A Study of the Mechanical Properties of Naturally-Inspired Tubular Structures Designed for Lightweight Applications

Abstract

Inspired by the macro/microstructures of starfish and beetle elytra, a series of bio-inspired structures (BSs) with improved comprehensive mechanical performance were proposed and fabricated. In the BS design, the principle of the branching structure of starfish was borrowed and each arm was endowed with calcified exoskeletons that can bend autonomously, enabling the starfish to move flexibly and adapt to changing shapes. At the same time, inspiration was taken from the concave-convex structure design principle of beetle elytra to enhance the internal complexity and mechanical performance of the BS. By increasing the number of polygons inside the thin-walled tubes, the performance of the BS in torsion and three-point bending was effectively improved. To evaluate the mechanical properties of the BS, finite element models were constructed using ANSYS and verified through experimental measurements. Universal testing machines and electronic torsion testers controlled by a microcomputer were used to study the compression, bending, and torsion properties of the BS. The results indicated that the differences in maximum compressive load-bearing capacity between each BS were small, and their lightweight compression values (LWN-C) remained unchanged, around 310 N/g. Increasing the number of polygons inside the thin-walled tubes effectively improved the performance of the BS in torsion and three-point bending. Moreover, the crashworthiness behaviors of the bio-inspired lightweight tube were also studied using a drop hammer impact tester. These findings have significant implications for the development of bio-inspired designs, particularly in the fields of machine arms, vehicle shafts, and bumpers, where lightweight yet high-strength structures are highly desirable.

1. Introduction

Human innovation and design are inextricably linked to nature, as it serves as an important source of inspiration and wisdom for human creativity. Ecological constructs are consistently produced with minimal energy consumption. Through long-term natural selection and evolution, organisms have been adapting to their natural environments via more complete internal organs and structures to withstand collisions and shock loads under complex conditions [1,2,3,4,5]. Therefore, humans draw inspiration from the bio-inspired structures or materials of organisms to design materials with better performance by imitating their biological morphology, structure, and control principles [6,7]. In recent years, natural biomimicry has provided direction (shape/structure) for lightweight design in various ways [8,9,10]. For instance, researchers have been inspired by biomimetic structures, such as spider webs, to design lightweight energy absorbers using fractal hierarchical hexagonal structures [11]. They found that increasing the hierarchy and fractality can improve energy absorption efficiency, resulting in better collision protection. Yang et al. extracted structural characteristics from the teeth of Odontodactylus scyllarus to create a new lightweight biomimetic double-sine wave corrugated (DSC) sandwich structure with excellent impact resistance and durability, which can be improved by adjusting the slope of the sine wave and layering [12]. Xiang et al. also drew inspiration from the internal structure of ladybug elytra to create a new biomimetic double-tube thin-walled structure (BBTS), which can improve energy absorption performance through adjustments to the thickness of the inner wall and cross-sectional configuration for better material protection [13]. In another study, Song et al. proposed four types of biomimetic foam-filled thin-walled structures based on typical straw structures (corn stalks and reeds). Nine out of twelve biomimetic samples had superior energy absorption capacity compared to their corresponding fully filled samples, and designs featuring four square holes and four conical holes achieved better energy absorption effects [14]. These biomimetic designs are based on the structural features and shapes of biological organisms and involve principles like hierarchy, fractals, sine wave corrugations, multi-channel structures, foam filling, and cavity design. Applying these principles through material selection, structural optimization, and process improvement can ultimately lead to better performance and results.

Owing to its advantages of light weight, low manufacturing cost, and high energy absorption efficiency [15,16,17,18], lightweight structures, especially thin-walled tube structures, have become an important trend in the development of modern industrial technology. They are widely used in aerospace, automotive and military equipment, among other fields [19,20,21]. For example, Song et al. designed a variable thickness structure (VTS) inspired by the thickness and node spacing gradient in bamboo growth direction and studied its energy absorption performance. The results demonstrated that the optimal VTS outperformed the circular tube in terms of energy absorption, with an improvement of 7.48% in crushing force efficiency and a 19.3% reduction in weight [22]. Hu et al. studied biomimetic graded-circle thin-walled structures under plane extrusion load through drop hammer tests, numerical simulations, and theoretical analysis. Inspired by the microstructure of bamboo vascular bundles, they proposed a biomimetic honeycomb tube-nested structure (BHTNS) and found that the specific energy absorption of BHTNS reached up to 29.3 J/g, providing a reference for efficient energy absorber design [23]. Zhang et al. proposed a set of biomimetic multi-cellular tubes (BMCT) with quadrilateral, hexagonal, and octagonal cross-sections, constructed by filling cylindrical tubes into different positions of the multi-cellular tubes. The results indicated that the sixth octagonal BMCT (O-BMCT-6) had the best impact performance and could be used as an energy absorber [24]. Ma et al. designed a biomimetic multi-cellular corrugated tube consisting of two parts: inner ribs and corrugated tube inserted into the inner ribs. The results demonstrated that the proposed tube had good crush resistance compared with traditional straight tube with the same inner ribs [25].

