Experimental and Numerical Study on the Quasi-Static Mechanical Behavior of Flexible Anti-Collision Ring (FACR) for Bridge Protection

Abstract

This study investigates the quasi-static mechanical behavior of a flexible anti-collision ring (FACR) for bridge protection through axial tests and finite element (FE) simulations. The FACR features a multi-layer steel wire rope coil (SWRC) encased in a chloroprene rubber matrix. Quasi-static tensile and compressive tests (80 mm/s) were conducted on both the SWRC and the FACR, with full-field strain distributions captured via digital image correlation (DIC). The results demonstrate that the rubber matrix significantly enhances load-bearing capacity (by 200% in compression and 337% in tension) and energy dissipation (by 403% and 620%, respectively), with bending identified as the dominant deformation mode. An FE model was developed and validated against experimental data, then employed for parametric analysis. The cross-sectional ratio, governed by the number of SWRC layers, exhibits a strong nonlinear influence on the tensile response, and a three-layer configuration is identified as optimal, achieving the highest energy absorption without compromising compressive performance. A layer-dependent mechanism analysis reveals that excessive layers lead to a drastic stiffness reduction in outer coils, impeding coordinated load sharing. Building upon this mechanism, an optimized two-layer arrangement maximizing the inner-layer SWRC proportion is proposed, achieving 2.0× and 1.9× improvements in peak tensile force and energy dissipation, respectively, while using fewer steel wires. This work provides a fundamental understanding and an efficient optimization strategy for FACRs.

1. Introduction

With the rapid development of the global shipping industry and the intensive construction of cross-waterway transportation infrastructure, collisions between vessels and bridges have become a critical threat to the safety of both water and land transportation [1,2,3,4]. The increasing size of vessels further exacerbates this risk, as the kinetic energy of such ships far exceeds the design thresholds of traditional collision protection facilities. The 2024 Guangzhou Lixinsha Bridge accident [2] and the 2024 Baltimore bridge accident [5] both resulted in severe consequences. These incidents not only reveal the combined risks posed by increasingly complex navigation environments and larger vessels but also highlight the limitations of existing collision avoidance technologies.

To address this challenge, researchers have proposed various design schemes for anti-collision devices. At present, mainstream vessel collision protection devices fall into two main categories: non-contact and contact types. In the field of non-contact protection, a representative solution is the group pile protection system. Based on the bow impact force versus penetration depth curve, Hoang and Lutzen [6] proposed a strength-ductility collaborative design criterion for elastic-plastic pile-column structures. El-Sawy et al. [7] optimized the buckling energy dissipation path of sacrificial piles through numerical simulation, while Carbonari et al. [8] developed a displacement-oriented design method for fender-flexible pile composite structures. In the field of contact protection, composite protection technology predominates. The corrugated steel plate-UHPFRC composite structure developed by Fan et al. [9,10,11] leverages synergistic material deformation, achieving a 38% reduction in impact force and a 2.1-fold prolongation of action duration. Fang et al. [12,13,14,15,16,17,18,19,20,21] proposed a fiber-reinforced polymer/ceramic particle-filled structure, which, through 45° winding angle optimization and particle size matching design, attains an impact force reduction rate of 25.23%. Xu et al. [22,23] constructed a multi-layer sandwich device that increases energy absorption density by 62% and exhibits favorable robustness against impact position. Cheng et al. [24,25,26] proposed a steel-GFRP-foam protective structure that reduces impact force by approximately 90% through steel ductility and core cushioning; their device achieves 92% reduction through steel yielding, GFRP buckling, and foam shear failure.

Although the aforementioned devices demonstrate certain effectiveness in bridge protection, they still face significant bottlenecks in meeting the demands of modern shipping development: irreversible damage to sacrificial components leads to limited service life of the devices, and coupled with high manufacturing costs, this severely restricts their engineering applicability. Moreover, the vessel classes that such devices can accommodate are limited, making it difficult to match the risks posed by the increasing size of ships. More critically, current protection systems mostly focus on single-object protection—the devices aim to reduce impact forces on bridge piers while neglecting damage control of the ship structure, and thus a ship-bridge-device synergistic protection has not yet been achieved.

