Gradient double-twisted Bouligand structural design for high impact resistance over a wide range of loading velocities

Abstract

Structural materials for protective applications are exposed to complex environments including impacts under a wide range of loading velocities. Bioinspired Bouligand-type structural materials show high impact resistance under quasi-static and low-velocity impacts. However, their protective performance under high-velocity impact is lacking investigation. Herein, we expand the Bouligand-type structure family by synergistically considering structural design and compositional regulation and highlight a double-twisted Bouligand structure with gradient composition (DT-Bou-G) for enhancing impact resistance under a wide range of loading velocities. As one demonstration, the DT-Bou-G structural material was fabricated by multimaterial fused deposition with stiff polylactic acid and soft thermoplastic polyurethane as raw materials. Experimental investigations show its superior impact-resistant capability under multiple loading velocities (0.5 millimeters per minute, 2.1 meters per second, 4.3 meters per second, and 120 meters per second). Finite element simulations further prove the mechanical result and reveal the underlying mechanisms. The DT-Bou-G structure will inspire the design of engineering protective materials capable of withstanding complex working conditions.

A bioinspired double-twisted Bouligand structure with gradient composition exhibits wide-spectrum impact resistance.

INTRODUCTION

With the development of modern industry, structural materials for protective applications (such as armors) are increasingly exposed to complex environments, including impacts under a wide range of velocities. Some engineering design schemes including the laminate structure (1–3), cellular structure (4–7), and sandwich structure (8–10) were proposed to enhance impact resistance in the past decades, but they were partly limited by undesirable situations of delamination, heaviness, and strength-toughness imbalance. Natural organisms have evolved armors to effectively resist predators’ attacks (11–16). Although composed of meager constituents, biological armors always exhibit sophisticated structures and, thus, superior protective properties. Deeply understanding the structure-property relationships of biological armors may provide valuable insight into the development of protective materials (17).

Scale, as the outermost protection tissue of fish, needs enough impact resistance and puncture resistance against external attacks (18–20). Most scales have a highly mineralized external layer and a slightly mineralized internal layer (21, 22). The external layer shows high rigidity to directly resist penetration, while the internal layer is specialized in mitigating impact waves and absorbing residual energy (23). In addition to the heterogeneous distribution in constituents, the single-Bouligand (S-Bou) structure assembled by collagen nanofibrils (within the internal layer) is a common scheme to enhance the impact resistance of scales (24, 25). More specifically, the S-Bou structure can toughen scales by nanofiber reorientation under quasi-static loading and low-velocity impact loading (26).

Different from the S-Bou structure found in most fish scales, an interesting double-twisted Bouligand (DT-Bou) structure was found in the scales of coelacanth fish (27). It has orthogonal bilayer building blocks and, thus, a composite helicoidal structure, attracting increasing attention in recent years. Quan et al. (27) built a model for the DT-Bou structure and revealed the structure-induced toughening mechanisms (such as fibril stretching, reorientation, sliding, etc.) under tensile loading. Using an extended finite element (FE) method, Yang et al. (28) found that compared to the S-Bou structure, the DT-Bou structure exhibited low internal damage and optimal interlaminar stress distribution under single-edge notched tensile loading. Yin et al. (29) compared the DT-Bou structure to the S-Bou structure by phase-field fracture mechanics analysis under tensile loading, highlighting the optimal fracture toughness of the former. Furthermore, they experimentally explored the difference in the bending performance between the DT-Bou structure and the S-Bou structure and found that the former showed much higher crack resistance and bending strength (29).

Moreover, Yin et al. (30) performed a pendulum impact test and FE analysis (FEA) to identify the difference between the two structures Experiments showed that compared to the S-Bou structure, the DT-Bou structure had a mixed failure mode including fiber breakage and matrix cracking. Meanwhile, the FEA showed a larger interlaminar stress generated in the DT-Bou structure. Overall, it was reported that the DT-Bou structure can exhibit high mechanical properties under quasi-static loading and low-velocity impact loading (28–30). It is worth mentioning that the impact resistance of the DT-Bou structure and S-Bou structure under a wide range of loading velocities, especially under high-velocity impact, was hardly investigated. Exploring the impact resistance of Bouligand-type structures under wide-spectrum loading velocities is essential because it can help to deeply understand natural toughening mechanisms and broaden their applications under complex environments.