Thin-walled tubes are widely used in engineering applications due to their lightweight, cost-effectiveness, and high strength-to-weight ratio. They find application in various fields such as aerospace, automotive, and civil engineering, for structural components, fluid transport, and energy absorption applications [26,27]. However, traditional designs of thin-walled tubes often result in suboptimal performance, particularly in terms of crashworthiness. Therefore, there is a growing interest in exploring novel approaches, such as biomimicry, to improve the mechanical properties and performance of thin-walled tubes. The study of natural structures and systems can provide valuable insights into how to design lightweight yet robust structures with superior mechanical properties. However, despite exhibiting excellent characteristics in the field of energy absorption, previous studies focused mainly on crashworthiness performance and did not pay sufficient attention to comprehensive mechanical properties, including compression, torsion, and bending behaviors, which dictate this performance for thin-walled structures [28,29,30]. Therefore, it is necessary to investigate the comprehensive mechanical properties of bio-inspired thin-walled tube structures to determine their potential for practical applications. In this study, we focus on the compression behavior of the thin-walled tube inspired by the elytra structure of the leaf beetle and the five-arm structure of the starfish. We believe that our research will provide crucial insights into the design of lightweight and highly efficient structures with the enhanced mechanical performance required for diverse engineering applications.

Starfish (genus Asterias) and leaf beetles (Cryptocephalus aureolus) are noteworthy organisms to inspire the development of lightweight structures. The body of a starfish consists of bone pieces of different shapes and sizes that can be interconnected to form complex skeletal structures. Meanwhile, the elytra of the leaf beetle possess a special network vein structure that exhibits high specific stiffness, strength, flexibility, and strong stability [31,32,33]. The unique reticular vein structure of the elytra is a mixture of quadrilateral and hexagonal structures, contributing to their excellent mechanical properties, including high specific stiffness and specific strength. These biological characteristics can inspire new designs for composite materials, connectors, and protective equipment, improving the stability, rigidity, and impact resistance performance of structures. Starfish also exhibit unique radial or pentaradial symmetry wherein their bodies are organized around a central axis, divided into five or more parts radiating outward from the center. This symmetry structure makes starfish a hot topic in biological research and bionics engineering. Moreover, starfish exhibit significant abilities such as multi-gait movement, large deformation, and complex environmental adaptability, providing inspiration and design ideas for developing novel locomotion systems and adaptable structures.

In this study, we designed a series of bio-inspired structures (BSs) informed by the Starfish (genus Asterias) and leaf beetle (Cryptocephalus aureolus). To investigate the static comprehensive mechanical behaviors of these BSs, we employed the finite element method. Furthermore, to verify the simulation results, we fabricated the proposed structures using SLA (Stereolithography Apparatus) technology with R4600 resin material. We studied the mechanical properties of different BSs and compared them with the simulation results. Finally, we discussed the impact of BSs on crashworthiness performance. Our findings have significant implications for designing lightweight structures, such as thin-walled and tubular structures (e.g., for a robot arm in aerospace engineering).

2. Materials and Methods

2.1. SEM

Starfish (genus Asterias) and leaf beetle (Cryptocephalus aureolus) used for the investigation were obtained from the Shandong and Yunnan Province, China, respectively. The leaf beetle’s body length is 16 ± 2 mm (mean ± SD, N = 5). For scanning electron microscopic examination, first, the specimens were cleaned with pure water and air dried for ~2 h. Then, the elytra of the leaf beetle were dehydrated using successive concentrations of alcohol (30%, 50%, 70%, 80%, 90%, and 100%) for about 30 min and air dried for ~1 h. Finally, all samples were coated with a gold-palladium alloy of approximately 20 nm thickness using a sputter coater and observed using SEM (TESCAN MIRA 4, Brno, Czech Republic) at 20 kV. The test specimens were maintained under a natural light cycle, at a temperature of 25 ± 2 °C and humidity of 50–70%. The field studies did not involve endangered or protected species, and no specific permission was required for the research activity at this location.

2.2. Mechanical Properties Test

2.2.1. Experimental Setup

The mechanical properties of the proposed structures were analyzed by finite element simulation under various load conditions. To validate the accuracy of the simulation results, 3D printing technology was employed to fabricate the proposed structures. Compression and bending tests were conducted using an Instron-5566 universal testing machine, while torsion tests were performed using a CTT500 microcomputer-controlled electronic torsion test machine. The compression tests were carried out at a loading displacement rate of 1 mm/min, and force-displacement curves were obtained. For the 3-point bending tests, a CMT5105 electronic universal testing machine with a loading displacement rate of 2 mm/min was used, with a setup consisting of a 20 mm diameter compression head and a 60 mm span. The crashworthiness behaviors of the proposed structures were evaluated using a drop impact tester (DIT302A-TS, Shenzhen Wance, Shenzhen, China).

