Bio-Inspired Sinusoidal Metamaterials: Design, 4D Printing, Energy-Absorbing Properties

Abstract

Conventional energy-absorbing components have limited adjustability under complex working conditions. To overcome this limitation, we designed a bio-inspired sinusoidal metamaterial (BSM) inspired by the efficient energy-absorbing structure of the mantis shrimp jaw foot and 4D printed it based on shape-memory polymer (SMP). The effects of single-cell structural parameters and gradient design on its force–displacement curves and energy-absorbing properties were explored. Based on the shape memory effect of SMP, the BSM can obtain arbitrary temporary shapes under the combined effect of temperature and force, realizing locally controllable compression deformation and programmable mechanical properties of the BSM structure. This research has a broad application prospect in the field of energy absorption and energy management and provides new ideas for the design of smart structural materials.

1. Introduction

Throughout the long evolutionary history of nature, living organisms have developed many ingenious structures and mechanisms to cope with the challenges of the external environment, especially in terms of energy absorption and dissipation [1,2,3]. For example, the exoskeletons of insects [4,5] and arthropods [6], animal sutural structures [7,8,9,10,11,12], and cellular structures [13,14,15,16] have demonstrated excellent energy absorption and dissipation capabilities. The unique geometry, material composition, and microstructure of these biological structures allow for efficient energy management in the presence of external forces, thereby protecting the integrity and function of the organism.

Inspired by biological structures in nature, designed and fabricated biomimetic structures have significantly improved energy absorption and dissipation methods compared with conventional structures. For example, inspired by the suture structure of a woodpecker’s beak, Yu et al. [17] proposed a biomimetic inlay structure with a suture interface, which achieved excellent damping performance. Malik et al. [18] investigated a “jigsaw” interlocking structure and developed a model that captures the pull-out process at the interface. The results show that the optimal energy absorption capacity is closely related to the sawtooth structure, with a low coefficient of friction and a high interlocking angle. Zhang et al. [19], inspired by the structure of a pomelo peel honeycomb, designed a bionic pomelo peel honeycomb with hierarchical levels of structure, and the results show that the synergistic effect of the order of the different levels produces a superior energy absorption and impact-resistance behavior. The equivalent platform stress and corresponding specific energy absorption obtained is about 1.5 times higher than those of conventional hexagonal honeycomb shape in out-of-plane crushing.

While considering a lightweight design, mechanical metamaterials, as representatives of lightweight structures that can produce different deformation characteristics under the excitation of external physical fields by manually designing the internal microstructure, have mechanical properties or functions that even natural materials do not have [20,21,22,23,24]. For example, a negative Poisson’s ratio, compression-torsion coupling, negative compression, and negative stiffness characteristics in response to stress fields [25,26,27], or negative thermal expansion characteristics in response to temperature fields [28,29]. Therefore, they are widely used in military, aerospace, medical, and other fields. Obtaining relevant advantageous functions by simulating and mimicking the typical structural features of biological systems is an important way to create new mechanical metamaterials. Mao et al. [30] investigated the mechanical properties of cuttlefish bone, where a complex s-shaped corrugated wall prevents the cuttlefish bone from buckling under high hydrostatic pressure at depth. Inspired by this, they designed 3D-printed bio-inspired mechanically efficient cellular materials, which are 2.5–20 and 3.5–25 times stronger and more energy absorbing than conventional polymer and metal foams. Inspired by Euplectella aspergillum, Sharma et al. [31] prepared a Ti-6Al-4V mechanical metamaterial based on selective laser melting, and the diagonal support design helped the loads to be uniformly distributed on the metamaterial, and its strength and elastic modulus were significantly increased. Liang Meng et al. [32] designed a hyperbolic lattice structure inspired by the double-layered morphology of the fore-wing shells of flying beetles, and tests showed that the structure has a significant torsional effect and energy absorption.

At present, due to the simple structure of traditional mechanical metamaterials, it is more difficult to meet the needs of some special applications, while some special structures exist in nature with special characteristics, making bio-inspired mechanical metamaterials gradually become a research hotspot. However, it is worthwhile to pay attention to the fact that once the current bio-inspired mechanical metamaterials are fabricated, their performance cannot be adjusted, and the energy-absorbing effect will rapidly deteriorate in the face of complex and changing working conditions. Therefore, it is particularly important to study mechanical metamaterials with tunable properties and excellent mechanical properties.

