8848 (8 2.356 (10

layers) layers) layers) layers) layers)

1.1780 0.9424 0.7068 0.4712 0.2356

(5 (4 (3 (2 (1

layers) layers) layers) layers) layer)

M3-1 M3-2 M3-3 M3-4

3×3 3×3 3×3 3×3

(n = 3) (n = 3) (n = 3) (n = 3)

55.73 55.73 55.73 55.73

0.4712 0.7068 0.9424 1.1780

layers) layers) layers) layers)

0.9424 0.7068 0.4712 0.2356

(4 (3 (2 (1

layers) layers) layers) layer)

(2 (3 (4 (5

Note that: the length and mass for all configurations are 100 mm and 43 g, respectively.

4.2.2. Description of optimization problem and iteration process SEA is the critical indicator reflecting crashworthiness and lightweight the energy-absorbing device, and thus SEA is chosen as the design objective. Due to the increasingly stringent requirement of weight reduction, the mass of the energy-absorbing device is chosen as the design constraint. Since the real impact direction is uncertain, a symmetric design is applied into this optimization. The four design variables, illustrated in Fig. 21, represent layer number of each corresponding side respectively. Note that the tube length and outer side length are constant with the tube considered in Table 8. Based on the abovementioned design variables, design objective and design constraint, the optimization problem can be formulated as follows (Eq. (5)):

Based on the FE models, the new objective function (F′) of the orthogonal array are calculated; Determining a new orthogonal array for the next iteration; In order to determine the optimal levels for the design variables, the analysis of mean (ANOM) is adopted, and the calculation method of ANOM is shown in Table 11. Subsequently, the optimal level determined by ANOM is taken as the second level for the next iteration. Convergence criteria. Once any convergence criteria is satisfied, the iteration process would be terminated. The two convergence criterias are defined as follows: (1) the responses of new levels are not further improved after five iterations; (2) the number of iterations reached the pre-defined maximum value.

Fig. 17. Comparison of crushing process between the CFRP multi-cell tubes with different configurations: (a) M1-1; (b) M2-1; (c) M2-2; (d) M2-3; (e) M2-4; (f) M2-5; (g) M3-1; (h) M3-2; (i) M3-3; (j) M3-4. 13

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Fig. 18. Comparison of force-displacement curves among different configurations with n = 1, n = 2 and n = 3: (a) Comparison between configurations with n = 1 and n = 2; (b) Comparison between configurations with n = 1 and n = 3.

Fig. 19. Comparison of energy-displacement curves among different configurations with n = 1, n = 2 and n = 3: (a) Comparison between configurations with n = 1 and n = 2; (b) Comparison between configurations with n = 1 and n = 3.

Fig. 20. Proportion of energy dissipated by different mechanisms on total energy absorption for the multi-cell tubes with n = 2 and n = 3: (a) Comparison between M2-2 and M3-2; (b) Comparison between M2-5 and M3-4.

⎧ Maxmize : SEA (x1, x2 , x3 , x 4 ) ⎪ Subjected to: m ≤ 45g ⎪ ⎪ x1 ∈ (0,1,2,3,4,5,6) ⎨ x2 ∈ (0,1,2,3,4,5,6) ⎪ x3 ∈ (0,1,2,3,4,5,6) ⎪ ⎪ x 4 ∈ (0,1,2,3,4,5,6) ⎩

mean, Table 13 illustrates the mean values of F′ for the first iteration. Since the design objective is maximizing F′, the optimum level of each design variable should be the one with the maximum mean value of F′. Based on the above description, the second levels of x1 and x2, the first level of x3 and the third level of x4 are assigned to be their second levels for the next iteration.

(5)

In order to enlarge the search space, the median value of design space for each design variable is served as its second level, and the neighboring values are allocated to the first and the third levels, respectively. The levels of the design variables and corresponding F′ for the first iteration are presented in Table 12. According to the analysis of

4.2.3. Optimization results The convergence history of F′ is plotted in Fig. 22, and the value of 38.68 in the initial design is F′ of M3-4. It can be seen that the F′ are not improved more than five from the third iteration. Thus, the iteration process is identified to be converged. According to Fig. 22, it is clear 14

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Table 9 Crashworthiness indicators for CFRP multi-cell tubes with different configurations. Specimens No.