2.2.2. Structural Crashworthiness Indicators

To evaluate the crashworthiness of the bio-inspired structures, it is important to define appropriate indicators. In this study, several parameters were used to assess the energy-absorption performance of the proposed structures, including total energy absorption (EA), specific energy absorption (SEA), mean crush force (P_m), maximum crush force (P_max), and crush load efficiency (CLE) [34,35].

EA represents the overall energy absorbed by the structure during impact deformation, indicating its capacity for absorbing energy. This value can be obtained by integrating the crush force-displacement curve using the following formula:

$$EA={\displaystyle {\int }_{\mathrm{\Omega }}E\left(\epsilon \right)}d\mathrm{\Omega }$$

(1)

where $E\left(\epsilon \right)$ represents the strain energy density of the structure, and $\mathrm{\Omega }$ represents the volume of the structure.

Specific energy absorption (SEA) is used to quantify the energy absorbed by the structure per unit mass, which can be calculated as:

$$SEA=\frac{EA}{M}$$

(2)

where M is the total mass of the structure.

The mean crush force P_m is defined as the average compression force resisted by the energy-absorber during the total plastic deformation process as expressed by:

$$P_m=\frac{E(d)}{d}$$

(3)

The energy absorbed at a given impact distance is denoted as E(d), with d representing the corresponding distance of impact.

The maximum crush force (P_max) is an indicator of the highest crushing force that occurs during the effective compression stroke of thin-walled tubes in axial-impact situations. As it is an injury-based metric, larger P_max values can result in greater deceleration and increase the risk of injury or damage to occupants. Therefore, it is imperative to minimize P_max or at least ensure it remains within safe levels.

CLE is used to measure load uniformity (i.e., the higher the CLE, the more efficient the structure). CLE can be calculated as the ratio of P_m to P_max:

$$CLE=\frac{P_m}{P_{\max }}$$

(4)

3. Results and Discussion

3.1. Bio-Inspired Tubes Design

The elytra of the leaf beetle have excellent mechanical properties, including high specific stiffness and specific strength. Its elytra are not only light, but also flexible with strong stability. This is mainly because they have a special reticular vein structure, which is a mixture of quadrilateral and hexagonal structures (Figure 1g,i).

Starfish, also known as starfish, exhibit a unique type of symmetry known as radial symmetry or pentaradial symmetry. This means that their body plan is organized around a central axis and can be divided into five or more equal parts radiating out from the center. This differs from bilateral symmetry, which is characterized by a body plan that can be divided into two mirror-image halves along a single plane. As one of the most familiar marine invertebrates, the starfish has a completely pentaradial symmetrical structure, with its body being flat and exhibiting mostly five-radial symmetry. The wrist of a starfish is wider near the central disc and tapers towards the end, with only a few arms being similar in size. While the length of the wrist generally ranges between 1–3 times the diameter of the central disc, some wrists can be 4–5 times longer. The “five” arm skeleton structure of a starfish provides support for its body. Even if an accident occurs and one of the arms breaks, the remaining structure can still support the body of the starfish as long as the central disk exists, providing strong stability and mechanical properties. In addition to its unique symmetrical structure, the starfish exhibits remarkable abilities such as multi-gait locomotion, large deformation, and complex environmental adaptability. These characteristics make starfish fascinating subjects for biological research and biomimetic engineering.

Driven by the above promising findings, according to the special structural characteristics of leaf beetle and starfish, a series of BSs were proposed, as illustrated in Figure 1k. This study aims to investigate the mechanical properties, crushing behaviors, and damage characteristics of these BSs under different mechanics and high-cycle impact conditions. In this present study, the total axial length is 100 mm, and the diameter is 60 mm for each BS. The thickness of all the BSs is 2 mm, and they have the same mass.

3.2. Mechanical Characteristics of BSs

To investigate the mechanical properties of the proposed structures, ANSYS, a commercial finite element software, was utilized to perform simulations under different loading conditions, such as compression, torsion, and bending. The 3D printer used in our study is the LianTai 3D Lite600, which uses SLA (Stereolithography Apparatus) technology for printing. It has a print platform size of 800 × 800 × 600 mm and a layer thickness range of 0.05–0.25 mm. Additionally, it has a high positioning accuracy of ±0.008 mm per layer and excellent printing precision, with a tolerance of ±0.1 mm for prints measuring up to 100 mm for larger prints. As R4600 resin material was used to manufacture the actual samples for 3D printing, its material properties were used in all simulations. Material properties of R4600 resin material are listed in

Table 1. Material properties of R4600 resin material.

Material Name	R4600 Resin Material
Density (g/cm3)	1.3
Young’s modulus (MPa)	2600
Poisson’s ratio	0.42
Elongation at break	10%
Tensile strength (MPa)	47

, as provided by the manufacturer. Additively manufactured tubes are illustrated in Figure 2.

