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Article

Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores

Institute of Structural Analysis, Faculty of Civil Engineering and Transport, Poznan University of Technology, 60-965 Poznan, Poland
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(19), 8898; https://doi.org/10.3390/app14198898
Submission received: 2 September 2024 / Revised: 27 September 2024 / Accepted: 30 September 2024 / Published: 2 October 2024
(This article belongs to the Special Issue Structural Dynamics and Protective Materials)

Abstract

:
Security is a crucial matter, and when it comes to road safety, barriers are increasingly needed to protect assets and pedestrians from intentional and accidental vehicular impacts. Hollow steel tubes are commonly used to produce bollards; however, their impact resistance and energy absorption are limited. Hence, the aim of this study is to investigate whether the addition of honeycomb and auxetic cellular cores can improve the energy absorption and protection level of existing bollards. Hollow bollard, a honeycomb–core bollard and an auxetic-core bollard were numerically modeled and tested (using Simulia Abaqus software, version 2019) against the impact of M1-class vehicles (of 1500 kg mass) at five different speeds (following PAS 68:2013 British standard). Hence, 15 cases/numerical models were considered, with 5 cases for each bollard type. The results revealed that the addition of an auxetic cellular core to the bollard system could increase its energy dissipation by 52% compared to the hollow steel bollard. Moreover, the proposed auxetic anti-ram bollard system was capable of stopping an M1-class vehicular impact of 64 km/h compared to only 32 km/h when using a hollow steel bollard. To the authors’ knowledge, the use of an auxetic core, explicitly for anti-ram bollards, can be considered the novel part of this research.