In this work, synergistically considering the composition and arrangement of fiber building blocks, we expand the Bouligand-type structure family as the S-Bou structure, DT-Bou structure, DT-Bou-alternating (DT-Bou-A) structure, and DT-Bou-gradient (DT-Bou-G) structure (Fig. 1A and fig. S1) by multimaterial fused deposition modeling (FDM) printing. A unidirectional layered (UL) structure was also constructed as a comparison. The gradient mentioned above is reflected in the material composition and can be realized by systematically regulating the proportion of stiff polylactic acid (PLA) and soft thermoplastic polyurethane (TPU) (Fig. 1B and fig. S2). Then, we investigate the mechanical responses of these structures via single-edge notched bend (SENB) test (0.5 mm/min), low-velocity pendulum impact test (2.1 m/s), drop-tower test (4.3 m/s), and high-velocity ballistic test (~120 m/s) (fig. S3). Experimental results show that DT-Bou exhibits enhanced impact resistance compared to UL and S-Bou under low-velocity loading but no obvious difference under high-velocity loading (Fig. 1C). Furthermore, DT-Bou-G exhibits superior impact resistance under wide-spectrum loading velocities because of newly added gradient design and underlying mechanisms (Fig. 1C). Crack analysis and FEA identify that compared to UL and S-Bou, DT-Bou has a coupled fracture mode (fiber blocking and crack twisting) under low-velocity impact, while DT-Bou-G further shows large deformation, wide stress distribution, and plastic dissipation to absorb energy under high-velocity loading (Fig. 1D).

Fig. 1. Design, fabrication, and properties of the DT-Bou-G structure.

(A) Schematic of DT-Bou-G structural design. DT-Bou consists of two orthogonal sets of S-Bou, and DT-Bou-G was constructed by introducing a gradient compositional change into DT-Bou. (B) Tensile modulus and load in each layer of DT-Bou-G structural material with different PLA/TPU contents. (C) Energy absorption of S-Bou, DT-Bou, and DT-Bou-G under different impact velocities, showing the superiority of DT-Bou-G. (D) Mechanical behaviors and toughening mechanisms of DT-Bou-G under impact. DT-Bou-G has stiff surface layers to reduce impact force and flexible bottom layers to absorb energy. It exhibits coupled fracture paths (including crack twisting and fiber blocking) under impact. (E and F) Sample of printed DT-Bou-G (E) and its microstructure (F).

RESULTS

Design and construction of the Bouligand-type structure family

The FDM technique was implemented to construct complicated fiber-based structures by using commercial PLA and TPU raw filaments. On the basis of common S-Bou, DT-Bou mimicking the structure of the coelacanth fish scale (27) was produced by helicoidally stacking orthogonal-bilayer fiber building blocks. The interlayered twisted angle of DT-Bou was set the same as that of S-Bou, and all the structures (DT-Bou, S-Bou, and UL) were set with the same thickness. Furthermore, compared to previous works (28–32), we expanded the Bouligand-type structure family by considering structural design and compositional regulation (table S1). Not limited to the structural design, the compositional regulation can be also realized by FDM, which can change the composition of the printed filament-based layers in a gradient style from stiff PLA to soft TPU to construct DT-Bou-G with stiff surface layers and flexible bottom layers (Fig. 1, E and F). As shown in Fig. 1B, the modulus in each layer of DT-Bou-G was experimentally tested to be decreased from 4738.94 to 82.27 MPa when the composition changes from PLA to TPU. Typical load-displacement curves further showed that layers with high PLA content show elastic failure mode, while layers with high TPU content show plastic failure mode (fig. S2). DT-Bou-A, with an alternant PLA layer and TPU layer along the thickness direction (fig. S1), was also designed to investigate the influence of composition distribution on mechanical response.

Low-velocity loading tests of the Bouligand-type structure family

SENB test was first carried out to identify the difference among these different structures under quasi-static loading. UL, S-Bou, DT-Bou, DT-Bou-A, and DT-Bou-G were printed (10 mm in width, 7 mm in depth, and 100 mm in length), notched, and tested (0.5 mm/min). DT-Bou exhibited a slightly higher modulus than UL and S-Bou, while DT-Bou-A and DT-Bou-G were much lower than them as shown in Fig. 2A. From typical load-displacement curves, DT-Bou-A and DT-Bou-G exhibited a gently elongated state when UL, S-Bou, and DT-Bou showed a sudden decline (Fig. 2B). Moreover, materials partly composed of TPU (DT-Bou-A and DT-Bou-G) had a much lower load compared to PLA-based materials (UL, S-Bou, and DT-Bou). This may be attributed to the intrinsic mechanical difference between PLA and TPU. In addition, samples with much larger size (20 mm in width, 14 mm in depth, and 100 mm in length) were printed and tested to consider the probable size effect in the SENB test. Investigation showed that the trend of mechanical variation was found to be consistent with that of small-size samples (fig. S4). More detailed information can be found in the crack propagation between S-Bou and DT-Bou. The typical twisted crack path can be observed in both S-Bou and DT-Bou (fig. S5, A and B), implying a helical fracture mode along the long axis of fibers. More sophisticated, DT-Bou exhibited a bidirectional crack propagation path because of the orthogonal fiber direction between layers (fig. S5B). As the intermediate state of the fracture process, fiber bridging exists in DT-Bou (fig. S5C), which cannot be found in the S-Bou structure. The unique fiber bridging can increase delamination resistance and interlaminar fracture toughness (33). Overall, the differentiated fracture morphologies reflect that the crack has to destroy the orthogonally arranged fibers to further extend, which can dissipate a large amount of energy.