Lightweight numbers (LWN) were used to evaluate the lightweight efficiency of each BS, which can be expressed as follows:

$$\mathrm{LWN}=\frac{\mathrm{Maxload}}{\mathrm{Weight}}$$

(5)

Further, LWN-C refers to compression, LWN-T is torsion, and LWN-B refers to bending.

3.3. Compressive Properties

The compressive properties of the proposed structures were investigated using both finite element analysis (FEA) and experimental methods. For the simulation, quasi-static compression was applied to the bottom surface of different structures while a displacement-controlled loading was directed downward along the central axis at the upper end. Grid convergence tests were conducted simultaneously in order to obtain force-displacement curves and maximum compressive loads [36,37]. To ensure the accuracy of the FEA results, a hexahedral element (Solid186) of 1 mm size was used in the simulation. The FEA model consisted of 595,700 nodes and 101,700 elements. In the experimental setup of our compression tests, friction-free boundary conditions were employed to ensure a uniaxial stress state during loading. Specifically, polyethylene sheets were interposed between the sample and the loading platens to minimize lateral confinement near the loading platens. This approach was adopted to accurately measure the compressive strength and avoid any potential influence on the stress distribution within the sample due to frictional forces at the boundary. It is widely acknowledged that the type of contact between the specimen surface and loading surface plays an instrumental role in the stress distribution, behavior under loading, and ultimately the compressive strength of the sample. For instance, using a rough surface, such as fine-grained sandpaper, at the loading platen as a boundary can result in increased friction and hinder the lateral expansion of the sample, thus inducing a confining stress near the loading platen. Moreover, placing a rough surface as a boundary condition may alter the mode of failure of the sample under certain circumstances. Conversely, adopting friction-free boundary conditions can mitigate these issues and help achieve a more accurate characterization of the compressive properties of the sample [38,39]. Taking BS-7 as an example, the compression finite element model is illustrated in Figure 3. Because the quality of the simulation models in this study is the same, according to the definition of the lightweight coefficient, there is only a one-coefficient relationship between the maximum load and lightweight coefficient, and thus the simulation results only yield the maximum load value (

Table 2. Comparison between compression data from experiments and simulations.

Type	Simulation/Test Values	Mass (g)	Maximum Compressive Load (N)	LWN-C (N/g)
BS-1	Simulation values	103.42	32,100	310.38
BS-2	Simulation values	103.42	31,875	308.21
BS-3	Simulation values	103.42	32,059	309.99
BS-4	Simulation values	103.42	32,128	310.66
BS-5	Simulation values	103.42	32,097	310.36
BS-6	Simulation values	103.42	32,106	310.44
BS-7	Test sample #1	103.44	32,317.29	312.43
	Test sample #2	103.43	31,380.76	303.40
	Test sample #3	103.43	31,754.47	307.01
	Simulation values	103.42	32,113	310.51

).

Figure 4 depicts the compressive properties of different BSs. From Figure 4a, it can be found that with the increase of displacement, the compression forces of the three sample values and the simulated values of BS-7 gradually increase, and then reach the maximum value when the displacement is about 4 mm, and finally gradually decline; that is, they all have the same compression change trend. Table 2 illustrates that the FE analysis results of BS-7 agreed with the test results well, and the maximum error is less than 8%. All the results demonstrate that the designed FE model is sufficiently accurate with the experiment samples. This indicates that the derived theoretical model can effectively predict the compression performance of other BSs. The finite element model can effectively and accurately reflect the experimental data and can be used for further study.

It can be observed in Figure 4b that when the displacement is close to 2 mm, the compression force of all BS theoretical models increases with the increase of displacement, and then the failure phenomenon occurs successively. It is obvious that BS-2 is the first to be damaged. Compared with other BSs, the damage caused by BS-2 is the most serious with the increase of placement, while the damage caused by other BSs is not much different. In particular, Figure 4c clearly illustrates the compression force corresponding to the failure of each BS. It can be found that the difference between the maximum bearing compression force of each BSs is very small, and according to Table 2, the LWN-C value of each BSs is basically the same, all of which are maintained at about 310 N/g. In addition, compared with other structures, BS-4, BS-6, and BS-7 have relatively large maximum bearing capacity, and the maximum bearing capacity of BS-4 can reach 32,128 N, while the minimum bearing capacity of BS-2 is 31,875 N. The reason is that compared with BS-2, BS-4, BS-6, and BS-7 has multilayer quadrilateral or hexagonal composite structures, which makes their compression performance superior. It can be observed from Figure 5 that BS-7 has a relatively stable deformation, and a big fold is generated after compression.

