In-plane dynamic crushing of a novel gradient square honeycomb with enhanced energy absorption Open Access

Lightweight honeycomb materials have high strengths, excellent crashworthiness, and extraordinary energy absorption properties. They are used widely in automotive, aerospace, and civil engineering.^1–8 Because of their superior energy absorption capacities, honeycomb structures have been investigated by numerous researchers. In the past several years, honeycomb structures with regular hexagonal,⁹ triangular,¹⁰ square,¹¹ and circular¹² unit cells have been investigated for in-plane and out-of-plane impacts. Over time, the functional requirements and capacities of traditional honeycombs have increased, and thus, honeycomb structures have gradually become a popular research subject. Square honeycombs have some advantages such as strong anisotropy¹³ and powerful plateau stress.¹⁴ In addition, the mechanical properties can be displayed using a simple formula.¹⁵ However, under the low- and mid-velocity impact, the drawback of the square shape is that it exhibits the worse stability that will make the obvious slippage¹⁶ appear in the honeycomb to affect the crashworthiness. In this study, a series of novel square honeycombs with fresh structures were investigated to further increase the energy absorption of square honeycomb structures.

Honeycombs are composed of unit cells arranged periodically, and the topologies of the cell elements strongly affect the mechanical properties under crushing. The original structures of traditional honeycombs can be varied as an effective route to improve their mechanical behaviors, and this has been discussed widely in many previous publications. For example, Yang et al.¹⁷ established a petal-shaped honeycomb (curved lines were added to the interior of the circular unit cell) and modified the length of the curved line to enhance the in-plane energy absorption capacity of the circular honeycomb, and He et al.¹⁸ proposed a novel circular honeycomb with a leaf-vein branched characteristic to improve the in-plane strength. In addition, Lu et al.¹⁹ and Wei et al.²⁰ presented a novel unit cell in which the fresh connection mode entered the star cell, and the mechanical properties were investigated by simulations and theoretical analysis. Similar designs^21,22 with various shapes of the unit cell wall have been established to pursue higher crashworthiness and energy absorption abilities of re-entrant hexagonal honeycombs. Furthermore, the in-plane energy absorption performance can also be increased by adding self-similar structures^23,24 and bionic designs.^25,26

There are various ways to refine the performances of honeycombs, and numerous researchers have investigated functional gradient honeycombs²⁷ in recent years. To differentiate the effects of the topological structure, gradient honeycombs have been studied by varying the arrangement of the unit cells. Graded gradient honeycombs, by combining several honeycombs with different properties, have been demonstrated to possess superior energy absorption abilities. Altering the geometric attribute in each layer (cell-wall thickness²⁸ and relative density²⁹) is a universal method to design graded honeycombs. With this design concept, Xiao et al.³⁰ performed systematic investigations and demonstrated that in-plane crashworthiness and energy dissipation were enhanced tremendously for re-entrant hexagonal honeycombs. In addition to varying the geometric attributes of the cell, changing the cellular category in each layer is another method to achieve graded capacities. With this popular concept, Li et al.³¹ experimentally examined the in-plane crushing behaviors of a functionally linear honeycomb and showed that the linear honeycomb provided better energy absorption compared to regular hexagonal honeycombs. Furthermore, Liu et al.³² and Qi et al.³³ conducted further intensive exploration, which proved that better impact-protection performance could be achieved by a gradient design.

In the above discussion, changing the topological structure and the gradient design are two effective methods to enhance the energy absorption capacities of honeycombs and refine the properties of conventional honeycombs. However, some investigations that changed the topological structure ignored the defect of the original structure to a certain extent while pursuing better crashworthiness, which made the research topic lack reasonability. Moreover, while maintaining the same size, previous studies rarely achieved the gradient design by changing the internal structure of the unit cells. In this paper, to strengthen the stability and energy absorbing property of the square cells, a novel honeycomb was established in which rods are added to the interior of the square unit cell. Subsequently, two gradient honeycombs were fabricated by changing the internal inclination angle in each layer of the novel honeycomb, and one “buffer” honeycomb was introduced based on the bionic design. These fresh designs not only resolve the default of traditional honeycombs but also improve the in-plane compression properties. Then, the effects of the geometric configuration, impact velocity, inclination angle, number of buffer strips on the dynamic unit-mass strain–stress curve, and energy absorption properties of these novel honeycombs were studied. The novel design concept provides a reference for the design of lightweight energy absorbers with enhancing crushing protection capacities under dynamic crushing.

