Self-contact snapping metamaterial for tensile energy dissipation

Abstract

Mechanical metamaterials for energy dissipation have received significant attention for vibration and impact mitigation. However, existing designs often neglect energy dissipation in the tensile direction, which is crucial for attenuating tensile load and controlling falling descent. Importantly, current energy-dissipating mechanisms including plastic deformation and friction mechanisms, suffer from drawbacks such as reversibility and self-recovery, restricting their effectiveness under tension. To address these limitations, we propose a novel mechanism utilizing self-contact snap-through buckling to develop an energy-dissipating metamaterial. Unlike previous metamaterials, the self-contact snapping metamaterial (SCSM) achieves tensile energy dissipation with fewer unit cells while exhibiting reusability, self-recovery, and low reliance on material selection. A theoretical model is established to explain its energy-dissipating mechanism from the perspective of buckling mode transition. Moreover, the proposed SCSM exhibits sequential snapping behavior and effectively mitigates tensile impacts, as demonstrated through quasi-static and dynamic tests. This work opens new avenues for achieving tensile energy dissipation and inspires future research on energy conversion employing self-contact interactions.

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New concepts

In this paper, we introduce a metamaterial specifically designed for tensile energy dissipation. This concept addresses the critical but often overlooked issue of energy dissipation in the tensile direction. Unlike traditional energy-dissipating methods such as plastic deformation and friction mechanisms, our metamaterial leverages self-contact snap-through buckling, which provides superior reusability and self-recovery. This innovative approach not only minimizes the reliance on material selection but also reduces the number of unit cells required, thereby enhancing both practicality and efficiency. The working mechanism proposed here is quantitively analyzed through buckling mode theory and its effectiveness is verified through quasi-static and dynamic tests. Our work presents a new design paradigm for achieving tensile energy dissipation and inspires further applications in robotic actuators and energy harvesters through self-contact interactions.

1. Introduction

Tensile energy dissipation plays a crucial role in mitigating the destructive effects of tensile loads. For example, insufficient energy dissipation in a fall protection lanyard can result in a fatal outcome when people experience a sudden tensile force during a fall from a significant height.^1,2 Similar phenomena occur in practical skydiving and cargo airdrop systems, where the repaid deployment of a parachute causes a sudden deacceleration known as “opening shock”.³ Such tensile force can lead to canopy damage, opening failure, and even injuries to skydivers.^4,5 Although researchers have explored various tensile energy-dissipating methods employing the inherent properties of materials, such as plastic deformation and viscous effect, these methods often suffer from either irreversible deformation or aging failure.^6,7

Metamaterials are man-made materials that derive their unique properties from the structure rather than material composition, allowing for unprecedented functionalities.^8–13 By rationally tailoring the geometry, mechanical metamaterials have been created to mediate mechanical deformation and energy, enabling programmable mechanical response,^14–18 shape reconfiguration,^19–24 energy harvesting,^25–27 vibration isolation,^28–30 and elastic wave modulation.^31–34 In recent years, energy-dissipating metamaterials using friction and snap-back mechanisms have been proposed for their reusability and programmability.^35–38 These metamaterials are characterized by hysteresis formed by the loading and unloading force–displacement curves, where the enclosed area represents the dissipated energy.^38,39 They hold promise as protection devices in engineering, such as reusable energy-absorption devices and dampers.^40,41

However, while most energy-dissipating metamaterials focus on compression behavior, studies on tensile energy dissipation remain limited.^42,43 Moreover, the friction in energy-dissipating metamaterials is easily affected by the contact surface quality and environments,^44,45 and it often hinders these metamaterials from returning to their undeformed state without the assistance of an external force.^39,46–48 Additionally, the snap-back mechanism proposed in recent years relies on the coupled vibration between numerous negative stiffness units, resulting in bulky and heavy metamaterials.^38,49 Despite various efforts to address these issues, the intricate structures^43,50 and a constrained selection of suitable materials^51,52 significantly constrain their practical applications. Therefore, developing tensile energy-dissipating metamaterials with a novel mechanism is imperative to overcome these limitations and improve comprehensive performance. Such advancements hold promise for applications in cable-stayed bridges, power transmission lines, aircraft carrier arresting cables, and high buildings subjected to wind and tensile loads.^53–56