To address the challenge of large-tonnage vessel impacts, Yang et al. [27] proposed a vessel collision protection device featuring stiffness-flexibility matching and flexible guidance, based on the principle of comprehensive protection for bridges, vessels, and anti-collision devices. The core advantage of this device lies in its ability to significantly prolong the impact duration, effectively reduce the peak impact force exerted by large-tonnage vessels on bridge piers, simultaneously deflect the vessel’s heading, provide sufficient space for the bow to turn and deviate from the pier, and dissipate most of the vessel’s kinetic energy. The collision protection principle of the flexible guided anti-collision device (FGAD) is shown in Figure 1. Wang et al. [28] first employed the finite element method to investigate the dynamic response and energy dissipation capacity of the device under vessel impact, and subsequently conducted full-scale vessel impact tests. The results show that the device converts concentrated impact loads into gradient distributed loads, resulting in a significant deflection of the vessel’s heading while reducing the peak impact force on the bridge pier by more than 40%. This indicates that through a “guiding instead of resisting” mechanism, the device enhances the economy of the protection system while ensuring navigation safety, providing a new technical pathway for vessel-bridge collision protection. Wang et al. [29] systematically investigated the FGAD adopted for the Zhanjiang Bay Bridge in Guangdong Province through finite element simulation, and evaluated the effectiveness of the device from three aspects: vessel impact force, energy dissipation, and vessel heading. Zhou et al. [30,31] analyzed the mechanical characteristics of a closed circular beam on an elastic foundation based on this device, and found that the ratio of the elastic foundation stiffness to the flexural stiffness of the circular beam plays a dominant role in the beam’s behavior. They also identified two key parameters: the aforementioned stiffness ratio and the foundation viscosity coefficient.

As the core component of the FGAD, the flexible anti-collision ring (FACR) plays a key role in transmitting and dispersing impact loads. Its mechanical performance directly affects the reusability and flexibility of the entire protection system, as well as the ship-bridge-device synergy. The FACR consists of an inner steel wire rope coil (SWRC) encapsulated within a chloroprene rubber matrix. However, the structural design of the FACR currently lacks a theoretical basis. Notably, the steel wire rope coil (SWRC) serves as the core skeleton of the FACR, and its design parameters—such as the number of layers and arrangement pattern—largely determine the overall mechanical characteristics of the FACR. In contrast, the outer rubber matrix primarily functions as a protective layer. Therefore, investigating the mechanical performance of the SWRC and optimizing its structure are of great significance for improving the overall anti-collision effectiveness of the device.

To this end, this study presents a component-level quasi-static mechanical behavior analysis of the FACR. Using a combined experimental and finite element analysis (FEA) approach, quasi-static axial loading tests (80 mm/s) are conducted to characterize the mechanical response of the FACR under compression and tension. A refined finite element model is then established, and parametric analysis is systematically performed to investigate the influence of the number of steel wire rope layers on the peak force and energy dissipation efficiency. The layer-dependent stiffness mechanism was first identified, based on which the load-bearing characteristics of different structural configurations were compared and the optimized wire-rope layout was proposed.

2. Mechanical Testing of the FACR

2.1. Structure of the FACR

The flexible anti-collision ring (FACR) investigated in this study features a multi-layer composite configuration. Its core comprises six concentric layers of steel wire rope coil (SWRC), arranged to form a triangular cross-sectional geometry. The SWRC is fabricated by coiling a 6 × 19 W + IWR steel wire rope with a nominal diameter of approximately 28 mm. In this rope construction, the outer layer comprises six strands of 19 wires each, while the core consists of an independent wire rope core (IWR), resulting in a total of 163 individual wires in the cross-section. The SWRC is encapsulated within a chloroprene rubber matrix, resulting in a synergistic load-bearing assembly. The overall structure adopts an annular shape with an outer diameter of 800 mm and an inner diameter of 380 mm. The cross-section presents a trapezoidal profile, with top and bottom base widths of 160 mm and 230 mm, respectively. The complete structural configuration and dimensional parameters are illustrated in Figure 2.