From the structural characteristics, the square cell belongs to the constantly variable system. When the square honeycomb (SH) sustains the mid- and low-velocity impact, two vertical cell walls slip outward due to the slight inertial effect, which produced no buckling. The slippage caused the performance of the square honeycomb to significantly decrease (Figs. 7–9 and 11). Thus, it is so crucial to promote the stability of a unit cell.

In this study, the novel square honeycomb (NSH) was created. Point O on the central axis of the square unit cell was defined, and rods connected point O to the four vertices, forming triangles in the interior of the NSH to improve the structural stability of the cell. The schematic diagram and geometric parameters of the NSH are shown in Fig. 1(a), where l and t denote the lengths of the cell wall of the NSH and the thickness of the cell wall, respectively. The inclination angle α in the interior of the cell can be introduced to represent the different positions of point O, and the smallest and largest values were α = 180° (NSH2) and α = 53°, as shown in Fig. 1(b).

During the design process, the performance can also be improved based on bionics. The introduction of buffer strips means that the initial peak stress of the honeycomb is conspicuously reduced under the unexpected impact. The B cell with the weaker yield strength is added in the honeycomb specimen that is composed of the A cell. In the dynamic crushing, the B cell first becomes damaged to alleviate shock, and the A cell buckles to absorb most energy subsequently. The clear division of labor makes the honeycomb acquire excellent crashworthiness. Herein, by using three types of NSHs (inclination angles α = 180°, 53°, and 90°), a buffered square honeycomb (BSH) was developed. The biomimetic process of BSHs is shown in Fig. 2, in which the structural characteristics of different unit cells are established such that the honeycomb is y-symmetric.

By varying the inclination angle α for four layers, a gradient square honeycomb (GSH) can be established, as shown in Fig. 3. In the present study, two types of gradient square honeycombs (GSH1 and GSH2) with a total of 20 layers (N = 20) are discussed. For the first gradient square honeycomb (GSH1), the inclination angle α decreased gradually from the top (α = 180°) to the bottom (α = 53°). In the meantime, an opposite regularity for the inclination angle α was applied for the second gradient square honeycomb (GSH2).

For a square honeycomb with wall thickness t and wall length l, the relative density (Δρ) can be calculated as follows:³⁴ 

where Δρ is the relative density of the honeycomb, ρ* denotes the density of the honeycomb, and ρ_s is the density of the matrix material.

For the novel square honeycombs (NSH1 and NSH2), gradient square honeycombs (GSH1 and GSH2), and buffered square honeycomb (BSH), whose dimensions were the same as those of the square honeycomb (SH), the relative density (Δρ) can be calculated as follows:³⁵ 

where l_i and t_i represent the wall length and wall thickness of the ith unit cell, respectively, and L₁ and L₂ denote the length and width of the honeycomb, respectively.

According to Eq. (2), the relative density of the gradient square honeycombs (GSH1 and GSH2) and the buffered square honeycomb (BSH) is defined as follows:

where Δρ_GSH and Δρ_BSH represent the relative density of the GSH and BSH, respectively.

The systematic investigations on the energy absorption behaviors of the novel gradient honeycombs under dynamic impact conditions were performed using the nonlinear finite element software ABAQUS/Explicit. The novel gradient honeycomb with dimensions of L × H × Z was simulated, in which L and H are the horizontal and vertical lengths of the novel gradient honeycomb, respectively, and Z is the out-of-plane length of the honeycomb, as shown in Fig. 4. The novel gradient honeycomb is composed of 20 cells in the horizontal direction and 18 cells in the vertical direction. In the model, the length of the cell wall was l = 5.4 mm, the out-of-plane thickness of the honeycomb was 1 mm, and the thickness of the cell depended on the relative density (unless stated otherwise, the relative density was Δρ = 0.15).

In the honeycomb, the unit cells were discretized using shell elements (S4R), and an average element size of 0.5 mm was adopted for the novel gradient honeycomb to ensure convergence and calculation precision. The surface-to-surface contact criterion was applied to simulate the contact behavior between the rigid plate and the novel gradient honeycomb, and the frictional coefficient was set as 0.2. Furthermore, the automatic self-surface contact was employed to describe the dynamic crushing behavior of the cell wall, which simulated frictionless contact between the cell walls.