In this paper, we propose an energy-dissipating metamaterial that employs snap-through buckling induced by self-contact interaction for tensile energy dissipation. The unit cell of our metamaterial is characterized by two thin-wall strips transversely inserted into an octagonal frame. Theoretical analysis reveals that, under vertical tension on the frame, the internal strips experience snap-through buckling induced by self-contact, thereby converting strain energy into kinetic energy for dissipation. Further investigation on the metamaterial pixel reveals a sequential snapping phenomenon. Results from both quasi-static and dynamic tests highlight the effectiveness of our proposed metamaterial in mitigating tensile mechanical energy with the characteristics of reusability and self-recovery. This work can broaden design paradigms in energy-dissipating metamaterials and inspire future research employing self-contact interaction for advanced applications, such as tensile dampers, robotic actuators, and energy harvesters.

2. Deformation mechanism

The self-contact snapping metamaterial (SCSM) proposed in our work consists of multiple metamaterial pixels with unit cells connected in series, as shown in Fig. 1(a) and (b). The basic configuration of the SCSM unit cell is an octagonal structure with two transversely inserted strips (yellow part, Fig. 1(c)). Utilizing the positive Poisson's ratio property, the octagonal frame converts vertical tensile loading into transverse compressive loading on the two-strip substructure. To ensure the reusability of the SCSM, limit structures are placed on the upper and lower edges of the unit cell frame to prevent plastic deformation of the internal two-strip substructure (Fig. 1(c)). Next, we investigate the compressive deformation of the two-strip substructure to thoroughly analyze the energy-dissipating mechanism of the SCSM. As depicted in Fig. 1(d), the two-strip substructure is defined by strip length L, the distance S between strips, and out-of-plane thickness b. Both strips are pre-curved with a concave offset Δ towards each other for subsequent contact under transverse compression. To clarify the underlying energy-dissipating mechanism, the buckling mode of the two strips under compression is systematically analyzed (for more details on the theory, see S1. Theory for SCSM, ESI†). According to Euler–Bernoulli beam theory,⁵⁷ the first two basic buckling modes w_i(x) (i = 0, 1) in the center line deflection curve of the strip can be obtained as follows:where the eigenvalues n_iL (i = 0, 1) correspond to different buckling modes. Thus, we can depict the deformation configurations of two strips through a superposition of these basic buckling modes.

Fig. 1 Schematic diagram of self-contact snapping metamaterial (SCSM) and its energy-dissipating mechanism. (a) SCSM composed of multiple SCSM pixels for tensile energy dissipation. (b) SCSM pixel composed of multiple unit cells connected in series. (c) Schematic diagram of SCSM unit cell under tension. The SCSM unit cell includes an octagonal frame with limit structures located at the top and bottom edges (depicted in grey), along with a two-strip substructure inverted transversely (depicted in yellow). The frame converts the vertical tensile loading y_tensile (indicated by yellow arrows) into transversely compressive deformation on the two-strip substructure (indicated by red arrows). (d) Dimensional diagram of two-strip substructure. (e) Deformation configurations of two-strip substructure including loading and unloading processes. Bottom numerical labels identify the specific deformation states under compression, where Snap 1 and Snap 2 dissipate strain energy through the rapid motion of the strip. The buckling modes of the two strips are indicated by different colors. (f) Potential energy of bifurcation buckling in the two contacting strips under compression. Starting from state III, the bifurcation buckling of the two strips involves the transition from the hybrid mode C₀w₀(x) + C₁w₁(x) to the high-order buckling mode w₁(x) (from state III to state V, shown with the orange arrow) and then return to the low-order mode w₀(x) (from state V to state VI, shown with the red arrow). Another bifurcation returns from C₀w₀(x) + C₁w₁(x) to w₀(x) (from state III to state IV, shown with the blue arrow). (g) Force–displacement curve of two-strip substructure including loading and unloading process as predicted by theory. The numerical labels marking the inflection points correspond to the deformation states in (e). The hysteresis area enclosed by the loading and unloading curves represents the dissipated energy U_dis.