Fig. 2. Quasi-static bending and low-velocity (pendulum and drop-tower) impact test of the Bouligand-type structure family.

(A and B) Modulus statistics (A) and typical load-displacement curves (B) of UL, S-Bou, DT-Bou, DT-Bou-A, and DT-Bou-G. (C) Energy absorption and impact strength of UL, S-Bou, DT-Bou, DT-Bou-A, and DT-Bou-G under pendulum impact. (D to F) Statistics of peak force and total energy (D), the typical force-displacement curves (E), and the typical residual velocity-time curves (F) of UL, S-Bou, DT-Bou, DT-Bou-A, and DT-Bou-G under drop-tower test. (G and H) Front (G) and back (H) sides of samples after drop-tower test. The yellow dotted frames represent complete break, and the blue dotted frames represent cracks. DT-Bou-G has the lowest damage degree.

Pendulum impact test was performed to explore the impact resistance of different structures under low-velocity loading. From the statistics of absorbed energy and impact strength, S-Bou and DT-Bou showed obvious enhancement compared to UL, while DT-Bou-G showed the highest energy absorption and impact strength (Fig. 2C). In detail, the impact strength of DT-Bou (~22.4 kJ/m²) is 23.1% higher than that of S-Bou (~18.2 kJ/m²) and 112.4% higher than that of UL (~1.83 kJ/m²), confirming the mechanical advantage of DT-Bou under pendulum impact. When the gradient composition was introduced into DT-Bou, the impact strength of the resultant DT-Bou-G was further improved to 37.4 kJ/m², which was 67% higher than that of DT-Bou and 21% higher than that of DT-Bou-A (~30.9 kJ/m²). Overall, DT-Bou-G enhanced the impact resistance compared to the composition-homogeneous DT-Bou and the composition-alternant DT-Bou-A under pendulum impact. Samples after pendulum impact loading were observed. A crack in UL was found to propagate along the long axis of fibers, leading to a flat crack plane (fig. S6A), while S-Bou showed a helical crack path (fig. S6B), which was consistent with that in the sample after SENB loading. DT-Bou was not completely ruptured, showing less damage to UL and S-Bou (both ruptured) (fig. S6C). DT-Bou-G was slightly bent and showed much less damage compared to DT-Bou (fig. S6D). It can be explained that the tough TPU molecules integrating into the fiber building blocks impart the bottom layers of DT-Bou-G much larger deformation and, thus, superior damage tolerance. This is a preliminary demonstration of the advantages of the synergy of compositional control and structural design.

Low-velocity drop-tower test was performed to further explore the impact resistance of different structures, compositions, and their combinations. Both pure PLA-based and pure TPU-based materials with UL, S-Bou, and DT-Bou structures were printed and tested. According to the mechanical statistics, the peak force and total energy of PLA-based materials increased gradually from UL (~2352.7 N, ~14.7 J) to S-Bou (~2466.0 N, ~20.8 J) and then to DT-Bou (~3340.2 N, ~27.2 J) (Fig. 2D). This trend was consistent with that of TPU-based materials, but the latter showed much lower peak force and higher absorbed energy (fig. S7). This mechanical result was closely related to the tough but less stiff TPU. Compared to the pure PLA-based material of DT-Bou, DT-Bou-A exhibited reduced peak force (~1938.1 N) but improved absorbed energy (~34.3 J). Compared to DT-Bou-A, DT-Bou-G exhibited a simultaneous improvement in the peak force (~3125.3 N) and the energy absorption (~46.1 J) for compositional gradient design (Fig. 2D). Furthermore, to investigate the influence of different gradients on the impact resistance, DT-Bou-G subsets with different PLA/TPU proportions in the final layer were printed and tested. We can observe that the peak force of these materials was almost the same, while the total energy decreased with the increase in PLA content in the final layer (fig. S8). It is due to the fact that the decrease in TPU content in the materials can lead to a reduction in energy absorption. More details can be observed from the typical force-displacement curves (Fig. 2E). All materials had similar trends in the initial stages of curves because of surface PLA layers. Curves of PLA-based materials and PLA/TPU composite materials diverged when displacements reached ~0.4 mm. For the former, UL, S-Bou, and DT-Bou maintained a rapid increase and a sudden decrease in the force-displacement curves. For the latter, because of the introduction of tough TPU, DT-Bou-A and DT-Bou-G maintained a gentle increase and decrease in the force-displacement curves, leading to much longer displacements.