2.2. Experimental Setup and Loading Conditions

This study performed quasi-static axial tensile and compressive tests to systematically characterize the mechanical properties of the SWRC and the FACR. Tests were carried out using an MTS 500 kN (±0.5%) electro-hydraulic servo actuator system with a stroke range of ±250 mm (±0.01%); loading and unloading were applied at a rate of 80 mm/s, with a maximum displacement of 200 mm. The data acquisition system comprised integrated high-precision sensors that synchronously recorded force-displacement responses at a sampling frequency of 1024 Hz. To replicate actual engineering conditions, the FACR was tested with a pair of fixtures taken directly from the protective device, whereas the fixture for the SWRC was redesigned on the basis of that used for the FACR. The imaging system consisted of a high-resolution industrial camera (ORX-10C-51S5M-C, FLIR Integrated Imaging Solutions, Inc., Richmond, BC, Canada) equipped with a 35 mm f/2.8 fixed-focal-length lens and a recording computer. The camera was positioned perpendicular to the specimen surface at a working distance of 1 m, capturing images at 30 fps with an effective resolution of 1720 × 1324 pixels. Digital image correlation (DIC) was employed as an auxiliary measurement technique to obtain full-field strain distributions on the FACR. The VIC-2D digital image correlation (DIC) analysis system (v8.0, Correlated Solutions Inc., Columbia, SC, USA) was uesd to measure the full-field strain distributions of the FACR. The calibrated spatial resolution was approximately 0.82 mm/pixel, with a subset size of 29 × 29 pixels and a step size of 7 pixels. The experimental setup is shown in Figure 3, and detailed loading parameters are provided in

Table 1. Test conditions for the SWRC and the FACR.

ID	Type	Condition	Loading/Unloading Speeds (mm/s)	Maximum Displacement (mm)
1#	SWRC	Compression	80	80/160/200
2#		Tension
3#	FACR	Compression
4#		Tension

.

2.3. Test Results and Analysis

2.3.1. Force-Displacement Response and Energy Dissipation

Figure 4 and Figure 5 present the compressive and tensile force-displacement curves of the SWRC and the FACR, respectively; the specimen deformation at the maximum imposed displacement is indicated in each figure. The test data reveal that under axial compression, both specimens exhibit an approximately linear increase in force with displacement. Under axial tension, both specimens display a distinct two-stage response: during the first half of the loading displacement (0–100 mm), the force increases linearly while the tensile stiffness remains nearly constant; during the second half (100–200 mm), a pronounced nonlinear stiffening occurs, with the force rising sharply.

Table 2. Comparison of load-bearing capacity and energy dissipation between the SWRC and the FACR.

Type	Compression Force (kN)	Tensile Force (kN)	Compression Energy (J)	Tensile Energy (J)
SWRC	11.20 ± 0.06	49.70 ± 0.25	304.5 ± 1.5	754.8 ± 3.8
FACR	33.70 ± 0.17	217.00 ± 1.09	1530.5 ± 7.7	5432.4 ± 27.2
Percentage increase	201 ± 2%	337 ± 3%	403 ± 3%	620 ± 5%

compares the peak forces and the corresponding energy dissipation values of the SWRC and the FACR. Relative to the SWRC, the FACR demonstrates a substantial performance enhancement: under compression, the peak force and energy dissipation increase by 201 ± 2% and 403 ± 3%, respectively; under tension, the increases reach 337 ± 3% and 620 ± 5%. These results underscore the critical contribution of the rubber matrix to both load-bearing capacity and energy dissipation.