Fig. 1(e) demonstrates the deformation process of the two-strip substructure in conjunction with finite element analysis (FEA). Under compression, the two strips are initially compressed (state I) and buckle into the low-order mode w₀(x), bending towards each other. Subsequently, they make contact (state II), limiting the progression of the low-order buckling mode. The strips then deflect around the contact point and transition into a hybrid buckling mode C₀w₀(x) + C₁w₁(x), where C₀ and C₁ represent the contributions of each basic buckling mode (state III). This hybrid mode is an intermediate state between the low-order mode w₀(x) and the high-order mode w₁(x). Increased contact interaction leads to further incompatibility, causing bifurcation in the strips. The right strip first snaps from the hybrid buckling mode to the low-order buckling mode (Snap 1), leading both strips into state IV. As compression continues, the deformation of the left strip is increasingly obstructed by the right strip and gradually develops into the high-order buckling mode w₁(x) (state V). With further compression, the left strip snaps into the low-order mode upon reaching the high-order buckling mode (Snap 2), causing both strips to buckle in the same direction (state VI). Throughout this double-snapping process, approximately one-third of the strain energy in the strips transforms into kinetic energy (Fig. S1, ESI†), which is ultimately dissipated as heat.^51,58 Since the two strips are identical, it is equally possible for Snap 1 to occur on the left strip and Snap 2 on the right. Furthermore, the elastic strips instantly and completely return to their undeformed states (state I) after unloading, indicating reusability and self-recovery. Fig. 1(f) demonstrates the variation in the potential energy of the strips during the double-snapping process. As compression increases, one strip degrades from the hybrid buckling mode to the low-order buckling mode with partial strain energy released, while the other strip transforms the hybrid buckling mode into the high-order buckling mode. With further compression, this high-order mode finally shifts into the same low-order buckling mode, releasing more energy (Fig. S2, ESI†). This process is analogous to electrons transitioning from high to low energy levels, accompanied by the outward release of energy. Compared with our previous work,^59,60 the mechanism proposed here reveals richer buckling mode transitions in interacting structures, significantly improving the energy-dissipation performance through their more synergistic deformation (Fig. S7, ESI†).

By incorporating the geometric constraint, we can determine specific buckling mode configurations of two contacting strips under different compressions. Following this analysis, we identify the critical configurations and corresponding compression for contact, Snap 1, and Snap 2 (see Fig. S4, ESI†). Next, we derive a theoretical model to predict the mechanical response of the two-strip substructure. As illustrated by the theoretical results in Fig. 1(g), the inflection points corresponding to different deformation states are first determined, and the transition between adjacent states is facilitated with linearity to obtain the force–displacement curves. The energy mediated in the two-strip substructure is initially stored as strain energy during self-contact interaction and is finally dissipated through snap-through buckling. This dissipation can be calculated by integrating the hysteresis area enclosed by the loading and unloading curves.