3.4. Torsion Properties

One end of the structure was fully constrained with six degrees of freedom, while angular displacement was applied to the other end. To obtain the torsional load, the reaction torque of the end face was fixed once the torsion angle was determined. We employed a similar testing approach to the compression test in our torsion experiment. The specimen was placed into the torsion instrument and loaded at a constant angular displacement rate of 1 degree per second until failure occurred. To minimize the impact of friction on the experimental results, we utilized the same friction-free boundary conditions as we did with the compression test and placed polyethylene sheets between the sample surface and the loading platen. Figure 6a demonstrates the torque-torque angle curve of the three samples and theoretical model of BS-7, which indicates that the torque increases with the increase in torque angle. When the torque angle reaches 22–23°, the torque of the BS-7 structure reaches its maximum, and then drops sharply. The experimental sample and theoretical calculation exhibit the same trend when the torsional angle is ≤20°, and the torque values are very close, which indicates that they hold a very small error. Thus, the theoretical model effectively predicts the torque values of actual BSs. Figure 6b illustrates the torque–torque angle characteristic curve of different BSs. The torque of all BSs increases with the increase in the torque angle. Notably, compared with other BSs, the torque of BS-2 is significantly lower than that of other BSs, and it is also the first to cause damage. This indicates that the internal support structure of BS-2 reduces the torsional strength of thin tubes. Moreover, the torques of BS-3 and BS-5 of a single-layer structure are lower than those of BS-4, BS-6, and BS-7 of a double-layer structure. Figure 6c clearly demonstrates the torsional strength of different BSs. BS-2 has the lowest torsional strength, only 63.71 N · m, and BS-4 has the highest torsional strength, 126.64 N · m. The torsional strength of BS-3 and BS-5 is close to that of BS-1, and slightly better than that of BS-1. Compared with BS-1, their torsional strength is increased by 0.5% and 2.2%, respectively. This indicates that adding a polygonal structure inside the thin tube can improve its torsional strength.

Notably, the torsional strength of BS-4, BS-6, and BS-7 is higher than that of BS-3 and BS-5, and their values are similar. The internal structure of BS-3 is a single quadrilateral, while that of BS-4 makes up two quadrilaterals. The torsional strength of BS-3 is 18% lower than that of BS-4. The internal structure of BS-5 is a single hexagon, while the internal structure of BS-6 includes two hexagons. The torsional strength of BS-6 is 12.1% higher than that of BS-5, and its torsional performance is better than that of BS-5. Therefore, increasing the number of polygonal structures inside the thin tube effectively improves the torsional performance. More importantly, BS-4 has the highest torsional strength, which is 3.4% and 2.1% higher than BS-6 and BS-7, respectively. BS-6 uses two adjacent hexagons to increase torsional strength. Although hexagons are more regular and symmetrical than quadrilaterals, each side of a hexagon is longer, and the angles of the hexagon are smaller, which may lead to excessive stress concentration and affect the torsional strength of the material. For BS-7, its internal structure is composed of a quadrilateral and an adjacent hexagon. Although this design can improve the stability of the tube, the two shapes are quite different, which may cause uneven stress distribution during torsion and reduce the torsional strength of the tube. Therefore, BS-4, with two adjacent quadrilaterals, can maintain a certain degree of symmetry while making full use of space to enhance the torsional strength and stability of the tube, making it superior to designs that use hexagons or combinations of different shapes.The torsional strength of BS-4′s structure is 18.6% higher than that of BS-1, indicating that it can effectively improve the torsional strength of thin tubes.

Figure 6d illustrates the actual torsion performance test results, where the final thin tubes are ultimately broken. The torsion test was conducted at a constant angular displacement rate of 1 degree per second until failure.

Table 3. Comparison of experimental and simulated torsion data.

Type	Simulation/Test Values	Mass (g)	Maximum Torsional Load (N·m)	LWN-T (N·m/g)
BS-1	Simulation values	103.42	106.8	1.03
BS-2	Simulation values	103.42	63.71	0.62
BS-3	Simulation values	103.42	107.35	1.04
BS-4	Simulation values	103.42	126.64	1.22
BS-5	Simulation values	103.42	109.16	1.06
BS-6	Simulation values	103.42	122.42	1.18
BS-7	Test sample #1	103.38	129.76	1.26
	Test sample #2	103.46	128.98	1.25
	Test sample #3	103.45	129.01	1.25
	Simulation values	103.42	124.02	1.20

illustrates that the maximum bearing torsional load error between the sample and the simulated value of BS-7 is within 4.6%. The experimental results are consistent with the simulation. The maximum torsional load carrying capacity of BS-2 obtained by simulation is significantly lower than that of other BSs, and the LWN-T value is also the lowest at 0.62 N · m/g. The difference between the maximum torsional load carrying capacity and LWN-T value of BS-3 and BS-5 is very small. Compared with BS-1, the maximum torsional load carrying capacity and LWN-T value of BS-3 and BS-5 are increased by 0.97% and 2.9%, respectively. The bearing capacity of BS-4, BS-6, and BS-7 outperforms other BSs, and the LWN-T value is likewise higher. The LWN-T value of BS-4 is the highest, at 1.22 N · m/g, which is 3.3% and 1.6% higher than that of BS-6 and BS-7, respectively. This indicates that BS-4 has good torsional performance across the seven BSs. Notably, the LWN-T value of BS-4 is 17.3% higher than that of BS-3, and the internal structure of BS-4 contains two quadrangles, whereas that of BS-3 is one quadrangle. The LWN-T value of BS-5 is 11.3% higher than that of BS-6, and the internal structure of BS-5 contains two hexagons, while that of BS-3 has one hexagon. This demonstrates that increasing the number of polygons inside the thin tube effectively improves the torsional performance.