Here, we design a bio-inspired sinusoidal metamaterial (BSM) inspired by the lamellar structure within the mantis shrimp jaw foot. First, the proposed BSM was analyzed from geometrical and hydrostatic points of view. Secondly, the effects of structural parameters on the energy absorption properties of the metamaterials are investigated in conjunction with the parametric design of single-cell structures. The gradient design strategy is applied to the design of BSMs to obtain tunable stress–strain curves and programmable energy absorption properties. Finally, the intelligent switching of the energy-absorbing properties of BSMs is realized with the help of the shape-memory property of polylactic acid (PLA).

2. Experimental Section

Design of bio-inspired sinusoidal metamaterials (BSM): The Mantis shrimp is a famously aggressive creature of the sea, known for its speed and power of attack. Their attacking organ is a pair of specialized jaw feet that can be catapulted in a very short time at speeds of up to 80 km/h, accelerating even faster than some handgun bullets, and generating a huge impact that is strong enough to smash hard-shelled animals such as shellfish and crustaceans. N.A. Yaraghi et al. [6] found a new structural feature, the sinusoidal structure, in addition to the laminar structure found in the mantis shrimp’s jaw foot portion by using high magnification differential interference contrast images. Here, we designed a bio-inspired sinusoidal metamaterial (BSM) structural unit based on this finding and obtained the BSMs by array (Figure 1). The structural unit is composed of two primary and secondary sinusoidal curves, which have the same period length and different amplitudes. Among them, the amplitude of the primary curve is A₁, and the amplitude of the secondary curve is A₂, with a period of 4 L. To achieve efficient energy absorption and dispersion of the structure, the parameter design of the sinusoidal curves is crucial. Specifically, different amplitudes and periods of the metamaterials have different respective application requirements. The energy absorption characteristics of the metamaterials can be precisely controlled by adjusting the structural parameters.

4D printing: the BSM in the study was prepared by a fused deposition molding (FDM) 3D printer (ALK200-2, Dongguan Ariku 3D Technology Co., Dongguan, China). The nozzle’s printing temperature was 220 °C, the printing platform temperature was 60 °C, and the fill rate was 100%. The printing filament was PLA filament, and its density was 1.26 g/cm³. The 4D printing in this paper is based on 3D printing, which is capable of generating spontaneous, programmable changes under the excitation of a thermodynamic field, integrating sensing, control, and response functions in a smart material system.

Single-axis compression test: the mechanical test equipment used is as follows: Shenzhen Sansi Zongheng Technology Co., Ltd. (No.8 Building, Hengmei Xinzaobang, 18th Building, Third Industrial Zone, Heshuikou Community, Matian Street, Guangming District, Shenzhen, China); Model UTM6104. 2 mm/min (low speed) and 20 mm/min (medium speed) are selected as the two speeds of compression.

3. Results and Discussion

A BSM was designed, inspired by the sinusoidal structure of the mantis shrimp jaw foot, and the BSM structure was stereo-molded using the FDM process. Firstly, we explored the deformation process and force–displacement curves of the structure under compressive loading, and we took a three-cycle metamaterial sample with five sample layers. The BSM structure was placed horizontally in the middle of the compression force test apparatus along the sinusoidal direction, and then compressed downward from the top to the bottom with a fixed velocity, and the results of the mechanical experiments are displayed in Figure 2. The whole compression process presents a complex mechanical process (Figure 2a), which can be divided into four stages as a linear elastic stage, plastic stage, platform stage, and densification stage, respectively. First, in the linear-elastic stage, with the gradual increase in the compression load, a small linear-elastic deformation of the unit wall occurs, and in this stage, the stress and strain show a linear relationship. In the plastic phase, when the load reaches the elastic limit value of the material, the material will undergo buckling changes, and this buckling phenomenon will lead to localized regional stress of the member exceeding the elastic limit of the material and entering the plastic state. In this process, the metamaterial structure begins to show local buckling and plastic instability, and the unit structure gradually loses stability. In this stage, the load decreases slightly with the increase in compression displacement. While in the platform stage, with the increase in compression displacement, more cell walls undergo local buckling and plastic deformation, and the sinusoidal structure tilts in this unstable state, causing the hinges to rotate and the structure to fold layer by layer. The load changes are relatively stable with increasing compression displacement in this stage. Finally, in the densification stage, most of the unit structure is folded and sufficiently compacted so that the load rises rapidly and the force–displacement curve rises steeply.

It is worth noting that the force–displacement curves in Figure 2a increase slightly in the second half of the platform stage. By analyzing the inset of Figure 2b, it can be found that as compression displacement increases in the longitudinal direction, the structure decreases in size in the transverse direction and the structure exhibits a significant negative Poisson’s ratio effect.