1. Introduction

Every year, around 1.3 million people’s lives are cut short as a result of traffic accidents. Non-fatal injuries affect between 20 and 50 million more people, with many of them resulting in disability as a result of their injuries. Individuals, their families, and nations suffer significant economic losses as a result of road traffic injuries. Losses can be estimated to constitute 3% of a country’s GDP [1,2]. Vehicle barriers can be placed around the perimeter of a protected area to prevent vehicular accidents. Such barriers are frequently used as bollards. This is because, as compared to other barrier systems, they may easily blend in with other architectural features and cause fewer disturbances to building’s functionality. Hollow steel tubes are employed in a wide range of barrier system applications where deformation-induced energy absorption is required [3].
The use of anti-vehicle barriers is critical in terms of protecting structures. They have the potential to block vehicles from passing through to other assets. The public, on the other hand, is less concerned about the use of bollards these days. Some believe that the use of bollards is inefficient and that they are only used for aesthetic reasons. As a result, most buildings do not employ bollards for security. Moreover, mounted bollards may be inappropriate in some locations. Some bollards around buildings are not stiff enough and, hence, cannot withstand strong impacts. Likewise, as a form of building protection, some important and historic structures require the installation of impact-resistant-type bollards [4]. Security bollards are used to defend buildings and personnel from intentional attacks or accidents as a cost-effective option. Hence, bollards can provide effective perimeter security by prohibiting vehicles from reaching pedestrian sidewalks or restricted zones, as well as collisions with structures. Common forms of bollard applications include governmental buildings, storefront security, and traffic control.
Bollards can be either crash or non-crash-resistant, and they can be fixed, removable, or retractable, depending on the application. Crash-resistant bollards should be certified through a crash test in line with an established standard. Anti-ram bollards are widely utilized because of their straightforward installation, resulting in minimal disruption and ease of integration into existing architectural features. The ability to manufacture bollard systems in a variety of shapes and sizes also helps to reduce installation and maintenance costs. Costs are kept low while the essential level of protection is maintained. Anti-ram bollard systems, which comprise mild steel tubes, are usually embedded into concrete foundations to provide the necessary stiffness and strength to withstand significant vehicle impacts. Because of their stiffness and energy-absorbing properties, thin-walled tubes are usually utilized in bollard designs [5,6].
Vehicle security barriers (VSBs) are evaluated using a variety of standards. The International Organization for Standardization (ISO), in its latest standard, ISO 22343-1:2023 [7], specifies the essential impact performance requirement for a vehicle security barrier (VSB) and testing methods used to rate its performance when subjected to a single impact by a test vehicle not driven by a human being. This ISO standard supersedes the well-known previous version (IWA 14-1) published in 2013. Publicly Available Specification PAS 68:2013 [8] defines the standard method to be used to test the impact performance and protection rating of a VSB when impacted by different categories of UK vehicles traveling at specified speeds. The American Society for Testing and Materials, ASTM F2656 [9], defines the method to be used for impact testing and assigning performance ratings for a VSB when impacted by different categories of vehicles. Between those standards, there are some minor differences relating to the tested mass of the vehicles, the speed at which the vehicle strikes the VSB and the possible angles at which it does so. These factors affect how well the VSB performs. Datum points on the VSB and the vehicle are used to measure the distance of vehicle penetration beyond the VSB during the impact test.
Hollow steel tube bollards have been used as structural elements in highway barriers and construction systems, and they absorb impact through plastic dissipation energy. They are primarily built of thin-walled sections because such sections are effective and adaptable. Steel sections are affordable and have good mechanical qualities for use in industry; however, because of their thin-walled elements, they are vulnerable to local failure [5]. Due to the plastic deformation of the cross-section walls, thin-walled sections fail when subjected to lateral impact loads. One can estimate the member strength and energy absorption capacity via yield line mechanism (YLM) analysis of the collapse mechanism, which provides a bending moment–rotation relationship. The amount of energy that the bollards absorb due to global deformation is not dramatically altered by increasing their size. Hence, extra energy absorbers (damping systems) might be necessary for anti-ram bollards.