3.5. Three-Point Bending Properties

During the three-point bending tests, the two ends of the bio-inspired structures (BSs) were fixed, and a displacement-controlled loading was applied to the middle portion. The loading was performed in 10 steps with a step length of 0.1 mm. Figure 7 presents the finite element model used in the three-point bending tests, which employed the shell 181 cell type and refined the contact area of the mesh.

Figure 8a illustrates the comparison between experimental results and the simulation of BS-7. The bending load of the three samples of BS-7 and the theoretical model exhibit a similar overall trend, rising with the increase in displacement, declining briefly when the displacement is 7–9 mm, and then increasing gradually. When the bending load of the BS-7 structure reaches its maximum, it starts to drop sharply, and damage occurs. Figure 8b illustrates the bending load displacement simulation curve of different BSs. The bending load of all BSs structures increases with the increase in displacement, and the bending loads reach the maximum when the displacement is 32–35 mm, and then starts to drop sharply. Evidently, BS-1 and BS-2 are damaged first, and the maximum bending load is small. Therefore, the three-point bending characteristics are also poor compared with other BSs. The maximum bending load of BS-4, BS-6, and BS-7 is large, and three-point bending characteristics are good.

Figure 8c clearly demonstrates the bending strength of different BSs. The minimum bending strength of BS-2 is 3684.3 N, and the maximum bending strength of BS-4 is 5339.8 N. The bending strength of BS-3 and BS-5 is close to that of BS-1, which increased by 5.3% and 8%, respectively. Moreover, the internal structure of BS-3 is a single quadrilateral, the internal structure of BS-5 is a single pentagon, and there is no polygon in BS-1, indicating that the addition of the polygon structure can improve the bending strength of thin tubes. Compared with BS-4, the bending strength of BS-3 is lower than that of BS-4, and the bending strength of BS-4 is 33.8% higher than that of BS-3. The internal structure of BS-3 is a single quadrangle, while that of BS-4 is two quadrangles. The bending strength of BS-6 is 25.1% higher than that of BS-5. The internal structure of BS-6 is two hexagons, while the internal structure of BS-5 is a single hexagon. According to Zhang et al. [11], the difference in bending strength between BS-6 and BS-5 can be attributed to the impact of fractal configuration and geometric shape on material properties. The study demonstrated that fractal configuration and sub-hexagon length have a strong influence on energy absorption, while Song et al. [40] and Lu et al. [41] found that hexagonal honeycomb structures have stronger bending performance. Therefore, BS-6 adopts an internal structure consisting of two hexagons, which is superior to BS-5’s single hexagon structure under the same conditions. This indicates that the fractal configuration of BS-6 is better and its internal structure is more complex, resulting in better material properties, especially in terms of bending strength. This demonstrates that the bending strength can be improved effectively by increasing the number of polygonal structures inside the thin tube. The bending strengths of BS-4, BS-6, and BS-7 are similar, whereas the bending strength of BS-4 is the highest, 4.2% and 5% higher than that of BS-6 and BS-7, respectively. This indicates that the bending strength of the two quadrangle structures in BS-4 is better than that of the two hexagon structures in BS-6 and the one hexagon structure in BS-7. Thus, BS-4 has better three-point bending characteristics.

Table 4. Comparison between bending data from experiments and simulations.

Type	Simulation/Test Values	Mass (g)	Maximum Bending Load (N)	LWN-B (N/g)
BS-1	Simulation values	103.42	3789.3	36.64
BS-2	Simulation values	103.42	3684.3	35.62
BS-3	Simulation values	103.42	3990.3	38.58
BS-4	Simulation values	103.42	5339.8	51.63
BS-5	Simulation values	103.42	4094.5	39.59
BS-6	Simulation values	103.42	5123.4	49.54
BS-7	Test sample #1	103.38	4769.855	46.14
	Test sample #2	103.44	4928.842	47.65
	Test sample #3	103.39	4853.417	46.94
	Simulation values	103.45	5087	49.17