2.3.2. Digital Image Correlation (DIC) Strain Field Analysis

Figure 6 and Figure 7 show the full-field axial strain (${\mathrm{e}}_{\mathrm{y}\mathrm{y}}$) distribution contour plots of the FACR under tension and compression tests, respectively. DIC observations indicate that the FACR exhibits a bending-dominated deformation mode with approximately symmetric strain distribution under compression and tension tests: the circumferential strain shows an “outer tension, inner compression” pattern under compression, and an “outer compression, inner tension” pattern under tension. At equivalent displacement amplitudes, the maximum strain under tension is markedly higher than that under compression, which aligns with the trends of superior tensile load capacity and energy dissipation observed in the force-displacement curves. This discrepancy is primarily attributable to the differing constraint effects of the fixture: under compression, the fixture exerts a minor influence on the deformation of the inner ring, whereas under tension, its constraining effect is substantial and cannot be neglected.

3. Numerical Modeling and Analysis of the FACR

3.1. Numerical Model of the SWRC

Figure 7a and Figure 7b display a tested segment of the steel wire rope and its cross-sectional morphology, respectively. Inspection of the post-test cross-section reveals no appreciable slippage among the wires within a strand; relative displacement arises predominantly from inter-strand friction [32,33]. On this basis, the cross-section of each strand is simplified into an equivalent tubular beam cross-section in the numerical model, with the following section control parameters: ELFORM = 1, CST = 1. Figure 7c illustrates a schematic of the simplified cross-section, while Figure 7d depicts the corresponding finite-element cross-section. This idealization considerably reduces the complexity of contact calculations and the number of elements, thereby facilitating convergence and improving computational efficiency.

In this study, numerical analyses were conducted using LS-DYNA (mpp s R13) finite element software. Default hourglass control (IHQ = 4, QH = 0.1) and time step control were applied, and no mass scaling was used. The finite element model of the SWRC is presented in Figure 7e. The steel cable ties are discretized using shell elements with a mesh size of ~6 × 6 mm², the fixtures are represented by solid elements with a mesh size of ~6 × 6 × 6 mm³, the clamping distance is kept the same as that in the experiment, and beam elements with a size of ~5 mm are also employed. The steel cable ties and fixtures were defined as elastic materials (*MAT_ELASTIC), whereas the SWRC was defined as an elastic-plastic material (*MAT_PLASTIC_KINEMATIC). Based on the experimental curve data from tension and compression tests, the material parameters of the steel wire rope were obtained through iterative inversion calculations. The corresponding material parameters are listed in

Table 3. Material parameters of the SWRC.

Parameters	Density (g/cm3)	Elastic Modulus (MPa)	Poisson Ratio (-)	Yield Strength (MPa)
Value	7.85	6000	0.3	100

. Additionally, the *AUTOMATIC_GENERAL contact was defined to simulate the friction effect between the wire ropes, with friction coefficients FS = 0.6 and FD = 0.6. The steel cable ties and fixtures were defined as elastic materials (*MAT_ELASTIC), whereas the SWRC was defined as an elastic-plastic material (*MAT_PLASTIC_KINEMATIC). Based on the experimental curve data from tension and compression tests, the material parameters of the steel wire rope were obtained through iterative inversion calculations. The corresponding material parameters are listed in Table 3.

Figure 8 shows the numerical and experimental force-displacement curves under axial compression and tensile tests. Good consistency is observed during both loading and unloading stages. For the compression test, the absolute error between the experimental peak load (11.24 kN) and the simulated value (10.64 kN) is 0.6 kN, corresponding to a relative error of 5.3%. The total deformation energy shows a absolute error of 71.7 J (6.5% relative error). For the tensile test, the experimental peak load (49.73 kN) shows a relative error of 3.9% compared to the simulated value (51.70 kN). The total deformation energy deviates from the experimental value by 184.35 J (7.1% relative error). These results demonstrate that the material parameter set is applicable across different loading conditions.