The typical residual velocity-time curves (Fig. 2F) showed that S-Bou and DT-Bou exhibited lower residual velocities (~3.2 and ~2.4 m/s, respectively) than UL (~3.7 m/s), indicating that the Bouligand structure can largely decelerate impact velocities. Besides the lower residual velocity (~2.4 m/s) mentioned above, the DT-Bou structure had a longer time (~5.3 ms) to resist impact compared to the S-Bou structure (~3.4 ms). Because of the presence of TPU, DT-Bou-A and DT-Bou-G exhibited much longer impact times compared to the composition-homogeneous UL, S-Bou, and DT-Bou. It is worth noting that compared to DT-Bou-A, DT-Bou-G can more decelerate external impact because of the reasonable gradient composition. Samples after drop-tower impact are shown in Fig. 2 (G and H). UL was destroyed into three pieces. S-Bou was also destroyed, while DT-Bou maintained its integrity with unpenetrated cracks. DT-Bou-A can resist external impact with less damage but be delaminated, while DT-Bou-G can avoid this problem by gradient modulus change (gradient composition) between each layer. Furthermore, DT-Bou-G can effectively resist the impact load with no visible cracks because of the tolerable deformation in the bottom layers. Overall, DT-Bou-G exhibited optimal impact resistance (integrated consideration of peak force, total energy absorption, residual velocity, impact time, and damage degree) compared to UL, S-Bou, DT-Bou, and DT-Bou-A.

High-velocity ballistic impact test of the Bouligand-type structure family

A high-velocity (~120 m/s) ballistic test was performed to further explore the impact resistance of different structures. All samples were printed into cylindroid samples (~100 mm in diameter and ~7.6 mm in thickness). Difference can be observed from the photographs captured by a high-speed camera. All samples were damaged in the initial stages. S-Bou and DT-Bou were easily perforated (Fig. 3, A and B, and movies S1 and S2), while DT-Bou-G can rebound the bullet (Fig. 3C and movie S3). More details can be found on the damaged samples. The back sides of the perforated S-Bou and DT-Bou showed typical conical damage zones. The broken area of DT-Bou (2.41 ± 0.25 cm²) was smaller than that of S-Bou (2.67 ± 0.30 cm²) (Fig. 3, D and E), meaning that DT-Bou was less destroyed. Furthermore, DT-Bou-G only exhibited crack damage on the back side, which still maintained structural integrity (Fig. 3F). On the basis of the perforation, we observed the cracks on the fracture surface. Crack propagation paths were not similar in S-Bou and DT-Bou. For S-Bou, a crack commonly propagated with a smooth helical style (Fig. 3G), consistent with the previous reports (34–36). For DT-Bou, an unusual helical crack mediated by the blocking effect of vertically aligned fibers was observed (Fig. 3H). Conceivably, the crack tip was hindered by the vertically aligned fibers and had to break them to continue propagation. Afterward, the crack can still helically propagate because of the Bouligand-type arrangement of part fibers until it was blocked by the next vertically aligned fiber. Under such circumstances, the crack propagation path was highly tortuous compared to that of S-Bou, which can effectively enhance energy absorption.

Fig. 3. High-velocity ballistic impact test of the Bouligand-type structure family.

(A to C) Impact process of S-Bou (A), DT-Bou (B), and DT-Bou-G (C). DT-Bou-G can rebound the bullet, while S-Bou and DT-Bou were perforated. (D to F) Representative patterns of the broken areas in the back side of S-Bou (D), DT-Bou (E), and DT-Bou-G (F) after ballistic impact. The black dotted frames represent the broken area, and the black arrows represent cracks. (G and H) Representative crack propagation paths in S-Bou (G) and DT-Bou (H). The black arrows indicate the crack propagation directions. A typical helical crack can be observed in S-Bou, which was blocked by vertical fiber in DT-Bou.