presents a comparison of the bending data between experiment and simulation. The error between the simulated value of the maximum bending load of BS-7 and the actual value is within 6.6%; that is, the simulation results are in good agreement with the experimental results. BS-2 has the lowest maximum bending load, and LWN-B is 3684.3 N and 35.62 N/g, respectively, while BS-4 has the highest maximum bending load, and LWN-B is 5339.8 N and 51.63 N/g, respectively. The difference between the maximum bending load and LWN-B value of BS-3 and BS-5 is very small, 5.3% and 8.05% higher than that of BS-1, respectively. The internal structures of BS-3 and BS-5 are a single quadrilateral and a single pentagon, respectively, which indicates that the LWN-B value is improved by adding a polygon structure inside the thin tube. The LWN-B value of BS-4 is 33.8% higher than that of BS-3, and the internal structure of BS-4 is two quadrangles, while that of BS-3 is one quadrangle. The LWN-B value of BS-5 is 25.1% higher than that of BS-6, and the internal structure of BS-5 is two hexagons, while that of BS-3 is one hexagon. This illustrates that increasing the number of polygons inside the thin tube effectively improves the three-point bending performance. The LWN-B values of BS-4, BS-6, and BS-7 are relatively close, with the highest being BS-4 at 51.63 N/g, which is 4.2% and 5% higher than BS-6 and BS-7, respectively. Thus, the design of the two quadrangle structures in BS-4 outperforms that of the two hexagon structures in BS-6 and the one quadrangle and one hexagon structure in BS-7.

3.6. Crashworthiness Behaviors

In order to investigate the crashworthiness of the proposed structures, their impact resistance was assessed using a drop impact tester (DIT302A-TS, Shenzhen Wance, Shenzhen, China). The bio-inspired structures were subjected to an impact from a set height with a hammer body of a specific mass and shape. The impact resistance of the samples was then evaluated based on the experimental results obtained after impact, as illustrated in Figure 9.

The force-displacement and energy-displacement curves of various bio-inspired lightweight tube samples are displayed in Figure 10. Technical parameters of the drop impact tester (DIT302A-TS, Shenzhen Wance, Shenzhen, China) are given in

Table 5. Technical parameters of DIT302A-TS.

Model	DIT302A-TS
Maximum impact energy (J)	300
Maximum sample diameter (mm)	100
Hammer lifting speed (m/min)	8.0
Height measurement error (mm)	≤±10
Lift hammer height range (mm)	300–2000

.

Table 6. Results of impact test.

Types	Samples	Mass (g)	Impact Distance (mm)	Pmax (kN)	EA (J)	SEA (J/kg)	Pm (kN)	CLE
BS-1	#1	103.41	22.31	3.41	20.15	194.86	0.90	0.26
	#2	103.39	21.25	3.26	19.86	192.09	0.93	0.29
	#3	103.42	22.19	3.33	20.07	194.06	0.90	0.27
BS-2	#1	103.42	18.14	2.80	19.67	190.21	1.08	0.39
	#2	103.41	18.46	2.85	20.12	194.57	1.09	0.38
	#3	103.38	17.68	2.62	19.23	186.01	1.09	0.42
BS-3	#1	103.39	6.63	7.91	29.05	280.97	4.38	0.55
	#2	103.40	6.53	7.62	28.64	276.98	4.39	0.58
	#3	103.39	5.86	6.56	26.35	254.86	4.50	0.69
BS-4	#1	103.43	10.74	9.58	36.26	350.58	3.38	0.35
	#2	103.44	11.62	10.22	37.19	359.53	3.20	0.31
	#3	103.41	9.78	8.89	36.21	350.16	3.70	0.42
BS-5	#1	103.39	11.96	9.70	29.63	286.58	2.48	0.26
	#2	103.38	10.43	8.68	27.26	263.69	2.61	0.30
	#3	103.41	11.28	9.26	28.61	276.67	2.54	0.27
BS-6	#1	103.42	31.86	4.37	37.88	366.27	1.19	0.27
	#2	103.44	30.52	4.32	36.72	354.99	1.20	0.28
	#3	103.42	32.65	4.43	38.34	370.72	1.17	0.26
BS-7	#1	103.41	27.29	5.07	32.11	310.51	1.18	0.23
	#2	103.39	27.37	5.34	33.56	324.60	1.23	0.23
	#3	103.43	27.17	5.31	33.29	321.86	1.23	0.23

lists the results of the impact test. To reduce accidental errors and ensure the accuracy of the test results, three samples were made for each thin tube structure, and the impact test was carried out separately. Table 6 demonstrates that the EA and SEA of BS-4, BS-6, and BS-7 are high and similar, which indicates that their energy absorption capacity is strong. The EA and SEA values of BS-1 and BS-2 are the lowest, and their energy absorption capacity is poor. The reason for the poor energy absorption capacity of BS-1 and BS-2 is due to their lower EA and SEA values, which can be attributed to the structure of the tubes. The tube with a star-shaped outline shaped like a starfish as its main framework structure has a more stable structure because of its high symmetry, which allows for a more uniform distribution of forces inside the entire tube, reducing the risk of local overloading, as well as deformations or failures. On the other hand, the tubes designed with four-sided and hexagonal structures within the five angles based on the star-shaped main framework structure have a relatively unstable structure. This irregular structure makes it prone to generate local overloads when subjected to external forces, thereby increasing the risk of tube deformation or failure.