In addition, we also analyzed the effect of different compression speeds on the force–displacement curves of metamaterials. We chose the sample with the sinusoidal equation of 4sin(0.5t) + 0.5sin(0.5t) and applied two compression speeds of 2 mm/min and 20 mm/min, respectively. The experimental results were verified and analyzed by finite element simulation, and the results are displayed in Figure 2b. The compression curves are slightly different; e.g., the peak force at partial compression displacements (8, 13, 16 mm, etc.) is slightly larger for 20 mm/min than for 2 mm/min. This is because, at higher compression speeds, the internal units of the structure do not have enough time to rearrange themselves, thus leading to larger peak forces. However, the overall trend is similar for both curves.

Next, we will focus on the effects of the BSM structural parameters on its compression resistance and energy absorption characteristics. First, we explore the effect of the primary curve amplitude A1 of the BSM structural units on their force–displacement curves and energy-absorption characteristics. We choose 4, 6, 8, and 10 mm principal curve amplitudes for quasi-static compression tests, and the results are shown in Figure 3. Comparing the force–displacement curves of the BSM structures with different primary curve amplitudes, it can be found that the structures show similar force–displacement curves, including the typical four stages, being the linear elasticity stage, plasticity stage, plateau stage, and densification stage. Moreover, as the amplitude of the primary curve increases, the EA (energy absorption) of the structure decreases from 41,419 mJ at A1 = 4 mm to 15,875 mJ at A1 = 8 mm, which is a decrease of 61.7%, and then increases to 23,084 mJ, which is an increase of 45.4%, showing a trend of decreasing and then increasing. This may be attributed to the decrease in energy absorption efficiency due to the increase in structural stiffness. However, when the primary curve amplitude continued to increase to a certain threshold, the structure added more favorable energy dissipation mechanisms for structural instability. Slightly different from the trend in EA, SEA gradually decreases, from 6342 mJ/g for A1 = 4 mm to 1590 mJ/g for A1 = 10 mm, which is a 74.9% decrease. This indicates that the structure’s energy absorption capacity per unit mass is decreasing (see Supplementary Materials for details of the analytical methods for EA and SEA).

As another key structural parameter of the BSM structure, the secondary curve amplitude, and its influence on the mechanical properties, has been further explored. We chose four secondary curve amplitudes, 0.5, 1, 2, and 6 mm, to investigate the influence of secondary curve amplitude on the mechanical properties of the structure. Figure 4a demonstrates the effect of secondary curve amplitude on the structural force–displacement curves, and the effective compression stroke of the BSM structure decreases significantly with the increase in secondary curve amplitude. Its EA and SEA show a trend of decreasing and then increasing (Figure 4b).

Another key structural parameter of the BSM is the cycle length; therefore, three different cycle lengths were designed and used to investigate the effect of cycle length on the compression characteristics of the structure, and the results are displayed in Figure 5. Figure 5a shows that the BSM structures with different cycle lengths have similar effective compression strokes, which is because the height of the BSM structure mainly depends on the amplitude of the primary and secondary curves in the longitudinal direction of the structure. From Figure 5a, it is found that the platform force of the structure increases with decreasing cycle length; conversely, it decreases. This is because, as the cycle length decreases, the apex of the curve takes on a sharp shape, and this structure can disperse the force better when under pressure, thus resisting compression and improving the compression resistance characteristics and peak force of the structure’s platform stage. Similarly, the cycle length of the structure is closely related to the EA and SEA of the BSM. The EA and SEA of the structure increase significantly with the decrease in the cycle length, especially in the SEA. Its SEA increases from 3817.5 mJ/g for L = 4 mm to 7746.04 mJ/g for L = 1 mm, which is an increase of 102.9%.

To make the macroscopic mechanics of metamaterials more adjustable, we introduced gradient design in the structural design of the BSM. The structural parameters of the unit structure, such as the primary curve amplitude A1 and the secondary curve amplitude A2, were changed according to a certain law, to realize a continuous change in physical properties at the macroscopic level, and this design method enables the metamaterials to show different mechanical behaviors in different regions, to satisfy the needs of specific application scenarios. First, we design the gradient of the primary curve amplitude of the BSM structure, and the A1 of the top-down BSM structure is 4, 4, 6, 8, and 10 mm, respectively. Compression tests are performed on the gradient structure to obtain the force–displacement curves as well as the energy-absorption properties, and the results are displayed in Figure 6a,b. The results show that the primary curve of the BSM structure utilizes the gradient design to obtain a similar force–displacement curve as A1 = 6, but the initial peak force of the structure is higher than that of the BSM structure with A1 = 6. The force decreases to 84.4 N after reaching the initial peak force and then increases sharply after a slow rise to about 678.5 N, with an increase in the force of 703.9% during this compression process. The area enclosed by the force curve and the horizontal coordinate is the absorbed energy. It can be seen from the analysis and comparison that the overall energy absorption characteristics of the structure are improved by the gradiented design. The EA and SEA of the designed gradient BSM structure increased by 69% and 133.8%, respectively, compared to the A1 = 6 BSM structure.