FE simulations of the Bouligand-type structure family

FE simulations under different loading velocities were further performed to identify the impact resistance and the underlying mechanisms of UL, S-Bou, DT-Bou, and DT-Bou-G. For the drop-tower impact simulation (Fig. 4, A and B), from the typical residual velocity-time curves, DT-Bou showed a much lower residual velocity (2.11 m/s) than UL (3.10 m/s) and S-Bou (2.82 m/s), and DT-Bou-G can further reduce the residual velocity (1.50 m/s) (Fig. 4C). From the force-displacement curves, it can be observed that compared to S-Bou and UL, DT-Bou showed a similar peak force but a larger displacement (Fig. 4D). Meanwhile, DT-Bou-G exhibited the highest peak force and energy absorption. These simulations are partly consistent with the experimental results (Fig. 2, E and F), proving that DT-Bou-G can more powerfully enhance the impact resistance under drop-tower impact than UL, S-Bou, and DT-Bou.

Fig. 4. FE simulations under drop-tower test.

(A and B) Models of S-Bou (A) and DT-Bou (B). (C and D) Residual velocity-time curves (C) and force-displacement curves (D) of UL, S-Bou, DT-Bou, and DT-Bou-G under drop-tower test. (E) Impact process of UL, S-Bou, DT-Bou, and DT-Bou-G under drop-tower test at the times of 1.6, 4.8, and 8.0 ms. The blue frames indicate the locally enlarged crack characteristics of S-Bou and DT-Bou. (F) Stress distribution in the front side of UL, S-Bou, DT-Bou, and DT-Bou-G at the time of 1.6 ms.

The failure process (Fig. 4E) and the corresponding stress distribution (Fig. 4F and fig. S9) were further analyzed to get a deeper understanding of the underlying mechanisms. UL exhibited a cruciform crack at the initial stage and quickly became defenseless. S-Bou exhibited a helical crack, implying improved impact resistance. Compared to S-Bou, DT-Bou exhibited a more complicated helical-based crack propagation path, because the crack had to propagate until it was blocked by the vertically aligned fiber and then deflected because of Bouligand-type arranged fibers. More details of the deformation mode can be observed in the crack propagation patterns between two adjacent layers within S-Bou and DT-Bou structures (fig. S10). In general, a crack can propagate in two distinct modes in Bouligand structural materials. One is along the interface between fibers, referred to as interfacial failure (IF); another one is perpendicular to the aligned direction of the fiber, termed material failure (MF). From a load history standpoint, cracks invariably initiate at the interface between fibers. The fibers experience tensile fracture as the load continues, leading to a crack perpendicular to the aligned direction of the fiber. The illustration reveals that crack propagation modes in adjacent layers of the S-Bou structure are consistent (fig. S10). Specifically, the crack in the upper layer propagates in the IF(MF) mode, and the crack in the lower layer also propagates in the same mode. Conversely, the DT-Bou model exhibits distinct crack propagation modes in adjacent layers, attributed to its orthogonal alignment of fibers. The arrangement of vertical fibers gives rise to cross cracks in adjacent layers during the initial phase of the load. This subsequently determines the location of MF crack initiation in the next layer. In the S-Bou structure, there is an absence of discernible patterns concerning the initiation location of MF cracks. The arrangement of crossing fibers modifies the trajectory of crack propagation, potentially extending the crack path. This alteration could lead to improved energy absorption. Furthermore, when considering the compositional gradient, DT-Bou-G appears to be more powerful to resist damage (Fig. 4E). The stress distribution of these four kinds of structures at the impact time of 1.6 ms is shown in Fig. 4F. DT-Bou-G showed a larger stress distribution area than that of other structures, indicating more extensive stress transfer (almost throughout the material).

The simulated high-velocity ballistic impact results present different failure modes to the drop-tower results. The stress distribution of the DT-Bou structure under drop-tower impact and ballistic impact is shown in Fig. 5 (A and B). In the initial stage (0.1 ms), the DT-Bou structure exhibited a much smaller stress distribution area and localized material deformation under high-velocity ballistic impact. At the time of 4 ms, fewer elements exhibited stress variation under high-velocity impact, implying that the one-sided structural design makes DT-Bou difficult to respond to the impact waves and timely activate toughening mechanisms. At the time of 8 ms, DT-Bou under both impact velocities was destroyed.

Fig. 5. FE simulations under ballistic test.