Protective structures may utilize cellular metals to absorb impact energy via plastic deformation [10]. In their detailed review, Costanza et al. [11] confirmed that cellular materials are commonly used as cushions and are loaded dynamically in real-life applications. These lightweight cellular metals have honeycomb or auxetic topologies. Honeycombs are 2-D cellular materials consisting of regular periodic microstructures inspired by biological structures such as bee hives, bamboo cross-sections, and abalone shells [12,13]. Honeycombs provide ideal solutions in terms of balancing high strength, high stiffness, and maintaining a light weight. In addition, honeycombs with regular hexagonal cells have perfect in-plane isotropy, considerably reducing the effort required for modeling and analysis [14]. The initial interest in honeycomb materials started with the German aircraft engineer, Hugo Junkers, who patented the first weight-saving sandwich panel designed for aircraft wing boxes in 1915. Since that time, lightweight sandwich beams and shells with honeycomb cores have been the most commonly manufactured cellular material products [15,16,17,18]. In recent years, applications of honeycomb designs as energy-absorbing structures for dynamic crushing [19,20,21], morphing wings [22,23], and non-pneumatic tires [24] have attracted attention. In addition, the capabilities of honeycomb structures in terms of heat dissipation [25,26], fire resistance [27], and noise insulation [28,29] have also been studied. A study looked at the effect of bollard energy absorption on vehicle damage [30], showing that as steel bollards cannot absorb shock, they seriously damage vehicles, leading to high repair costs. Therefore, this study suggests the use of honeycomb structures made of polylactic acid (PLA) to reduce vehicle damage. Numerical simulations with LS-DYNA were performed to create a honeycomb-inserted bollard that was intended to be used in actual vehicle–bollard collision tests.
Auxetic materials are receiving special interest in technical sectors due to their attractive mechanical behaviors that lead to improved mechanical properties, such as improved energy absorption, fracture toughness, indentation resistance, sound absorption, and shear modulus [31,32,33,34]. Poisson’s ratio is defined as the ratio between lateral strain to the longitudinal strain for a material undergoing tension in the longitudinal direction. Commonly, all materials possess a positive Poisson’s ratio. For example, materials shrink laterally under tensile loading and expand transversely when subjected to compressive loading. However, in auxetic materials, the phenomenon is reversed. For example, when the material is stretched, it expands transversely and contracts during compression, i.e., they exhibit a negative Poisson’s ratio [35,36,37,38,39]. Research in this field confirms that auxetic metamaterials outperform traditional honeycomb structures in terms of their energy absorption characteristics [40,41,42,43,44].
Luo et al. [45] provided a detailed review of auxetic tubular structures (in general) and their state-of-the-art applications. Researchers focused on the possibilities of improving a vehicles’ front end (bumper) by incorporating novel auxetic systems that could absorb crash-induced energy [46]. Zhou et al. [47] suggested adding auxetic energy absorbers in an automobile’s front end (bumper) to improve pedestrian lower leg protection. The study concludes that pedestrian lower leg protection was improved significantly by optimizing the NPR structure. Tan et al. [48] proposed an auxetic hierarchical crash box for front bumpers composed of an auxetic filling in a square, thin-walled tube. Numerical results proved that vehicle crashworthiness remarkably improved after adding the auxetic hierarchical crash box, with a specific energy absorption (SEA) of 29.26%, which was higher than that of a traditional crash box [48]. A study conducted by Apak et al. [49] performed anti-ram bollard tests numerically using LS-DYNA software and tested different types of vehicles with different specifications/categories. For the M1 category of vehicles, those with a mass of 1500 kg, different speeds were used in the simulation to measure how bollards react to each of the crashes. It is important to highlight that the research [49] covered only hollow-steel pipe bollards with no additional cellular cores. The research concludes that “existing fixed bollard systems are not sufficient for the protection of hazardous roadside facilities and need to be improved” [49].
Based on the reviewed literature, hollow-steel bollards and honeycomb-core bollards were tested and examined by previous researchers, such as [49] and [30], respectively. However, to the authors’ knowledge, the use of auxetic core explicitly in anti-ram bollards was not examined before and can be considered the novel part presented in this paper. Hence, the aim of this study was to numerically simulate a bollard crash test (following PAS 68:2013 [8]) and to check the deformations and energy absorption of the bollard with and without non-auxetic and auxetic cellular cores. The objectives of this research can be described as follows:
  • Numerical modeling of hollow-steel bollards during sudden vehicle impact.
  • Introducing a new cost-effective bollard with a honeycomb cellular core.
  • Improving the impact absorption of the steel bollard using an auxetic cellular core.