In addition, the CLE value of BS-3 is the highest, which indicates that its load uniformity is good. In turn, BS-3 has low EA and SEA values and poor energy absorption capacity. The CLE values of other BSs are relatively similar. BS-4 has the highest P_max, and BS-2 has the lowest P_max.

To further study the crashworthiness characteristics of thin-walled tubes, the data in Table 6 are further processed to obtain

Table 7. Crashworthiness indicators of each BS (Mean ± SD).

Types	Pmax (kN)	EA (J)	SEA (J/kg)	Pm (kN)	CLE
BS-1	3.33 ± 0.075	20.03 ± 0.150	193.67 ± 1.426	0.91 ± 0.017	0.27 ± 0.015
BS-2	2.76 ± 0.121	19.67 ± 0.445	190.26 ± 4.280	1.09 ± 0.006	0.40 ± 0.021
BS-3	7.36 ± 0.711	28.01 ± 1.455	270.94 ± 14.065	4.42 ± 0.067	0.61 ± 0.074
BS-4	9.56 ± 0.665	36.55 ± 0.552	353.42 ± 5.293	3.43 ± 0.253	0.36 ± 0.056
BS-5	9.21 ± 0.512	28.50 ± 1.189	275.65 ± 11.479	2.54 ± 0.065	0.28 ± 0.021
BS-6	4.37 ± 0.055	37.65 ± 0.835	363.99 ± 8.108	1.19 ± 0.015	0.27 ± 0.010
BS-7	5.24 ± 0.148	32.99 ± 0.771	318.99 ± 7.471	1.21 ± 0.029	0.23 ± 0

and Figure 11. Table 7 illustrates that the EA and SEA values of BS-3 are close to those of BS-5. Compared with BS-1, the EA and SEA values of BS-3 are 28.5% and 28.5% higher than that of BS-1, respectively. Compared to BS-2, the EA and SEA values of BS-3 are 29.8% and 29.8% higher than that of BS-2, respectively. This is because the internal structure of BS-3 and BS-5 is a quadrilateral and a pentagon, respectively, while the internal structure of BS-1 and BS-2 has no polygons. This demonstrates that by adding a polygon structure into the thin tube, the EA and SEA values can be increased, and the energy absorption capacity of the thin tube can be improved. Comparing BS-3 with BS-4, the EA and SEA values of BS-4 are 23.4% and 23.4% higher than those of BS-3, respectively. The internal structure of BS-4 is two quadrangles, while the internal structure of BS-3 is a quadrangle. Comparing BS-5 with BS-6, the EA and SEA values of BS-6 are 24.3% and 24.3% higher than those of BS-5, respectively. The internal structure of BS-6 contains two hexagons, while the internal structure of BS-5 is a hexagon. This demonstrates that the energy absorption capacity of the double-layer structure is stronger than that of the single-layer structure. Increasing the number of polygons in the thin tube effectively improves the energy absorption capacity. The EA and SEA values of BS-4, BS-6, and BS-7 are higher and close to those of other BSs, and their energy absorption capacity is stronger than that of other BSs, indicating that the energy absorption capacity of the double-layer structure inside the thin tube is generally superior to that of the single-layer structure. The highest value of BS-6 is 37.65 J and 363.99 J/kg respectively, and the EA value is 2.9% and 12.4% higher than that of BS-4 and BS-7, respectively, whereas the SEA value is 2.9% and 12.4% higher than that of BS-4 and BS-7 respectively. Moreover, the P_max of BS-6 is likewise low, namely 54.2 and 16.6% lower than that of BS-4 and BS-7, respectively. The CLE value is 25% lower than that of BS-4 and 14.8% higher than that of BS-7. In general, in the impact test, the design of the two hexagon structures of BS-6 outperforms that of the two quadrilateral structures of BS-4 and the one quadrilateral structure and one hexagon structure of BS-7.

4. Conclusions

This study investigated the mechanical properties and crashworthiness of a series of bionic thin-walled tubes inspired by sea stars and leaf beetles, using systematic experiments, numerical simulations, and theoretical analysis. The main findings are as follows:

(1)

The maximum compression bearing capacity of each bionic structure (BS) is similar, with a lightweight compression value (LWN-C) of about 310 N/g. BS-4, BS-6, and BS-7 have relatively high maximum bearing capacities.

(2)

Increasing the number of polygonal structures inside the thin tube can effectively improve the torsional performance of BS. The torsional strengths of BS-4, BS-6, and BS-7 are significantly higher than those of BS-3 and BS-5.

(3)

Multi-layer quadrilateral and hexagonal column structures can improve the bending performance of BS. BS-4 has the highest maximum bending load and LWN-B.

(4)

Double-layer structures inside the thin tube generally have stronger energy absorption capacity than single-layer structures. BS-4, BS-6, and BS-7 have higher EA and SEA values, indicating their better energy absorption capacity compared to other BSs.