Aluminum was chosen as the matrix material of the novel gradient honeycomb, and the cell wall was modeled as an elastic-perfectly plastic material with Young’s modulus E = 68 GPa, yield stress σ_s = 76 MPa, mass density ρ = 2700 kg/m³, and Poisson’s ratio μ = 0.3. When the vertical crushing experiment was simulated, the degrees of freedom of the fixed rigid plate were constrained. The displacement of all the nodes of the honeycomb along the out-of-plane direction was restricted to prevent the honeycomb from undergoing out-of-plane expansion.

To comprehensively evaluate the differences of the energy absorption properties and crashworthiness of the novel gradient honeycomb compared to those of the square honeycomb, various mechanical indices, including plateau stress σ_p, densification strain ε_d, specific energy absorption (SEA), and crushing load efficiency (CLE), will be compared.

The plateau stress σ_p and densification strain ε_d are the important indicators of the mechanical capacity of a honeycomb, which can be defined as follows:^36,37

where ε_p is the plateau stain; ε_w and σ(ε) denote the initial strain of the strain–stress curve (the strain at which the stress reached the initial peak) and the nominal stress, respectively; and ε_d is the densification strain, which is defined as the last maximum point on the energy efficiency–strain curve, in which E(ε) is the energy absorption efficiency of the honeycomb (the ratio of the energy absorption to the nominal strain).

Under vertical collapse, the energy absorption performance of the honeycomb can be reflected directly by SEA, and a better SEA is beneficial for creating a better lightweight energy absorber. The SEA is defined as follows:³⁸ 

where U denotes the total energy absorption, m is the total mass of the honeycomb, and Δρ and ρ_s are the relative density and the density of the matrix material, respectively.

Finally, the ratio of the plateau stress to the initial peak stress is expressed as the crushing load efficiency, in which a higher CLE indicates that the honeycomb can more easily absorb more energy during the dynamic crushing. It is defined as follows:³⁹ 

where σ_m represents the initial peak stress of the honeycomb.

To guarantee the accuracy of the simulation, a suitable mesh size is crucial to enhance computational efficiency. A mesh sensitivity study was conducted based on GSH2, with the impact velocity and relative density set as V = 10 m/s and Δρ = 0.15, respectively. Some different element sizes, 1, 0.5, 0.4, 0.3, and 0.2 mm, were employed for the unit-mass stress–strain curve and the energy absorption–strain curve, as shown in Fig. 5. With the decrease in the element size, the extent of the plateau stage increased, and the unit-mass strain–stress curve became more stable. When element sizes decrease, the curve will be converged gradually. The gap of curves between the element size of 0.5 mm and other smaller sizes was insignificant. With the consideration of computational accuracy and efficiency, the average element size of 0.5 mm is adopted to simulate this investigation.

Similar to the analysis presented in Sec. III A, a validation study was performed to ensure that the dynamic crushing behavior of the honeycomb could be simulated accurately by the finite models. A numerical model of a previously reported square honeycomb structure was established, and the boundary conditions and material information were the same as those used in the previously reported experiments⁴⁰ (the impact velocity and thickness were V = 70 m/s and t = 0.5 mm, respectively). The comparison of the deformation modes is shown in Fig. 6(a). Moreover, the trend of force–displacement curves⁴¹ was also compared with another finite model under the same conditions. The differences of the deformation modes were small [Fig. 6(a)]. They produced similar crushing bands, the trends of the curves were also basically consistent, the locations of the initial peak forces were similar, and the plateau fields were similar. Thus, the established finite element model had reliable precision for dynamic crushing simulations.

To explore the crashworthiness of the novel gradient and square honeycombs, a systematic study was performed to demonstrate the influence of several factors, such as the geometric configuration and the impact velocity, on the deformation modes and energy absorption of the honeycombs under dynamic crushing.

The deformation maps of the novel gradient honeycomb at the nominal strain of ε = 0.4 were compared, and the different velocities of the unit-mass strain–stress curves are shown in Figs. 7–9. By observing the variations of the deformation maps and the unit-mass strain–stress curves, the influence of the geometric configuration can be determined.