2. Case Study and Modelling

In this research, the bollard (Figure 1a) was modeled as a cylindrical shell that was 1500 mm in length, 76.2 mm in radius, and 8 mm thick, as also studied by Apak et al. [49]. Modeling was conducted in Abaqus/CAE, while the analysis was performed using Abaqus/Explicit solver for hollow-pipe, honeycomb-core, and auxetic-core bollards. The cores (Figure 1b,c) were made of folded–welded sheets to create such a geometry. This method was adopted from Al-Rifaie et al. [35], and the dimensions were chosen to match bollard and core sizes. The geometrical parameters of the honeycomb and re-entrant auxetic cells were chosen based on a detailed parametric study [40] carried out earlier by the authors to find the most effective topologies that can result in higher energy absorption.
As is known, a full 3D modeling of a detailed impacting car would lead to a heavy computational model with millions of degrees of freedom. Hence, a simple shell presenting the vehicle was used in the simulation as the research aims to improve the bollard’s impact behavior rather than the car itself. The car body (Figure 1d) was modeled as a rigid body with a mass of 1500 kg (M1-class vehicles). Such an assumption is more conservative and would reveal a more critical impact on the bollard (conservative design).
Regarding the material model, an elasto-plastic material model was used, which incorporates Johnson–Cook strain hardening and damage initiation. The Johnson–Cook material model is a constitutive model that replicates the plastic behavior of the material under high strain rates and high temperatures. In the Johnson–Cook model, the material flow stress σ considers strain rate hardening and thermal softening effects, as shown in Equation (1) [50,51,52,53]:
σ = A + B   ε n   1 + C   ln ( ε ˙ ε 0 ˙ )   1 ( T ^ ) m
where, A, B, C, n, and m represent yield stress, pre-exponential factor, strain rate factor, work-hardening exponent, and the thermal-softening exponent, respectively. They are material parameters measured at or below room temperature. Moreover, ε is the plastic strain,   ε ˙ is the plastic strain rate, ε 0 ˙ is the reference plastic strain rate, and T ^ is the dimensionless temperature parameter that depends on the current material temperature, room temperature, and melting point of the material.
The plastic strain at failure ε f depends on non-dimensional plastic strain rate ε ˙ ε 0 ˙ , pressure to Mises’ stress ratio p q , dimensionless temperature parameter T ^ and ( d 1 d 5 ) failure parameters, as shown below in Equation (2):
ε f = d 1 + d 2 exp ( d 3   p q ) 1 + d 4   ln ( ε ˙ ε 0 ˙ )   ( 1 + d 5   T ^ )
The material used for bollard pipe was Weldox 460E Steel [54] due to its high strength and ductility, as listed in [55]. Based on material mass density, in order to manufacture one hollow bollard shell, 46.2 kg of Weldox 460E Steel is required. On the other hand, the chosen material of the core (honeycomb and auxetic) was Aluminum Alloy AL7075-T651. The detailed material parameters/properties were adopted from Flores-Johnson et al. [56]. In order to manufacture one cellular core, 9.1 kg and 14.5 kg of AL7075-T651 are needed for honeycomb and auxetic cores, respectively. Hence, the total masses of the hollow bollard, honeycomb–core bollard, and auxetic-core bollard are 46.2 kg, 55.3 kg, and 60.7 kg, respectively. Detailed material parameters of Weldox 460E Steel and AL7075-T651 Aluminum are listed in Table 1. Vehicle material was arbitrarily defined, as it is defined as an undeformable/rigid body, as mentioned earlier.
Dynamic explicit analysis was used with a total time of 0.3 s. Due to the expected large deformation, geometric nonlinearity was toggled on. Adiabatic heating effects were included to consider the heat resulting from plastic deformations. Contact definition was made by defining tangential behavior with the ‘penalty’ friction formulation (friction coefficient = 0.3) and normal behavior with “Hard” contact. Separation after contact was allowed. The interaction was created using built-in general contact (Explicit) in Abaqus.
A value of −9810 mm/s2 was applied for gravity acceleration for the whole model, as shown in Figure 2a. The impact velocity of the vehicle was applied at 16, 32, 48, 64, and 80 km/h (as specified in PAS 68:2013 standard) with the equivalent in mm/s. This resulted in five sub-models for each main model assembly, meaning that the total number of simulations was 15 models. The application of impact velocity was simulated using “predefined field” feature applied to the reference point (RF) of the car rigid body (Figure 2b). In this model, only the V3 (velocity in 3rd/Z-direction) component was set to the desired velocity as the analysis concerns the effect of one-directional impact of a speedy vehicle on a bollard (Figure 2c).
A mesh study was performed using a hollow-steel bollard and one impact velocity of 64 km/h, comparing three element sizes (30, 20, and 10 mm). Based on the mesh study (Table 2), it was found that 10 mm is the most suitable finite element size for the bollard from both cost-effectiveness and accuracy point of views. Reducing the mesh size below 10 mm did not reveal a noticeable change in the results, although computational time increased dramatically. Figure 2d shows the meshed numerical model.
The numerical simulations covered 15 cases (Figure 3); each case refers to a particular velocity impacting a bollard type. The outcomes requested were deformation, the velocity–time history of the impacting vehicle, plastic dissipation energy, maximum equivalent plastic strain, and potential damage to the bollards or the honeycomb/auxetic cores. Based on those parameters, it is possible to have a detailed understanding and beneficial conclusions about the adopted anti-ram bollard system and also the validity of using cellular cores.