3. Results and discussion

The samples used in this work were printed via fused deposition modeling (FDM) with PLA. The material properties, determined through tensile dog-bone tests,⁶¹ are characterized by Young's modulus E = 2650 MPa and yield strength σ_s = 48 MPa (Fig. S10, ESI†). Displacement-controlled loading and unloading tests were conducted on the samples (Movie S1, ESI†). Fig. 2(a) illustrates that FEA accurately captures specific deformation configurations in experiments, particularly the double snap-through processes of the two strips (for more information, see S2. FEA of SCSM and S3. Experiment preparation, ESI†). The consistency among force–displacement curves from theory, FEA, and experiments is shown in Fig. 2(b), with the blue triangular corresponding to the geometrical parameters detailed in Fig. 2(e) and (f). Furthermore, the loading–unloading curve from FEA presents extra hysteresis due to buckling recovery caused by traverse offset Δ, which is also observed in experiments during unloading (refer to the unloading stage in Fig. 2(a)). In Fig. 2(c), the effect of the distance S between two strips on the critical strain ε_cr for Snap 2 is studied, with both FEA and theoretical analysis showing excellent prediction accuracy. These results indicate that an increase in the distance S leads to a higher critical strain, as well as increased dissipated energy (Fig. S11a, ESI†). Fig. 2(d) investigates the effect of the thickness of strips t on the dissipated energy U_dis through theoretical analysis, FEA, and experimental results. It is observed that increasing t enhances the dissipated energy, while the critical strain for Snap 2 remains insensitive to this parameter (Fig. S11b, ESI†). Fig. 2(e) further verifies that increasing both S and t synergistically maximizes energy dissipation. Therefore, we can program deformation states and dissipated energy by tuning the appropriate geometrical parameters of the two-strip substructure. Moreover, the deformation distance D can be calculated from the critical deflection of the strip after Snap 2, which is mainly affected by the two-strip distance S, as depicted in Fig. 2(f). This parameter is crucial for designing limit structures in further studies.

Fig. 2 Experimental results, FEA, and theoretical predictions of two-strip substructure. (a) Deformation configurations of two-strip substructure under compression from FEA and experimental results. Snap 1 and Snap 2 occur during loading while bulking recovery occurs during unloading. Scale bar, 1 cm. (b) Force–displacement curves obtained from experiments (blue area), FEA (red solid line), and theory (black dotted line). The loading and unloading curves from FEA are indicated by red arrows. The geometric parameters are selected as L = 80 mm, b = 15 mm, S = 10 mm, t = 1 mm, and Δ = 0.5 mm. (c), (d) Comparison of critical strain ε_cr with varying two-strip distance S and dissipated energy U_dis with varying strip thickness t, as calculated from theoretical analysis, FEA, and experiments. (e) and (f) Phase diagrams illustrating dissipated energy U_dis and deformation distance D in two-strip substructure, varying with strip distance S and strip thickness t from FEA. The inset diagram in (f) indicates that the effective limit distance is determined by the deflection of the snapped strip with a low-order bulking mode after Snap 2. The blue triangular marks the specific two-strip substructure with its mechanical responses shown in (b). Other geometric parameters remain consistent with those in (b).