Under the in-plane crushing of the honeycombs at a low impact velocity of V = 3 m/s, the deformation characteristics of each honeycomb were different [Fig. 7(a)]. Compared to the leftward slip of the SH under crushing, the slip of the novel gradient honeycomb decreased significantly. At the same impact velocity, the unit cells with the inclination angles α = 53° and 180° in the gradient square honeycomb and buffer square honeycomb buckled first. In GSH1 and GSH2, the top and bottom layers were destroyed, and two deformation bands were generated. In the BSH, the unit cells located at the bottom were protected temporarily because both sides of the middle layers flexed initially. In contrast, NSH1 and NSH2 exhibited a negative Poisson ratio effect and a zero Poisson ratio effect under quasi-static collapse, respectively.

The unit-mass strain–stress curves of the different honeycombs at an impact velocity of V = 3 m/s are shown in Fig. 7(b). During the deformation of the SH, the degree of slip increased gradually. As a result, the curve oscillated significantly, and the rising section of the curve occurred later than for the other structures. Encouragingly, compared to the SH, higher plateau stress was obtained via the novel gradient honeycomb, and the trends of the curves were more stable. GSH2 had the highest plateau stress, and a double-plateau phenomenon appeared in the unit-mass stress–strain curve of the BSH.

When the impact velocity increased to V = 10 m/s, the deformation mode of the honeycomb transformed from the low-speed rotary mode to a transitional mode, and the deformation behaviors of each honeycomb changed, as shown in Fig. 8(a). In the SH and novel square honeycombs (NSH1 and NSH2), two crushing bands appeared near the rigid plate under mid-velocity crushing. Unlike the deformation behavior under low-speed crushing, the cell elements not only produced unique structural deformation but were also affected by the gradually fortified inertial effects in the mid-velocity mode. Accordingly, the degree of slip was inhibited in the SH. The unit-mass strain–stress curves are presented in Fig. 8(b). Although the slip of the SH decreased, the significant issue of the curve exhibiting intense oscillations was not resolved. Thereafter, the gradient square honeycombs (GSH1 and GSH2) and the BSH could withstand higher plateau stresses and lower initial peak stresses based on the comparison with the SH and novel square honeycombs (NSH1 and NSH2).

At an impact velocity of V = 100 m/s, the maps of the deformation modes and the unit-mass stress–strain curves are shown in Fig. 9. When the honeycomb was under a high-velocity impact, the deformation behaviors of the unit cells were dominated mainly by strong inertial effects, in which the cells have insufficient time to exhibit the characteristic distortion. During the process of warping, the cells of each honeycomb located on the top layer were destroyed, and an “I”-shaped band appeared in the honeycomb. In this pattern, the sliding displacement of the SH was so small that the oscillations of the curve were indistinguishable, and the plateau stress achieved significant improvements. In the above investigation, the crashworthiness properties of the SH exhibited high sensitivity to slip. Under high-velocity dynamic crushing, the plateau stress of all the honeycomb structures increased significantly, in which the novel gradient honeycomb did not exhibit improvements compared to the SH.

The SEA is a dominant indicator for directly measuring the energy absorption capacity of lightweight materials. The SEA–strain curves of different honeycombs at an impact velocity of V = 10 m/s are shown in Fig. 10. For the minimum strain (ε < 0.379), the slip phenomenon of the deformation behavior was so negligible under the mid-velocity crushing that the value of SEA was higher than those of the others. With the increase in the nominal strain ε, the novel gradient square honeycombs (NSH1 and NSH2) and the gradient square honeycombs (GSH1 and GSH2) exhibited better energy absorption performance, which is the greatest energy absorption at the maximum strain. In this study, the value of SEA corresponding to the densification strain (ε_d) was chosen from the SEA–strain curve to better present the gap of different honeycombs. As shown in Table I, the enhancement of SEA was about 29.77% for GSH1 compared to that of SH, and the crashworthiness was improved significantly by introducing the gradient in the structure. In addition, the CLE of the BSH increased by 218.68% compared to that of the SH, and the lowest initial peak stress was present in the BSH. The lower initial peak stress indicated better protective ability when the honeycomb endured the instant force.

In Fig. 11, the values of the specific energy absorption for the novel gradient honeycombs with different deformation modes are compared. To ensure the accuracy of the comparison, the value of SEA corresponding to the densification strain (ε_d) was selected from the SEA–strain curve to present the differences in different honeycombs. When the impact velocity increased, the SEA of each honeycomb improved with varying degrees. Under low- and mid-velocity crushing, the introduction of the gradient in the structure led to the best SEA. For the low-velocity mode, GSH2 had the best SEA, with a maximum increase of ∼34.92% compared to that of the SH. For the mid-velocity mode, GSH1 had the best SEA, with a maximum increase of about 29.77% compared to that of the SH. In contrast to the above condition, with the gradual decrease in the movement degree of the SH, the SH had more outstanding SEA than the novel gradient honeycomb in the high-velocity mode.