3. Results and Discussion

This section shows the crashworthiness performance of the hollow-steel, honeycomb-core, and auxetic-core bollards against a single M1-class vehicle impact with varying speeds of 16, 32, 48, 64, and 80 km/h. Table 3 shows the maximum deformation in the impact direction (Z) for the 15 cases considered. The table only considers the deformation of the bollards, while vehicle maximum movement/penetration is represented by the rigid ‘grey’ model. In parallel, Figure 4 compares the maximum displacement in the top center reference point of the bollards for all the cases in one bar graph.
At lower velocities of 16 and 32 km/h (the 1st and 2nd rows of Table 3), the hollow-steel bollard was successful in preventing the vehicle from penetrating the barrier/bollard. In other words, the inclusion of cellular cores might not be necessary for such low vehicular impact speeds. However, at 48 km/h (3rd row of Table 3), the hollow-steel bollard noticeably bends, and the role of cellular cores is visible. At 48 km/h, the maximum displacement in the top center reference point (Figure 4) was reduced from 643.1 mm (for the hollow bollard) to 509.2 (for the honeycomb-core) and 466 mm (for the auxetic-core). In other words, a reduction in the maximum displacement of 20.8% and 27.5% occurred when with the addition of the honeycomb-core and auxetic-core bollards, respectively. At 64 km/h, the vehicle fully penetrated the hollow-steel bollard, and the cellular cores played a vital role in preventing full penetration of the vehicle, reducing the maximum displacement of the bollard’s top center reference point (Figure 4) from 688 mm (for the hollow bollard) to 669.1 (for the honeycomb-core) and 618.2 mm (for the auxetic-core). At a high speed of 80 km/h (5th row of Table 3), it appears that none of the models were successful in preventing the vehicle from penetrating the barrier. The maximum displacements of the bollard’s top center reference point (Figure 4) were almost the same for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to an M1-class vehicle impact of 80 km/h.
It is also important to look at the velocity–time history of the impacting vehicle to check the effectiveness of the bollards in stopping vehicle penetration. Figure 5 shows the velocity (km/h) vs. time (s) of the vehicle before and after crashing the hollow-steel, honeycomb-core, and auxetic-core bollards. When the vehicle had initial impact velocities of 16 and 32 km/h (Figure 5a,b), the hollow-steel, honeycomb-core, and auxetic-core bollards were not only successful in stopping the vehicle but also in reversing the vehicle back, showing negative velocity values. At 48 km/h (Figure 5c), honeycomb-core and auxetic-core bollards were able to stop the vehicle (~zero velocity) compared to the hollow-steel bollard (~10 km/h). The difference is more dominant at 64 km/h, where the auxetic-core bollard outperformed the other two in terms of reducing the velocity of the vehicle to only 6.5 km/h (~90% reduction). At a low velocity of 6.5 km/h, the vehicle is not expected to fully penetrate the bollard and reach the target. As mentioned earlier, at 80 km/h (Figure 5e), none of the bollards were able to stop the vehicle (reduce the velocity close to zero). In short, a hollow-steel bollard can successfully sustain a vehicular impact of 32 km/h, while using the proposed auxetic-core bollard can increase the crash resistance to 64 km/h.
As the aim of this study was to design a new energy-absorbing anti-ram bollard, the plastic dissipation energy (PDE) of the whole numerical model (steel pipe + core) is an important factor to assess. According to the findings of Maduliat et al. [5], due to local deformations, the energy absorption of hollow-steel bollards can be increased by decreasing its width-to-thickness ratio, i.e., by reducing the diameter or increasing the thickness. In this paper, the inclusion of a cellular core may change the behavior. Figure 6 compares the plastic dissipation energy (PDE) in (kJ) of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h. The differences start to appear when the bollard is more deformed when subjected to impact speeds of 48, 64, and 80 km. As 64 km/h is the highest speed that was successfully suppressed by the auxetic-core bollard, more results will be discussed here. The records (Figure 6, at 64 km/h) show PDE values of 116.7, 164.7, and 177.5 kJ for the hollow-steel, honeycomb-core, and auxetic-core bollards, respectively. Keeping the hollow-steel bollard as a benchmark, it is clear that the PDE sharply increased by 52% when adding the re-entrant auxetic core. This is linked to the auxetic lateral shrinkage due to the negative Poisson’s ratio that condenses the structure and causes increased plastic strain. The findings agree with the conclusions of [30] that the addition of cellular cores (in their case, honeycomb topology) improved the shock-absorption capability compared to conventional steel bollards.
Figure 7 shows the energy components of the auxetic-core bollard when subjected to the M1-class vehicle impact speed of 64 km/h. The kinetic energy is dramatically reduced with a negative slope at the end, indicating that it could go closer to zero if the analysis total time were conducted for more than 0.3 s. Moreover, the internal energy (yellow curve) is mainly composed of plastic dissipation energy and frictional dissipation energy, which reflects the superior performance of the proposed auxetic-core bollard. The strain energy and damage dissipation energy are small due to the relatively small deformed and damaged area compared to the whole mass of the model.
Figure 8 shows the maximum equivalent plastic strain among all section points (denoted in Abaqus as PEEQMAX) of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h. The values are higher for the steel pipe (1.72) compared to 0.5 for the inserted auxetic core. This reflects that the auxetic material could have been more effectively used if it covered the steel pipe rather than being inserted in. In such a design, the ‘sacrificial’ cellular material may plastically deform more than the ‘more rigid’ supporting steel pipe. Hence, in future research, authors suggest checking the performance of anti-ram steel bollards that are ‘covered’ with protective cellular materials. Lastly, Figure 9 presents the JC-Damage Initiation Criterion of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h. As the auxetic core is aluminum, more damage is seen there than in the steel pipe. The location of damage is either that in contact with the vehicle or the yielding/bending zone near the ground surface (assumed boundary condition). The results agree with the findings of [5], where tested bollards showed local plastic failure. Maduliat et al. [5] stated that “Steel sections are economical and provide valuable mechanical properties for use in industry; however, they are prone to local failure due to their thin-walled elements”. The authors also believe that if the vehicle was modeled as a non-rigid body with deformable front bumpers, the auxetic-core bollard would have shown further protection capacity.