The secondary curve amplitude is another key parameter for gradient design, and the bottom-up secondary curve amplitudes are 0.5 mm, 0.5 mm, 1 mm, 1 mm, and 2 mm, respectively. The force–displacement curves of the BSM structure with the gradiented design for secondary curve amplitude during quasi-static compression are shown in Figure 6c. Compared with the BSM structure with homogenized secondary curve amplitude, the force of the structure with the gradient design rises more slowly in the plateau stage, from 403.5 N to 678.5 N, which is only increased by 94.5%. In response to the energy absorption characteristics of the structure, it can be found that the gradient design of the secondary curve amplitude reduces the energy absorption characteristics of the structure significantly. Compared with the BSM structure with A2 = 1 mm, its EA and SEA are reduced by 25.7% and 18%. Above all, it can be found that the force–displacement curves and energy-absorption characteristics of the structure can be programmed by the gradient design of the primary curve magnitude A1 and the secondary curve magnitude A2.

PLA, as a typical shape-memory polymer (SMP), has unique shape-memory properties. It is capable of obtaining arbitrary temporary shapes under specific conditions, as shown in Figure 7a. In the programming stage, the SMP is made soft and deformable by heating, and an external force is applied to mold the BSM structure into the desired temporary shape, as shown in Figure 7b. While maintaining the shape, the temperature is lowered below the glass transition temperature (Tg) to allow the polymer to cure and remain deformed. The glass transition temperature Tg of PLA material from a solid to viscous flow state with fluidity was obtained by differential scanning calorimetry (DSC). The results are shown in Figure 7c, and the Tg temperature of PLA is 58 °C. To achieve good shape-memory characteristics, we set the deformation temperature to 65 °C (slightly higher than Tg). Meanwhile, the BSM structure is compressed to obtain BSM structures with different temporary compression shapes. During compression, the unit structure undergoes different degrees of buckling, which in turn changes the structural parameters of the BSM structure and may affect the compression force–displacement curves and energy-absorption properties of the BSM structure.

To study the effect of structural parameters of BSM on its energy absorption effect, we took a sample of metamaterial with a sinusoidal function of 10sin(0.25t) + 2sin(0.25t) and heated it to the glass transition temperature. Then, we manually set it to 10%, 20%, and 30% compressive strain as different temporary shapes of the BSM and analyzed the metamaterials by compression test, the results of which are shown in Figure 7d. The setting of the temporary shape affects the force–displacement curves and energy absorption characteristics of the structure. As the compressive strain of the temporary shape increases, the effective compressive stroke of the structure decreases significantly (Figure 7d). The changes in EA and SEA of the temporary shapes are more significant (Figure 7e); 10% has the highest EA and SEA, which are 25,238.2 mJ and 1932.6 mJ/g. As the compressive strain of the temporary shapes increases, the EA and SEA of the structures significantly decrease. When temporary shape 3 is reached (compressive strain of 30%) the EA and SEA are 17,503.4 mJ and 1348.4 mJ/g, respectively, which are both reduced by about 30%. This is mainly attributed to the gradual decrease in the effective compression stroke of the structure as the degree of compression of the temporary shape increases with the adjustment of the structural units, which leads to a significant decrease in the EA and SEA of the structure.

4. Conclusions

In this study, we successfully demonstrated the 4D printing of a BSM. By precisely tuning the structural parameters of the sinusoidal metamaterial during the design process, the metamaterial is endowed with unique tunable energy absorption properties. For example, by tuning the amplitude of the main curve of sinusoidal metamaterial, the EA and SEA of the structure were reduced by 61.7% and 74.9%, respectively. Combined with the shape-memory property of PLA material, it exhibits predetermined shape changes and mechanical adjustments under external stimuli. Through the setup of temporary shapes, we reveal the intrinsic link between the structural transformation of metamaterials and their macroscopic energy absorption properties, with up to 30% reduction in the EA and SEA of metamaterials between different temporary shapes. The sinusoidal metamaterial developed by this institute have programmable energy-absorption properties comparable to conventional energy-absorbing materials. In addition, the mechanical metamaterial has excellent mechanical properties and does not suffer from fracture failure. Therefore, the sinusoidal mechanical metamaterial designed in this paper is expected to play an important role in the fields of protective equipment, vibration control box energy harvesting, etc., especially in scenarios that require adaptive and reconfigurable functions.