3.2. Numerical Model of the FACR

As shown in Figure 9, the finite element model of the FACR incorporates the previously described SWRC model as the inner core, which is encased by an outer rubber matrix discretized with solid elements, with element dimensions of approximately ~10 × 10 × 10 mm³. The fixtures are also represented by solid elements, with dimensions identical to those used in the experiments. The *AUTOMATIC_BEAMS_TO_SURFACE contact was defined to simulate the wire rope–rubber contact, using FS = 0.15 and FD = 0.1. The rubber matrix is described by the Ogden hyperelastic material model (*MAT_OGDEN_RUBBER). The material parameters were inversely calibrated via an iterative procedure using the experimental curves shown in Figure 5. The calibrated values are presented in

Table 4. Material parameters of the rubber.

Parameters	Density (g/cm3)	Poisson Ratio (-)	Prony Series (-)	G (MPa)	SIGF (MPa)	μ1 (MPa)	μ2 (MPa)	μ3 (MPa)
Value	1.25	0.499	2	50	0.2	0.9	−0.18	0.09
Parameters	α1 (-)	α2 (-)	α3 (-)	g1 (MPa)	β1 (-)		g2 (MPa)	β2 (-)
Value	1.0	−3.0	8.5	0.4	1.5		0.15	0.005

.

To validate the accuracy of the material model parameters, two additional cyclic tensile tests with different displacement amplitudes (80 mm and 160 mm) were used to compare with the model predictions. As shown in Figure 10, for the three displacement levels (80 mm, 160 mm, and 200 mm), the prediction errors of the peak force using this material model are 4.3%, 14.6% and 5.9%, respectively.

To further assess the predictive capability of the model, the full-field strain distributions extracted from the numerical simulation at a displacement of 200 mm were compared with the DIC measurements. As shown in Figure 11 and Figure 12, good agreement is observed between the numerical and experimental strain fields. These results confirm that the developed numerical model of the FACR is capable of capturing the complex interaction mechanisms inherent in the composite structure.

3.3. Energy Dissipation Mechanism of the FACR

Figure 13 presents the internal energy time-history curves of the two constituent components of the FACR: the inner SWRC and the outer rubber matrix, which can be used to analyze its energy dissipation characteristics during deformation.

For each component, The peak values of the internal energy curves correspond to the absorpted energy at the maximum displacement (t = 2.5 s). Both the SWRC and the rubber matrix absorb considerably more energy under tension than under compression. Under compression, the absorpted energy of the outer rubber (2.38 kJ) is approximately 2.22 times that of the SWRC (1.07 kJ); under tension, the corresponding ratio is 1.56 (5.36 kJ vs. 3.44 kJ). These results indicate that the outer rubber plays a more prominent role in energy absorption.

The final values of the internal energy curves (t = 5 s) represent the dissipated energy during deformation, whereas the difference between the peak and final values corresponds to the recoverable deformation energy. Under both compression and tension, the outer rubber dissipates a large fraction of its deformation energy (86.54% in compression and 65.51% in tension). In contrast, the SWRC dissipates only 9.36% under compression, with this fraction rising significantly to 47.11% under tension. This pronounced difference is likely attributable to the restraining effect of the fixture: under tensile loading, the steel wire rope in the vicinity of the fixture undergoes substantial plastic deformation.

From a structural-functional perspective, the SWRC acts as the load-bearing skeleton of the FACR, imparting the necessary rigidity and stability. The outer rubber matrix, in turn, not only provides corrosion resistance but also substantially enhances the overall energy absorption efficiency through its viscoelastic dissipation. On the basis of the above energy dissipation analysis, the structural parameters and optimization of the FACR will be further investigated.

4. Parameter Analysis of the FACR

4.1. Effect of Cross-Sectional Ratio

In current engineering practice, the cross-sectional ratio between the inner SWRC and the outer rubber matrix of the FACR is determined largely empirically, which constrains the achievement of optimal mechanical performance. This section numerically investigates the influence of the cross-sectional ratio on the mechanical response of the FACR. Configurations with different cross-sectional ratios were obtained by changing the number of SWRC layers ($n$ = 0 to 6). Specifically, $n$ = 0 corresponds to the pure rubber matrix control group, and the proportion of SWRC within the cross-section increases with the layer count (Figure 14). Both tensile and compressive simulations were performed on the seven configurations, yielding a total of 14 loading cases as summarized in

Table 5. Parameters of the FACR configurations.