4. Conclusions

This study looks at whether the energy absorption and protection level of existing bollards may be increased by adding honeycomb and auxetic cellular cores. The impact of an M1-class vehicle (1500 kg mass) at five different impact velocities of 16, 32, 48, 64, and 80 km/h was studied computationally on hollow, honeycomb-core, and auxetic-core bollards. According to the results, compared to a hollow-steel bollard, the inclusion of an auxetic cellular core to the bollard system could increase its energy dissipation by 52%. Furthermore, it was demonstrated that the suggested auxetic anti-ram bollard could stop an M1-class vehicle collision at 64 km/h, compared to just 32 km/h when employing the hollow steel bollard. Hence, the proposed auxetic bollard can be considered to be a novel alternative to the bulky traditional hollow-steel bollards, i.e., a promising solution for crash prevention and public safety. Future research can consider experimental validation of the proposed solution measuring the specific energy absorption as an indicator of crashworthiness.

Author Contributions

Conceptualization, H.A.-R.; methodology, H.A.-R. and A.H.; software, H.A.-R. and A.H.; validation, H.A.-R.; formal analysis, H.A.-R.; investigation, H.A.-R. and A.H.; resources, H.A.-R. and A.H.; data curation, H.A.-R.; writing—original draft preparation, H.A.-R. and A.H.; writing—review and editing, H.A.-R.; visualization, H.A.-R.; supervision, H.A.-R.; project administration, H.A.-R.; funding acquisition, H.A.-R. All authors have read and agreed to the published version of the manuscript.