Further investigation was conducted to analyze the tensile energy-dissipating behavior of the SCSM unit cell. The critical parameters of the octagonal frame are provided in Fig. 3(a), including the transverse length a, the vertical height c, the thickness t of the inclined walls, and the distance d between the limit structures and the two-strip substructure. The distance d is determined based on Fig. 2(f) to prevent excessive deflection of the snapped strip without affecting its snap-through process (Fig. S12, ESI†). In Fig. 3(b), both experimental results and FEA demonstrate the double-snapping deformation of the internal strips induced by the tension applied to the octagonal frame (Movie S2, ESI†). Fig. 3(c) illustrates the loading–unloading mechanical responses of the SCSM unit cells, with the green circle representing the geometrical parameters demonstrated in Fig. 3(d) and (e). The force–displacement curve presents obvious hysteresis, verifying the consistency between experimental results and FEA. Additionally, the curve exhibits subsequent increases in the overall stiffness of the SCSM unit cell, attributed to the obstruction caused by the limit structure on the snapped strip. Fig. 3(d) and (e) investigate the effects of geometrical parameters a/c and t₀/t on the critical strain for Snap 2 of the two-strip substructure and the dissipated energy. The critical strain increases only with a/c, while the dissipated energy increases with both a/c and t₀/t. However, the energy dissipation of the SCSM unit cell is less than that of the single two-strip substructure under compression according to FEA results (Fig. S13a, ESI†). This discrepancy is due to shear deformation in the octagonal frame, which arises from the asymmetrical configuration of the internal contacting strips during deformation (Fig. S13b, ESI†). To validate this deduction, we restricted shear deformation by thickening the inclined walls of the frame. Consequently, the energy dissipation of the SCSM unit cell approaches the upper limit provided by the single two-strip substructure as t₀/t increases, and the corresponding experimental results also demonstrate this tendency (Fig. 3(f)). Moreover, the energy dissipation of experimental results surpasses that predicted by FEA and even exceeds its upper limit, which is related to the viscous effect of the constitutive material during large deformation. In addition to axial tension, in-plane inclined tension and out-of-plane tension on the SCSM can also induce snap-through buckling, facilitating effective energy dissipation under complex loading conditions (Fig. S15 and S16, ESI†). Furthermore, a metal-based SCSM was fabricated using NiTi to demonstrate the applicability of our proposed metamaterial. Cyclic testing demonstrates its outstanding reusability, with only a 2.3% reduction in strength after 500 cycles (Fig. 3(g)). This performance surpasses previous energy-dissipating methods using friction,⁴⁴ and unlike the snap-back mechanism, it achieves effective energy dissipation without compromising reversibility⁶² or relying on the shape memory effect,⁶³ confirming its reduced material reliance. Additionally, the metal SCSM unit cell was tested under varying strain rates to verify its effectiveness under low-speed loading (Fig. 3(h)), and its high-speed performance may be compromised if its internal snapping speed does not significantly exceed the external loading speed.⁴⁹

Fig. 3 Mechanical response of SCSM unit cell. (a) Dimensional diagram of SCSM unit cell. The geometrical parameters include the traverse length a = 30 mm, the vertical height c = 10 mm, and the thickness t₀ = 1 mm of the four identical inclined walls. The limit distance is selected as d = 5.5 mm considering the deformation distance D of the two-strip substructure and the deformation of the external frame. Other unspecified parameters are the same as those in Fig. 2(b). (b) Deformation configurations of SCSM unit cell under tension as observed in FEA and experiments. Snap 1 and Snap 2 occur on the internal two strips during tensile loading. Scale bar, 2 cm. (c) Experimental (blue area) and FEA (red solid line) force–displacement curves of SCSM unit cell. The loading and unloading curves from FEA are indicated by red arrows. The numerical labels correspond to different deformation states in (b). (d) and (e) Phase diagrams illustrating critical strain and dissipated energy with varying parameters a/c and t₀/t from FEA. The grey region represents plastic deformation. The green circle indicates the specific SCSM unit cell with its mechanical responses shown in (c). (f) Dissipated energy calculated from experiments and FEA for various t₀/t. The inset diagram demonstrates the shear deformation of the SCSM unit cell using PLA under tension. The dotted blue line represents the ideal dissipated energy calculated from the two-strip substructure through FEA in Fig. 2(b). (g) and (h) Effects of loading cycles and strain rates on force–displacement curves of metal-based SCSM unit cell. The inset diagrams provide a structural overview of the metal SCSM unit cell. Scale bar, 2 cm.

While a single unit cell effectively demonstrates the concept of tensile energy dissipation, exploring the mechanical behavior of its serial arrangement in the metamaterial is instructive. Fig. 4(a) presents the deformation configurations of the SCSM pixel, where multiple unit cells are connected along the tensile direction. During the tension of the SCSM pixel, the previous double-snapping process within the unit cell degenerates into a single snapping event due to increased shear deformation along the serial connection. Additionally, each unit cell snaps in sequence caused by the fabrication defects and varying boundary conditions (Movie S3, ESI†). The serrated force–displacement curve in Fig. 4(b) verifies this sequential snap-through buckling phenomenon. Furthermore, the SCSM pixel allows for programmable mechanical responses by discretizing it into pre-designed unit cells, which can achieve multiple force thresholds (Fig. 4(c)) and strain thresholds (Fig. S17, ESI†). This programmability enables the metamaterial to resist various load intensities and potentially incorporate complex textured surfaces under tension for mechanical information encryption.