(A and B) Stress distribution of DT-Bou under drop-tower test (A) and ballistic test (B) at the times of 0.1, 4, and 8.0 ms. (C and D) Force-displacement curves (C) and the residual velocity-time curves (D) of UL, S-Bou, DT-Bou, and DT-Bou-G. (E) Plastic dissipation of different structures under high-velocity impact. (F) Impact snapshots of S-Bou, DT-Bou, and DT-Bou-G at the time of 0.25 ms, showing the final state of the ballistic impact. (G) Stress distribution of S-Bou, DT-Bou, and DT-Bou-G at the time of 0.15 ms. (H) Stress distribution of DT-Bou and DT-Bou-G (cross-sectional view) at the times of 0.025, 0.125, and 0.225 ms. The curved arrow indicates the trend of bullet rebound.

The difference among the Bouligand-type structure family under ballistic impact simulation was further revealed. From the force-displacement curves under ballistic impact simulation, the peak force of DT-Bou-G was similar to that of other structures, implying that stiff surface layers in DT-Bou-G can provide enough strength to reduce impact force (Fig. 5C). The residual velocity-time curves under ballistic impact simulation are much different from those of the drop-tower impact simulation (Figs. 4C and 5D). UL, S-Bou, and DT-Bou showed the same residual velocities, indicating a uniform protecting effect under high-velocity impact. In contrast, DT-Bou-G can rebound the bullet and avoid being completely destroyed. The similar mechanical response can also be found in the simulated residual velocity-time curves under impact velocities of 30 and 70 m/s (fig. S11). DT-Bou-G can show much lower residual velocities than UL, S-Bou, and DT-Bou. Overall, the effectiveness of structural design under high-velocity impact is diminished because of the increasingly localized material deformation. The distant materials cannot respond to the impact load on time, and energy dissipation predominantly depends on the material’s plastic deformation and failure. As shown in Fig. 5E, compared to nongradient structures, gradient structures exhibited superior plastic dissipation (more than twice) under high-velocity (120 m/s) impact. This is primarily because the TPU in the bottom layers offers greater ductility, enabling larger plastic deformation. The difference of protective effect between DT-Bou-G and others can be further confirmed by the impact process patterns at the time of 0.25 ms (the final stage of the ballistic impact process) (Fig. 5F and fig. S12). In addition, we found that the stress distribution area in DT-Bou-G was higher than that in S-Bou and DT-Bou under ballistic impact (Fig. 5G and fig. S13). From the perspective of sample cross section, we can find that at the time of 0.125 ms, DT-Bou was destroyed, while DT-Bou-G can withstand the stress; at the time of 0.225 ms, DT-Bou was perforated, while DT-Bou-G can absorb most of the impact energy by deformation in bottom layers and prompt bullet rebound (Fig. 5H). All these simulated results under ballistic impact indicated that the structural design (DT-Bou) can hardly improve impact resistance when suffering from high-velocity impact, while the compositional regulation (introduction of gradient composition) can effectively provide protective performance.

DISCUSSION

In this work, synergistically considering the composition and arrangement of fiber building blocks, we expand the Bouligand-type structure family and highlight a DT-Bou-G structure for high impact resistance under a wide range of loading velocities. Fracture crack analysis and computational modeling showed that inheriting the mechanical characteristics of the DT-Bou structure, the DT-Bou-G structure exhibits complex crack propagation behaviors including crack twisting and fiber blocking. In addition, gradient compositional design provides the DT-Bou-G structure with characteristics of wide stress distribution and large plastic dissipation, which effectively improves impact resistance under high-velocity loading. Overall, as one reasonable product of synergetic regulation of composition and structure, the highlighted DT-Bou-G implies a feasible two-sided design path to construct advanced bioinspired structural materials for withstanding complex working conditions.

MATERIALS AND METHODS

Preparation and characterization of materials

The raw materials PLA and TPU were commercial filaments (1.75 mm in diameter) (Esun Co., Shenzhen, China). Various structures (UL, S-Bou, and DT-Bou) were designed by computer-assisted design. Materials with various structures were printed by a commercial fused-deposition 3D printer (M2030X, Soongon Co., Shenzhen, China), which has two inlets of raw filaments and one nozzle (outlet). The two raw filaments can mix with different proportions in the nozzle by controlling their feed rates. To ensure the total change of composition between layers, one kind of material-changed procedure was used, where the nozzle can exhaust the material from the previous layer and confirm that the feed has been adjusted according to the predesigned proportion for the next layer.

Mechanical testing

Quasi-static mechanical tests were carried out on an Instron 5565 A equipped with a 5000-N load cell. Samples for the tensile test were printed into thick layers (8.2 mm in width, 0.8 mm in depth, and 55 mm in length) with different PLA/TPU contents. All SENB test samples were printed into rectangular solids (10 mm in width, 7 mm in depth, and 100 mm in length), and a notch of 1 mm in depth was prefabricated in all samples. The bending rate was set as 0.5 mm/min, and the span was 40 mm. At least three specimens were tested for one group.