Simulation Groups	Number of Steel Wire Ropes	Loading Type	Loading Speed
$1(n=0$)	0	Compression	80 mm/s
		Tension
$2(n=1$)	1	Compression
		Tension
$3(n=2$)	3	Compression
		Tension
$4(n=3$)	6	Compression
		Tension
$5(n=4$)	10	Compression
		Tension
$6(n=5$)	15	Compression
		Tension
$7(n=6$)	21	Compression
		Tension
$1(n=0$)	0	Compression
		Tension

.

The resulting force-displacement curves are shown in Figure 15, while the peak forces and energy dissipation values over the entire loading history are compared in Figure 16. As shown in Figure 15, the pure rubber ring displays only a weak tension-compression asymmetry, whereas the incorporation of the SWRC markedly amplifies this asymmetry. Figure 16a further reveals that the number of SWRC layers exerts a pronounced influence on the tensile mechanical response. Under axial tension, the peak force initially increases with the layer count and then stabilizes at a high level. The maximum value of 235.0 kN is reached at $n=3$, corresponding to a 562% increase over the pure rubber configuration ($n=0$); further increases in layer count do not lead to a significant decline, with the peak force remaining essentially stable. In contrast, the compressive response is only weakly sensitive to the layer count, with the peak force staying within a narrow range of 30.9–35.5 kN (variations below 15%).

The energy dissipation characteristics (Figure 16b) further point to a structural optimum. As the layer count increases from 0 to 3, the tensile energy dissipation rises steadily from 3503.8 J to 8569.0 J, corresponding to an increase of 144.7%, whereas the compressive dissipation remains relatively stable. This indicates that a three-layer SWRC configuration maximizes the tensile energy absorption efficiency without significantly compromising the compressive performance. When the layer count exceeds three, the tensile dissipation starts to decline, falling to 6315.3 J at six layers (a 26.3% reduction relative to the peak value). Concurrently, the compressive dissipation decays more markedly, reaching 2226.9 J at six layers—a decrease of 36.1% compared with the pure rubber ring.

Cross-validation of these results confirms that the three-layer SWRC configuration achieves the optimum compromise between axial peak load capacity and energy dissipation.

4.2. Layer-Dependent Mechanical Response Mechanism

Given that the number of SWRC layers exerts a more pronounced influence on the mechanical response of the FACR under tension, the tensile condition is selected herein for mechanistic analysis to elucidate the structural optimization principles. The von Mises stress distributions of the SWRC at the maximum displacement are extracted for simulation groups 2–7 (corresponding to $n=1-6$) under axial tension, as shown in Figure 17.

Analysis of the stress distributions in Figure 17 reveals that the single-layer configuration exhibits global stress saturation, with the entire coil approaching its yield stress. In configurations with two or more layers, the innermost layer consistently dominates the load-bearing response; the stress level decreases markedly from the inner to the outer layers, and the outer layers contribute very limited load-bearing capacity. This leads to a substantial increase in material redundancy, while simultaneously reducing the volume of the rubber matrix and consequently impairing the overall energy dissipation capability. To further characterize the mechanical response of individual SWRC layers under identical displacement levels, finite element models of a single wire rope coil from layers 1 to 6 were constructed, using the same fixture constraints as those in the actual tests (Figure 18a). A loading speed of 80 mm/s and a maximum displacement of ${\mathrm{u}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=100$ mm were applied; the resulting load–displacement curves are presented in Figure 18b. The nominal stiffness ${\mathrm{K}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}$, defined as ${\mathrm{K}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}={\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}/{\mathrm{u}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is summarized in

Table 6. Mechanical response parameters of SWRCs at different layers.