Fig. 4 Mechanical behavior of SCSM and its dynamic response. (a) Deformation configurations of SCSM pixel under tension. Scale bar, 3 cm. The sequential snap-through buckling of each unit cell is captured and highlighted by the gradient dotted circles. (b) Force–displacement curves of SCSM pixel from experimental results (blue area) and FEA (gradient solid line). The loading and unloading curves from FEA are indicated by gradient arrows. The numerical labels correspond to specific deformation states in (a). The geometrical parameters are scaled to 0.6 times those of the unit cell in Fig. 3(b). (c) Programmable force–displacement curve of SCSM pixel with multiple force thresholds. The partial curves corresponding to force thresholds are indicated by different colors. The incline wall thickness of serial unit cells is programmed with t₁ = 1.2 mm and t₂ = 1.4 mm, respectively. Other parameters are consistent with those in (a). (d) Deformation configurations of SCSM composed of SCSM pixels. Scale bar, 2 cm. (e) Experimental force–displacement curves of SCSM including loading and unloading processes. The shaded region represents the dissipated energy. (f) Comparison of SCSM and representative single-beam metamaterial⁴⁹ on the dissipated efficiency η with different number of unit cells N in series. The dissipated efficiency is calculated as η = (U_dis,N/N)/(U_dis,20/20), where N is the number of unit cells in series and U_dis,N denotes the dissipated energy of metamaterials with N unit cells in series. The average dissipated energy per unit cell is given by U_dis,N/N, which is then normalized by the average dissipated energy of 20 serial unit cells in each metamaterial, U_dis,20/20. The dissipated energy of the serial SCSM is obtained from FEA. (g) Experimental setup of impact test. The upper part of the SCSM pixel is fixed, while the bottom part connects to the impactor (doll model) through an inelastic rope. The impactor is released from varying heights, which is measured by the ruler. (h) Sequential snapshots capturing snap-through buckling of SCSM pixel under falling height H = 30 cm. (i) Peak acceleration of impactor at different releasing heights and corresponding rate of increase. The increasing rate of peak acceleration is determined by calculating the slope of each segment within the peak acceleration-height curve. It shows a lower increase across a wide range of releasing heights within the force mitigation regime (blue region).

To improve energy-dissipation performance, we extended SCSM pixels into the SCSM without the constraints of transverse connection (Fig. 4(d); see Fig. S18 in ESI† for details).⁶⁴ As depicted in Fig. 4(e), the SCSM exhibits hysteresis while maintaining self-recovery and reusability, indicating its potential to mitigate tensile energy, such as protecting individuals from high falls (Movie S4, ESI†). We further compared the energy-dissipation efficiency between the SCSM and the previously studied single-beam metamaterial⁴⁹ regarding the number of serial unit cells, as illustrated in Fig. 4(f). The single-beam metamaterial relies on the snap-back mechanism, which involves coupling vibrations across multiple serial unit cells but lacks inherent energy dissipation in the individual unit cell.⁶⁵ In contrast, the SCSM dissipates energy through two distinct mechanisms: snap-through buckling induced by self-contact within each unit cell, and the snap-back mechanism facilitated by vibration coupling among serial unit cells (see Fig. S19 in ESI† for the mechanical responses and energy dissipation with varying numbers of unit cells). Both metamaterials tend to maximize energy dissipation with an increasing number of serial unit cells, owing to their common reliance on the snap-back mechanism. However, the SCSM can dissipate energy with fewer unit cells, which is attributed to additional energy dissipation from snap-through buckling induced by self-contact within each unit cell.