EA (J)

PCF (kN)

SEA (J/g)

M1-1 M2-1 M2-2 M2-3 M2-4 M2-5 M3-1 M3-2 M3-3 M3-4

924 1356 1561 1577 1563 1632 1614 1598 1517 1663

31.09 29.46 28.86 33.00 31.81 32.36 32.55 34.21 32.76 32.51

21.50 31.53 34.76 36.67 35.36 37.95 37.53 37.16 35.28 38.68

Table 12 The levels of design variables corresponding F′ for the first iteration. Experiment No.

1 2 3 4 5 6 7 8 9

Levels of design variables

1 2 3 4 5 6 7 8 9

Design variables

F′

x1

x2

x3

x4

1 1 1 2 2 2 3 3 3

1 2 3 1 2 3 1 2 3

1 2 3 2 3 1 3 1 2

1 2 3 3 1 2 2 3 1

F′

x1

x2

x3

x4

2 2 2 3 3 3 4 4 4

2 3 4 2 3 4 2 3 4

2 3 4 3 4 2 4 2 3

2 3 4 4 2 3 3 4 2

33.92 37.10 −1.60 37.96 28.65 38.98 −33.80 34.52 −3.70

Table 13 Mean of F′ corresponding to each level.

Table 10 An orthogonal array involving 4 design variables, 3 design levels and 9 tests. Experiment No.

Levels of design variables

x1 x2 x3 x4

F′1 F′2 F′3 F′4 F′5 F′6 F′7 F′8 F′9

Levels of design variables 1

2

3

23.14 12.69 35.81 19.62

35.20 33.43 23.79 14.09

−0.51 11.23 −2.25 23.63

Table 11 Mean of F′ corresponding to each level. Design variables

Levels of design variables 1

2

3

x1

1/3(F1'+F'2 + F'3 )

1/3(F 4' +F5' + F6' )

1/3(F 7' +F8' + F 9' )

x2

1/3(F1'+F'4 + F 7' )

1/3(F 2' +F5' + F8' )

1/3(F3' +F6' + F 9' )

x3

1/3(F1' +F6' + F8' )

1/3(F 2' +F 4' + F 9' )

1/3(F3' +F5' + F 7' )

x4

1/3(F1' +F5' + F 9' )

1/3(F 2' +F6' + F 7' )

1/3(F3' +F 4' + F8' )

Fig. 22. The convergence history of F′. Table 14 The design variables for the initial and optimum designs. Design variables

Initial design

Optimum design

x1 x2 x3 x4

1 1 5 5

2 5 2 6

that the value of F′ for the optimum design is 40.49, which is about 4.68% higher than the initial design. Table 14 illustrates the four design variables for the initial and optimum designs, respectively. Besides, Fig. 23 illustrates crushing process, force-displacement curve and proportion of energy dissipated by different mechanisms on total energy absorption for the optimum design. It is indicated that the optimum design generates progressive failure modes and exhibits superior energy-absorbing characteristics. Additional, the mass of the optimum design is 44.9 g, which meets the condition of constraint. Therefore, the abovementioned discrete optimization model is considered to be

Fig. 21. The variable distribution of multi-cell tube with n = 3.

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Fig. 23. Numerical results of the optimum design: (a) Cross section view; (b) Crushing process; (c) Force-displacement curve; (d) Proportion of energy dissipated by different mechanisms on total energy absorption.

found that their energy-absorbing capacity can be slightly improved by raising cells number (n). Besides, varying layer number of inner cross beam and outer tubal wall is capable to affect the energyabsorbing capacity of the multi-cell tubes. (5) Based on the discrete optimization model, SEA of the CFRP multicell tube is improved by 4.68% from the initial design.

effective to enhance the energy-absorbing characteristics of the CFRP multi-cell tube. 5. Conclusion This study innovatively explores crashworthiness characteristics of CFRP multi-cell tubes through experimental and numerical approaches, and the comparative analysis between CFRP single-cell and CFRP multicell tubes is carried out under the condition of the same overall dimensions and mass. The underlying energy-absorbing mechanisms and the influence factors on energy-absorbing characteristics are further investigated through numerical simulations. Finally, the multi-cell tube with n = 3 is optimized to further enhance its energy-absorbing capacity. Within the limitations, the following conclusions can be drawn from this study:

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported by National Key R&D Program of China (2017YFC0803904), National Natural Science Foundation of China (51905042) and the Youth Innovation Team of Shaanxi Universities.