Funding

This research was partially funded by the Faculty of Civil and Transport Engineering, Poznan University of Technology, Project no. 0411/SBAD/0006.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be made available upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Geometry and 3D views of the case study: (a) hollow-steel bollard; (b) honeycomb core; (c) auxetic core; (d) car body.
Figure 1. Geometry and 3D views of the case study: (a) hollow-steel bollard; (b) honeycomb core; (c) auxetic core; (d) car body.
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Figure 2. Numerical modeling of the assembly (car and the bollard): (a) applied gravity acceleration; (b) applied velocity and boundary conditions; (c) side view of the assembly; (d) meshed numerical model.
Figure 2. Numerical modeling of the assembly (car and the bollard): (a) applied gravity acceleration; (b) applied velocity and boundary conditions; (c) side view of the assembly; (d) meshed numerical model.
Applsci 14 08898 g002
Figure 3. The considered cases in this study (15 numerical models in total) for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to the M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Figure 3. The considered cases in this study (15 numerical models in total) for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to the M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Applsci 14 08898 g003
Figure 4. Maximum displacement in the impact direction (Z), for the top center reference point of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Figure 4. Maximum displacement in the impact direction (Z), for the top center reference point of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
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Figure 5. Velocity (km/h) vs. time (s) of the M1-class vehicle with initial impact velocities of 16, 32, 48, 64, and 80 km/h before and after crashing into the hollow-steel, honeycomb-core, and auxetic-core bollards.
Figure 5. Velocity (km/h) vs. time (s) of the M1-class vehicle with initial impact velocities of 16, 32, 48, 64, and 80 km/h before and after crashing into the hollow-steel, honeycomb-core, and auxetic-core bollards.
Applsci 14 08898 g005
Figure 6. Comparison between plastic dissipation energy (PDE) in (kJ) of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Figure 6. Comparison between plastic dissipation energy (PDE) in (kJ) of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
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Figure 7. The energy components of auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
Figure 7. The energy components of auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
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Figure 8. Maximum equivalent plastic strain among all section points (PEEQMAX) of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
Figure 8. Maximum equivalent plastic strain among all section points (PEEQMAX) of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
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Figure 9. JC-Damage Initiation Criterion of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
Figure 9. JC-Damage Initiation Criterion of the auxetic-core bollard when subjected to an M1-class vehicle impact speed of 64 km/h.
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Table 1. Johnson–Cook material model parameters for Weldox 460E Steel (adopted from [54,55]) and AL7075-T651 Aluminum (adopted from [56]) used for the bollard and its cellular core, respectively.
Table 1. Johnson–Cook material model parameters for Weldox 460E Steel (adopted from [54,55]) and AL7075-T651 Aluminum (adopted from [56]) used for the bollard and its cellular core, respectively.
CategoryConstantDescriptionUnitWeldox 460EAL7075-T651
Elastic constantsEModulus of elasticity G P a 20070
νPoisson’s ratio-0.330.3
DensityρMass density k g / m 3 78502700
Yield stress and strain hardeningAYield strength M P a 490520
BUltimate strength M P a 807477
nWork-hardening exponent-0.730.52
Strain-rate hardening ε 0 ˙ Reference strain rate S 1 5 × 10 4 5 × 10−4
CStrain rate factor-0.01140.001
Damage evolution D c Critical damage-0.30.3
p d Damage threshold-00
Adiabatic heating and temperature softening C p Specific heat m m 2 . K / S 2 452 × 10 6 910 × 106
χTaylor–Quinney empirical constant/inelastic heat fraction-0.90.9
T m Melting temperature K 1800893
T 0 Room temperature K 293293
mThermal-softening exponent-0.941.0
Fracture strain constants d 1 --0.07050.096
d 2 --1.7320.049
d 3 --−0.54−3.465
d 4 --−0.0150.016
d 5 --01.099
Table 2. Mesh study considering element sizes of 10, 20, and 30 mm for a hollow-steel bollard when subjected to an M1-class vehicle at a 64 km/h impact.
Table 2. Mesh study considering element sizes of 10, 20, and 30 mm for a hollow-steel bollard when subjected to an M1-class vehicle at a 64 km/h impact.
Finite Element Size [mm]
302010
Applsci 14 08898 i001Applsci 14 08898 i002Applsci 14 08898 i003Applsci 14 08898 i004
Table 3. Maximum deformation in the impact direction (Z) for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Table 3. Maximum deformation in the impact direction (Z) for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.
Speed (km/h)U (mm)Hollow-SteelHoneycomb-CoreAuxetic-Core
16Applsci 14 08898 i005Applsci 14 08898 i006Applsci 14 08898 i007Applsci 14 08898 i008
32Applsci 14 08898 i009Applsci 14 08898 i010Applsci 14 08898 i011Applsci 14 08898 i012
48Applsci 14 08898 i013Applsci 14 08898 i014Applsci 14 08898 i015Applsci 14 08898 i016
64Applsci 14 08898 i017Applsci 14 08898 i018Applsci 14 08898 i019Applsci 14 08898 i020
80Applsci 14 08898 i021Applsci 14 08898 i022Applsci 14 08898 i023Applsci 14 08898 i024
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Al-Rifaie, H.; Hassan, A. Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores. Appl. Sci. 2024, 14, 8898. https://doi.org/10.3390/app14198898

AMA Style

Al-Rifaie H, Hassan A. Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores. Applied Sciences. 2024; 14(19):8898. https://doi.org/10.3390/app14198898

Chicago/Turabian Style

Al-Rifaie, Hasan, and Ahmed Hassan. 2024. "Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores" Applied Sciences 14, no. 19: 8898. https://doi.org/10.3390/app14198898

APA Style

Al-Rifaie, H., & Hassan, A. (2024). Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores. Applied Sciences, 14(19), 8898. https://doi.org/10.3390/app14198898

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