Next, we investigated the dynamic response of the SCSM pixel through impact tests, as shown in Fig. 4(g) (see S3. Experiment preparation and Fig. S20 in ESI† for details). An impactor weighing m = 150 g was tethered to the bottom of the SCSM pixel by an inextensible rope, simulating scenarios where a parachutist jumps from high altitude and the metamaterial cushions the impact force during descent. By releasing the impactor from different heights, the metamaterial underwent tension impact as the stretched rope transmitted the force (Movie S5, ESI†). The acceleration response of the falling impactor was then recorded, with snapshots confirming deformation configurations similar to those observed in quasi-static tension (Fig. 4(h)). To analyze the dynamic response of the SCSM pixel, we recorded peak acceleration and calculated the corresponding increasing rate of peak acceleration k across various falling heights, as depicted in Fig. 4(i). The falling height was divided into three regions: R1, R2, and R3, based on the trend of the peak acceleration-height curve. For each region, we further calculated the average increasing rate of peak acceleration, denoted as k⃑_i (i = 1, 2, 3), for comparison. In R1, the peak acceleration increases proportionally with height (k⃑₁ = 0.444), where the impact force is insufficient to exceed the threshold of snap-through buckling. Upon reaching R2, the peak acceleration exhibits a much lower increase with k⃑₂ = 0.177. In this region, the strips snap in sequence, resisting the peak acceleration and achieving force mitigation (refer to Fig. S21 in the ESI† for detailed analysis). The average impact force (F = ma_peak) is 16.44 N, which is close to the average serrated force of 13.24 N observed in quasi-static results. Besides, The input energy E_inp in R2 ranges from 220 mJ to 478 mJ, comparable to the quasi-static absorbed energy, represented by the area beneath the force–displacement loading path after all strips have snapped (217 mJ, Fig. 4(b)). R3 marks the region where the SCSM pixel is fully stretched with all strips snapping. In this phase, the acceleration increases rapidly due to the remnant kinetic energy, and the increasing rate is k⃑₃ = 0.632, surpassing even k₁ from the initial region, which is attributed to the stiffening effect from the limit structure. Moreover, the programmability of the SCSM allows regulation of the length of R2 by altering the effective working range of the SCSM, such as varying the number of SCSM unit cells in series and the distance between two strips within the unit cell. Additionally, the peak acceleration amplitude within R2 can be tuned by modifying the peak force of the SCSM, involving adjustments in the number of SCSM unit cells in parallel and the thickness of the frame and strips within the unit cell.

4. Conclusion

In summary, we propose a mechanical metamaterial featuring two strips transversely inserted into an octagonal frame for tensile energy dissipation. The underlying energy-dissipating mechanism leverages the snap-through buckling of internal strips caused by self-contact, dissipating energy through the rapid motion of snapping strips. Theoretical analysis elucidates this mechanism through buckling mode transitions and provides quantitative predictions for the mechanical response of the two-strip interaction, all of which are confirmed by FEA and experimental results. Various materials employed in fabrication verify the universality of our designed metamaterial. Due to the elastic snapping deformation, our metamaterial can dissipate energy in a reusable and self-recoverable manner. Furthermore, the SCSM exhibits sequential snap-through buckling and mitigates tensile loads in dynamic tests. The tensile energy-dissipating metamaterial opens potential applications in cable-supported buildings, descent control devices, and structures designed to withstand blast and wind loads. Notably, the self-contact-induced snap-through buckling, which converts strain energy into kinetic energy, can serve not only for energy dissipation in mechanical protection but also for energy conversion in energy harvesters and robotic actuators. This mechanism holds broad applicability to various topological configurations where thin-wall structures interact, such as multilayer shells and porous structures. Although the proposed metamaterial dissipates limited energy due to its elastic deformation nature and is confined to a single loading direction. Future studies can incorporate additional energy-dissipating mechanisms, including the friction mechanism and material viscosity, to enhance energy-dissipation performance and enable bi-directional energy dissipation under complex load conditions.

Data availability

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

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This work was supported by National Natural Science Foundation of China (52332006), the National Key R&D Program of China (2022YFB3806000, 2023YFB3811401), and Southwest United Graduate School Research Program (202302AO370008).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4mh01013b

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