(1) In spite of the similar overall dimensions and the mass between the single-cell and multi-cell tubes, the topological configuration of multi-cell is more likely to develop the progressive failure pattern, and as a result multi-cell tubes exhibit higher energy-absorbing capacity. (2) Based on the developed FE models, the numerical simulations in terms of the crushing process and crashworthiness indicators show a high correlation with the tests. (3) According to the energy-absorbing mechanisms analysis, it can be concluded that the intra-laminar energy, characterized by the fibre breakage, matrix cracking and shear plastic deformation, is the primary energy-absorbing mechanism for all specimens. In addition, the intra-laminar energy, the frictional energy and the interlaminar energy of the multi-cell tubes are much higher than those of the single-cell tube. (4) By comparing the multi-cell tubes with different configurations, it is

References [1] Alexander JM. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Q J Mech Appl Math 1960;13(1):10–5. [2] Wierzbicki T, Abramowicz W. On the Crushing Mechanics of Thin-Walled Structures. J Appl Mech 1983;50(4):727–34. [3] Abramowicz W, Jones N. Dynamic progressive buckling of circular and square tubes. Int J Impact Eng 1986;4(4):243–70. [4] Xu F, Zhang S, Wu K, et al. Multi-response optimization design of tailor-welded blank (TWB) thin-walled structures using Taguchi-based gray relational analysis. Thin-Walled Struct 2018;131:286–96. [5] Xu F, Wang C. Dynamic axial crashing of tailor-welded blanks (TWBs) thin-walled structures with top-hat shaped section[J]. Adv Eng Softw 2016;96:70–82. [6] Zhang H, Sun G, Xiao Z, et al. Bending characteristics of top-hat structures through tailor rolled blank (TRB) process. Thin-Walled Struct 2018;123:420–40. [7] Duan L, Jiang H, Geng G, et al. Parametric modeling and multiobjective

16

Composite Structures xxx (xxxx) xxxx

G. Zhu, et al.

[8]

[9]

[10] [11] [12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20] [21] [22] [23]

[24] Zhao X, Zhu G, Zhou C, et al. Crashworthiness analysis and design of composite tapered tubes under multiple load cases. Compos Struct 2019;222:110920. [25] Zhu G, Sun G, Yu H, et al. Energy absorption of metal, composite and metal/ composite hybrid structures under oblique crushing loading. Int J Mech Sci 2018;135:458–83. [26] Zhu G, Sun G, Li G, et al. Modeling for CFRP structures subjected to quasi-static crushing. Compos Struct 2018;184:41–55. [27] Liu K, Jiang L. Bio-inspired design of multiscale structures for function integration. Nano Today 2011;6(2):155–75. [28] Kim HS. New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency. Thin-Walled Struct 2002;40(4):311–27. [29] Zhang X, Cheng G, Zhang H. Theoretical prediction and numerical simulation of multi-cell square thin-walled structures. Thin-Walled Struct 2006;44(11):1185–91. [30] Zhang X, Zhang H. Axial crushing of circular multi-cell columns. Int J Impact Eng 2014;65(2):110–25. [31] Zhang X, Zhang H. Energy absorption of multi-cell stub columns under axial compression. Thin-Walled Struct 2013;68:156–63. [32] Sun G, Liu T, Fang J, et al. Configurational optimization of multi-cell topologies for multiple oblique loads. Struct Multidiscip Optim 2018;57. [33] Huang Z, Zhang X, Yang C. Static and dynamic axial crushing of Al/CRFP hybrid tubes with single-cell and multi-cell sections. Compos Struct 2019;111023. [34] Liu Q, Ma J, He Z, et al. Energy absorption of bio-inspired multi-cell CFRP and aluminum square tubes. Compos B Eng 2017;121:134–44. [35] Sun G, Wang Z, Hong J, et al. Experimental investigation of the quasi-static axial crushing behavior of filament-wound CFRP and aluminum/CFRP hybrid tubes. Compos Struct 2018;194:208–25. [36] Esnaola A, Elguezabal B, Aurrekoetxea J, et al. Optimization of the semi-hexagonal geometry of a composite crush structure by finite element analysis. Compos B Eng 2016;93:56–66. [37] Cousigné O, Moncayo D, Coutellier D, et al. Numerical modeling of nonlinearity, plasticity and damage in CFRP-woven composites for crash simulations. Compos Struct 2014;115(18):75–88. [38] Sokolinsky VS, Indermuehle KC, Hurtado JA. Numerical simulation of the crushing process of a corrugated composite plate. Compos A 2011;42(9). [39] Hussein RD, Ruan D, Lu G, Sbarski I. Axial crushing behaviour of honeycomb-filled square carbon fibre reinforced plastic (CFRP) tubes. Compos Struct 2016;140:166–79. [40] Hussein RD, Ruan D, Lu G. An analytical model of square CFRP tubes subjected to axial compression. Compos Sci Technol 2018;168:170–8. [41] Mcgregor CJ, Vaziri R, Poursartip A, et al. Simulation of progressive damage development in braided composite tubes under axial compression. Compos A Appl Sci Manuf 2007;38(11). [42] Lee KH, Yi JW, Park JS, et al. An optimization algorithm using orthogonal arrays in discrete design space for structures. Finite Elem Anal Des 2003;40(1):121–35.