The variations of the SEA and CLE at different impact velocities are presented in Fig. 12. The SEA of the SH was enhanced effectively by the novel gradient honeycombs at low crushing velocities (impact velocities, V = 3–20 m/s), and the best SEA was achieved by the gradient honeycombs (GSH1 and GSH2). When the deformation mode changed from the transitional mode to the inertial mode, the SEAs of all novel gradient honeycombs were lower than those of the SH [Fig. 12(a)]. As shown in Fig. 12(b), compared to the SH, which had a small value of CLE, the crushing load efficiency could be improved significantly by adding the novel gradient honeycomb to the structure under the low- and mid-velocity crushing. For instance, GSH1 exhibited remarkable CLEs at all the velocities considered. Based on the above discussion, the greatest crashworthiness performances were shown by GSH1.

When the crushing velocity increased, the highest increment of the SEA was obtained by introducing a gradient into the design of the structure. However, the shortcomings of the SH can be resolved by the proposed designs of the square honeycomb. In this subsection, the influence of the change in the inclination angle α is explored for the novel square honeycombs.

The energy absorption indices with different inclination angles α are compared in Fig. 13. In the NSH, the lengths of the internal rods will be influenced by the inclination angle α. As shown in Figs. 7 and 8, the deformation characteristics of NSH1 and NSH2 were different under the low- and mid-velocity impact. In NSH1, the inner rods wound first around the central point O when the honeycomb was undertaking the dynamic crushing. Subsequently, the corner of the cell became the second rotating central that the external cell wall buckled. In this process, the turning of the two rotating centers was so opposite that the zero Poisson ratio was present. With the design concept of NSH2, the interior of a unit cell only added the two rods to enhance the capacity. Under the dynamic crushing, the external cell wall was first buckled and the corner of the cell became the uniquely rotating central. As the degree of rotation increased, the inner rods were twisted around the rotating central. On both sides of the honeycomb, the turning of the cell was reversed, and the negative Poisson ratio was exhibited that the displacement of the X-direction gradually reduced. In the deformation of the cell, the number and rotating degree of the cell wall played a key role in energy absorbing performance under dynamic crushing. The more rods and larger bending angles indicated that the plastic hinge can absorb more energy under dynamic crushing.

Hence, adding rods in the interior of the square cell not only allowed the favorable deformation modes of the NSH to appear under dynamic crushing but also dissipated more energy by the plastic hinges formed during the rod winding. In NSH1 (α = 90°), due to the fixed lengths of the internal rods, the four rods in the interior of the cell had the maximum twisting angles about the central point O, and the best plateau stress was obtained. In NSH2, the dissipated energy of the plastic hinges decreased because it had only two rods in the cell structure, and the minimum plateau stress was achieved [Fig. 16(a)]. When the inclination angle α = 53° and 180°, the cells had only two rods, and the honeycombs had the highest CLEs. In addition, the lowest CLEs were obtained by increasing (decreasing) the angle to near 90°.

Similar to the trend of the plateau stress–inclination angle curve, the maximum value of the SEA was observed when the angle was near 90°, as shown in Fig. 14(a). For the novel square honeycombs with different inclination angles α, the gap of the SEA was enhanced gradually by improving the impact speed. To thoroughly explore the effects of the gap, the rates of increase in the SEA for the three deformation modes (low-, mid-, and high-velocity impacts), defined as Δδ, are shown in Fig. 14(b). Under low- to mid-velocity impacts, the rate of increase in the SEA decreased as the inclination angle increased (Δδ_1max = 13.7% and Δδ_1min = 4%). Furthermore, NSH2 had the maximum increment of Δδ_2max in the deformation mode from the mid-velocity impact to the high-velocity impact (Δδ_2max = 214.7% and Δδ_2min = 150.2%).

In the present study, a buffer square honeycomb was proposed based on the buffer principle in mechanical applications. The BSH exhibited a better crashworthiness performance than the SH and NSH under the low- and mid-velocity crushing. To obtain more detailed results, the capacities of honeycombs with different numbers of buffer strips were explored.