The pendulum impact test was carried out on a Charpy test device (XJJY-5, Chengde Bao Hui Testing Machine Manufacturing Co., Ltd., China) with an impact energy of 4 J and a span of 40 mm. All samples were printed into rectangular solids of 10 mm in width, 7 mm in depth, and 60 mm in length. At least three specimens were tested for one group.

Low-velocity impact test was carried out on a drop-tower impact testing system (Instron 9350) equipped with a 5000-N load cell. All samples were printed into cylindrical solids (~50 mm in diameter and ~7 mm in thickness) and clamped by a pneumatic hollow clamp (the diameter of the hollow area is 40 mm). The testing system was equipped with a 45-kN load cell and a hemispherical-tip impactor (20 mm in diameter). The impact energy was 50 J for all impact tests with a corresponding initial contact velocity of 4.3 m/s. At least three specimens were tested for one group.

For the high-velocity ballistic impact test, the printed cylindrical samples (~100.0 mm in diameter and ~7.6 mm in thickness) were hit by a steel bullet (8 mm in diameter and 2.1 g in weight) with an incident velocity of 120 m/s launched by a gas gun. The impact process was captured by a high-speed camera.

FE simulations

The layered structure and four distinct types of Bouligand structures were constructed. These Bouligand structures encompass single-twisted (S-Bou), double-twisted (DT-Bou), single-twisted gradient (S-Bou-G), and double-twisted gradient (DT-Bou-G). The Bouligand structure is composed of 20 layers of oriented single-layer fiber structures. Each single-layer fiber structure is constructed by arranging a series of slender fiber rods in a specific orientation quantitatively described using rotation angle. In the single-twisted structure, the rotation angle increases uniformly per layer from 0° to 180° along the thickness direction. However, in the double-twisted structure, it increases linearly every two layers with an adjacent layer difference of 90°. The cross section of the fiber rod is a rectangular shape with a width of 0.8 mm and a thickness of 0.4 mm. The material used for the Bouligand structure is pure PLA, while the material for the corresponding gradient structure gradually transitions from PLA (front) to TPU (back) along the thickness direction.

The FE simulations of the impact process of the drop hammer, with an initial velocity of 4.32 m/s and a kinetic energy of 50 J, and the bullet, with an initial velocity of 120 m/s and a kinetic energy of 15 J, were conducted using the commercial software ABAQUS/Explicit. The mechanical behavior of PLA, TPU, and their blends under impact loadings was characterized using a linear plastic hardening constitutive model. The parameters of PLA were reasonably evaluated according to the data in the literature (37), those of TPU were obtained from a tensile test with standard dog bone–shaped samples (10 mm in width, 1 mm in depth, and 155 mm in length), and the stress-strain curves are shown in fig. S14. Their blends with different component contents were appropriately reduced in strength and increased in fracture strain, and the specific curves are shown in figs. S15 and S16. The behavior of interfaces between materials is extremely complex and thus difficult to precisely describe, especially when the materials involved are spatially gradient. Therefore, all the interfaces between fiber rods in this study, including those between different materials, were approximately simulated by a simple bilinear cohesive model. The cohesive zone model was used to describe the dynamic mechanical behavior of the adhesive layer between fibers. The cohesive zone model was widely used to simulate the adhesive layer bonding two different materials. The organic matter acting as glue within the Bouligand structure can be considered negligible in terms of mass. The primary intrinsic mechanism influencing the toughness of the materials is their mechanical response. Hence, a cohesive contact method (without solid material) is adopted for numerical simulations. The traction-separation law describes the relationship between the cohesive nominal traction stress vector $\mathbf{T}={[T_{\mathrm{n}},T_{\mathrm{s}},T_{\mathrm{t}}]}^T$ and the corresponding separations $\mathrm{\delta }={[{\mathrm{\delta }}_{\mathrm{n}},{\mathrm{\delta }}_{\mathrm{s}},{\mathrm{\delta }}_{\mathrm{t}}]}^T$ , where the subscripts n, s, and t denote the normal and two tangential components, respectively. $\mathbf{K}={[K_{\mathrm{n}},K_{\mathrm{s}},K_{\mathrm{t}}]}^T$ is defined as the stiffness along the normal and tangential directions and satisfies $\mathbf{T}=(1-D)\mathbf{K\delta }$ , where D is the damage variable. A simple bilinear traction-separation law is depicted in fig. S17B, where $T_i^0(i=\mathrm{n},\mathrm{s},\mathrm{t})$ represents the peak values of the traction stress when the separation is either purely normal to the interface or purely in the first or second shear direction (fig. S17A), respectively. Likewise, ${\mathrm{\delta }}_i^0(i=\mathrm{n},\mathrm{s},\mathrm{t})$ represents the values corresponding to the peak values of the traction. Damage begins to occur when the following criterion is satisfied