Category	First Layer	Second Layer	Third Layer	Fourth Layer	Fifth Layer	Sixth Layer
$\mathrm{d}$ (mm)	448	504	560	616	672	737
${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (kN)	3.43	1.90	1.01	0.59	0.38	0.26
${\mathrm{K}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}$ (kN/mm)	0.0343	0.0190	0.0101	0.0059	0.0038	0.0026
Relative Stiffness (%)	100%	55.4%	29.4%	17.2%	11.15%	7.6%

, with the relative stiffness normalized to that of the first layer.

Correlating the load–displacement curves in Figure 18 with the nominal stiffness parameters in Table 6 demonstrates that the nominal stiffness decreases significantly with increasing layer number (i.e., with increasing coil diameter). From the first to the third layer, the stiffness drops by up to 70%, while from the fourth to the sixth layer it remains at a consistently low level, representing only 20% to 5% of the first-layer stiffness. This trend indicates that an excessive number of layers—corresponding to an overly large variation in coil diameter—hinders coordinated load sharing among the SWRC layers, thereby pointing the way toward an optimal design of the FACR.

4.3. Optimization of Steel Wire Rope Arrangement

To enhance the structural efficiency of the FACR, this section optimizes the steel wire rope arrangement based on the mechanical response mechanism identified above and compares the resulting configuration with the original one. The number of SWRC layers is reduced from six (21 wires) to three (6 wires), and a new two-layer (6 wires) cross-sectional layout is further proposed, in which the proportion of the inner-layer SWRC is maximized, as illustrated in Figure 19. The numerical analyses adopt the same loading protocol and boundary conditions as those used in the experiments to ensure comparability; the results are presented in Figure 20.

As shown in Figure 20, the mechanical response of the three layout configurations differs only marginally under axial compression. Under tensile loading, however, the new steel wire rope arrangement markedly enhances the performance of the FACR. Compared with the original 6-layer and 3-layer distributions, the new configuration attains peak tensile capacities that are 2.0 and 1.8 times as high, and energy dissipation values that are 1.9 and 1.4 times as large, respectively. By reconfiguring the spatial distribution of the SWRC, this optimized design substantially improves material utilization efficiency while reducing steel consumption, thereby significantly strengthening the mechanical performance of the FACR.

5. Conclusions

This paper systematically examined the mechanical performance of a multi-layer steel wire rope–rubber composite FACR through experimental characterization and numerical modeling. Parametric studies elucidated the effect of the cross-sectional ratio and the underlying layer-dependent mechanisms, leading to an optimized wire rope arrangement. The key findings are summarized as follows:

(1)

Quasi-static tests reveal that the rubber matrix plays a critical role in enhancing both load-bearing capacity (increased by 200% in compression and 337% in tension) and energy dissipation (increased by 403% in compression and 620% in tension), resulting in substantial performance gains over the bare SWRC. The deformation is dominated by bending, producing opposite radial strain distributions under compression and tension, and the introduction of the SWRC significantly amplifies the tension–compression asymmetry.

(2)

The number of steel wire rope layers has a pronounced nonlinear effect on the tensile mechanical response. A three-layer configuration achieves the optimal balance between peak force (33.5 kN in compression, 186.3 kN in tension) and energy dissipation (3437 J in compression, 7934.2 J in tension), as it maximizes the effective utilization of the inner coils while avoiding the rapid stiffness decay observed in outer layers when the layer count exceeds three. Excessive layers hinder coordinated load sharing among the coils and reduce the rubber volume, thereby degrading overall performance.

(3)

An optimized two-layer steel wire rope arrangement that maximizes the inner-layer proportion is proposed based on numerical simulations. Compared with the original six-layer and three-layer designs, this configuration shows increases in peak tensile force and energy dissipation of up to 2.0 and 1.9 times, respectively, while reducing steel consumption. These numerical results suggest that optimizing material distribution according to the layer-dependent mechanism could be an effective strategy for improving anti-collision performance. However, experimental verification is still needed to confirm the actual performance of the proposed design.