As shown in Fig. 15, the number of buffer strips was varied while maintaining the stationary quantity of the three cell elements and the symmetry of the whole honeycomb (maintaining a constantly relative density and structural characteristics). When the deformation of the BSH occurred at an impact velocity of V = 10 m/s, the different trends of the unit-mass stress–strain curves for various numbers of buffer strips are shown in Fig. 16. For BSH1 and BSH2, the curves contained two plateau stress stages. The gap between the first plateau stage and the second plateau stage decreased as the number of buffer strips increased [Fig. 16(b)]. When the BSHs were impacted, the unit cells (inclination angle α = 53° or 180°) located in the buffer zone buckled first, and the first plateau stage of the curve appeared. With the increase in the nominal strain, the other cells (inclination angle α = 90°) that had not collapsed under the small deformation began to become damaged, and the unit-mass stress–strain curve exhibited a second plateau stage. As the number of buffer strips increased, three types of cell elements kept approximate quantity in the middle part of the honeycomb. In this condition, the mechanism of the buffer honeycomb was gradually diminished by the three kinds of cells that were destroyed at the same time under the large deformation. In the meantime, the second plateau stage also vanished.

In Table II, the performances of the BSHs are compared for an impact velocity of V = 10 m/s, and differences of the BSHs compared to the SH and NSH1 were calculated. The change in the plateau stress was unrelated to the number of buffer strips in the BSH, and the introduction of a buffer design in the structure of the honeycomb can be considered to be a new concept to effectively enhance the crashworthiness of the SH and NSH. Under similar plateau stress conditions, a better SEA was achieved for BSH1 and BSH2, which expressed the second plateau stage in the strain–stress curve, whereas BSH3 and BSH4 had only one plateau stage, and the maximum increment of SEA reached 24.92% and 8.12% for SH and NSH1, respectively, compared with that for BSH2. In contrast to the negative correlation of the SEA with the number of buffer strips (as the number of buffer strips increased, the SEA decreased), a positive correlation was achieved between the CLE and the number of buffer strips. By adding the buffer strips to NSH1, the maximum increment of CLE can reach 119.79% (BSH4 compared with NSH1). Moreover, whatever the changed number of buffer bands are, the initial peak stress of NSH1 can be greatly refined.

In this investigation, novel square honeycombs, including an ordinary square honeycomb, a gradient square honeycomb, and a buffer square honeycomb, were designed to enhance the energy absorption performances of the traditional square honeycomb. In-plane dynamic crushing, experiments were numerically simulated to examine the differences between the novel gradient square honeycombs and the traditional square honeycomb by using the nonlinear finite element software ABAQUS/Explicit. Subsequently, a systematic study was performed to explore the influences of several factors (geometric configuration, impact velocity, inclination angle, and buffer strips) on the energy absorption, CLEs, deformation modes, and crashworthiness of the honeycomb structures. The above findings can be summarized as follows:

• (1).

  The geometric configuration had a significant effect on the deformation modes under low- and mid-velocity impacts. As the impact velocity increased, the sensitivity of the deformation behavior to the geometric configuration decreased. The design of the novel gradient square honeycomb could effectively control the degree of slip, for which NSH1 and NSH2 exhibited a negative Poisson ratio effect and a zero Poisson ratio effect, respectively. The SEA of GSH1 and the CLE of the BSH improved by 29.77% and 216.68% under the mid-velocity crushing compared to those of the SH, respectively.

• (2).

  As the impact velocity was increased, the rate of increase in the SEA for the novel gradient square honeycomb decreased gradually compared to that for the SH. The maximum rate reached 34.92% under the low-velocity impact and 29.77% under the mid-velocity impact. For the inertial mode, the crashworthiness improvements of the novel gradient square honeycomb diminished with the decreased slippage of the SH. In addition, the CLE of the SH improved significantly at all velocities.

• (3).

  The plateau stress and SEA of the NSH varied with the length of the internal rods. When the inclination angle α = 90°, the highest plateau stress and SEA were achieved. The best CLE was obtained for inclination angles α = 53° and 180°. The energy absorption performances of the BSHs were related to the number of buffer strips. A lower number of buffer strips were beneficial for the enhancement of the SEA, and the opposite correlation was found for the CLE.

The authors acknowledge LetPub for its linguistic assistance during the preparation of the manuscript.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.