$${\left(\frac{\langle T_{\mathrm{n}}\rangle }{T_{\mathrm{n}}^0}\right)}^2+{\left(\frac{T_{\mathrm{s}}}{T_{\mathrm{s}}^0}\right)}^2+{\left(\frac{T_{\mathrm{t}}}{T_{\mathrm{t}}^0}\right)}^2=1$$

where $\langle T_{\mathrm{n}}\rangle =T_{\mathrm{n}}$ if $T_{\mathrm{n}}>0$ (tension) and $\langle T_{\mathrm{n}}\rangle =0$ otherwise (compression), which signifies that a purely compressive stress state does not initiate damage. The Benzeggagh-Kenane fracture criterion (38) was adopted to describe damage evolution and failure of the interface (fig. S17C). When the crack propagates in mixed mode, equivalent traction stress and separation are defined as

$$T_{\mathrm{m}}=\sqrt{{\langle T_{\mathrm{n}}\rangle }^2+T_{\text{shear}}^2}=\sqrt{{\langle T_{\mathrm{n}}\rangle }^2+T_{\mathrm{s}}^2+T_{\mathrm{t}}^2}$$

$${\mathrm{\delta }}_{\mathrm{m}}=\sqrt{{\langle {\mathrm{\delta }}_{\mathrm{n}}\rangle }^2+{\mathrm{\delta }}_{\text{shear}}^2}=\sqrt{{\langle {\mathrm{\delta }}_{\mathrm{n}}\rangle }^2+{\mathrm{\delta }}_{\mathrm{s}}^2+{\mathrm{\delta }}_{\mathrm{t}}^2}$$

The fracture energy $G^{\mathrm{C}}$ required to cause failure in mixed-mode loading is defined as

$$G^{\mathrm{C}}=G_{\mathrm{n}}^{\mathrm{C}}+(G_{\mathrm{s}}^{\mathrm{C}}-G_{\mathrm{n}}^{\mathrm{C}}){\left(\frac{G_{\text{II}}}{G_{\mathrm{I}}+G_{\text{II}}}\right)}^{\mathrm{\eta }}$$

where $G_{\mathrm{I}}=G_{\mathrm{n}},G_{\text{II}}=G_{\mathrm{s}}+G_{\mathrm{t}}$ , and η is a cohesive property parameter; $G_{\mathrm{n}},G_{\mathrm{s}},\text{and}{G}_{\mathrm{t}}$ denote the work done by the tractions and their conjugate separations in the normal, first shear, and second shear directions, respectively; and the superscript C refers to the fracture energy required to cause failure in the corresponding directions. The fracture equivalent separation can be from ${\mathrm{\delta }}_{\mathrm{m}}^{\mathrm{f}}=2G^{\mathrm{C}}/T_{\mathrm{m}}^0$ , damage variable from

$$D=\frac{{\mathrm{\delta }}_{\mathrm{m}}^{\mathrm{f}}({\mathrm{\delta }}_{\mathrm{m}}^{\text{max}}-{\mathrm{\delta }}_{\mathrm{m}}^0)}{{\mathrm{\delta }}_{\mathrm{m}}^{\text{max}}({\mathrm{\delta }}_{\mathrm{m}}^{\mathrm{f}}-{\mathrm{\delta }}_{\mathrm{m}}^0)}$$

where ${\mathrm{\delta }}_{\mathrm{m}}^{\text{max}}$ refers to the maximum value of the effective separation attained during the loading history. In this study, the mechanical behaviors along two shear directions are assumed to be the same ( $K_{\mathrm{s}}=K_{\mathrm{t}}$ , $T_{\mathrm{s}}^0=T_{\mathrm{t}}^0$ , and $G_{\mathrm{s}}^{\mathrm{C}}=G_{\mathrm{t}}^{\mathrm{C}}$ ), with specific parameters detailed in tables S2 and S3.

Supplementary Materials

The PDF file includes:

Figs. S1 to S17

Tables S1 to S3

Legends for movies S1 to S3

Other Supplementary Material for this manuscript includes the following:

Movies S1 to S3