crashworthiness design optimization of a new front longitudinal beam. Struct Multidiscip Optim 2019;59:1789–812. Duan L, Xiao NC, Li G, et al. Bending analysis and design optimisation of tailorrolled blank thin-walled structures with top-hat sections. Int J Crashworthiness 2016;22(3):1–16. Gao Q, Wang L, Wang Y, et al. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin-Walled Structures 2016;100:105–12. X. Zhao Q. Gao L. Wang et al. Dynamic crushing of double-arrowed auxetic structure under impact loading. Mater Des. 2018. Zhu G, Li S, Sun G, et al. On design of graded honeycomb filler and tubal wall thickness for multiple load cases. Thin-Walled Struct 2016;109:377–89. Sun G, Xu F, Li G, et al. Crashing analysis and multiobjective optimization for thinwalled structures with functionally graded thickness. Int J Impact Eng 2014;64:62–74. Koricho EG, Belingardi G. An experimental and finite element study of the transverse bending behaviour of CFRP composite T-joints in vehicle structures. Compos B Eng 2015;79:430–43. Li Y, Lin Z, Jiang A, et al. Experimental study of glass-fiber mat thermoplastic material impact properties and lightweight automobile body analysis. Mater Des 2004;25(7):579–85. Jiang H, Ren Y, Liu Z, et al. Low-velocity impact resistance behaviors of bio-inspired helicoidal composite laminates with non-linear rotation angle based layups. Compos Struct 2019;214:463–75. Sun G, Wang Z, Yu H, et al. Experimental and numerical investigation into the crashworthiness of metal-foam-composite hybrid structures. Compos Struct 2019;209:535–47. Jiang H, Ren Y, Liu Z, Zhang S. Microscale finite element analysis for predicting effects of air voids on mechanical properties of single fiber bundle in composites. J Mater Sci 2019;54(2):1363–81. Mamalis AG, Manolakos DE, Ioannidis MB, et al. On the response of thin-walled CFRP composite tubular components subjected to static and dynamic axial compressive loading: experimental. Compos Struct 2005;69(4):407–20. Mamalis AG, Manolakos DE, Ioannidis MB, et al. Crashworthy characteristics of axially statically compressed thin-walled square CFRP composite tubes: experimental. Compos Struct 2004;63(3–4):347–60. Liu Q, Ma J, Xu X, et al. Load bearing and failure characteristics of perforated square CFRP tubes under axial crushing. Compos Struct 2017;160:23–35. Liu Q, Ou Z, Mo Z, et al. Experimental investigation into dynamic axial impact responses of double hat shaped CFRP tubes. Compos B Eng 2015;79:494–504. Liu Q, Shen H, Wu Y, et al. Crash responses under multiple impacts and residual properties of CFRP and aluminum tubes. Compos Struct 2018;194. Zhu G, Zhao X, Shi P, et al. Crashworthiness analysis and design of metal/CFRP hybrid structures under lateral loading. IEEE Access 2019;7:64558–70.

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