3D self-locking granular metamaterials.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Adv . 2026 Apr 10;12(15):eaec8845. doi: 10.1126/sciadv.aec8845 Search in PMC Search in PubMed View in NLM Catalog Add to search 3D self-locking granular metamaterials TongTong Liu TongTong Liu 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by TongTong Liu 1, † , Tao Sun Tao Sun 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by Tao Sun 1, † , Ning Cao Ning Cao 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - review & editing Find articles by Ning Cao 1 , Yue Shen Yue Shen 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by Yue Shen 1 , Kailun Wang Kailun Wang 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Formal analysis, Investigation, Writing - review & editing Find articles by Kailun Wang 1 , Haichao Long Haichao Long 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Validation, Writing - review & editing Find articles by Haichao Long 1 , Yongbin Guo Yongbin Guo 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Formal analysis, Resources, Validation Find articles by Yongbin Guo 1 , Yang Zhang Yang Zhang 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Funding acquisition, Validation, Writing - review & editing Find articles by Yang Zhang 1 , Xiang Li Xiang Li 2 School of Physics and Mechanics, Wuhan University of Science and Technology, Wuhan 430065, China. Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing - original draft, Writing - review & editing Find articles by Xiang Li 2, * , Ying Wu Ying Wu 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. Conceptualization, Data curation, Formal analysis, Funding acquisition, Project administration, Resources, Supervision, Validation, Writing - original draft, Writing - review & editing Find articles by Ying Wu 1, * Author information Article notes Copyright and License information 1 School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China. 2 School of Physics and Mechanics, Wuhan University of Science and Technology, Wuhan 430065, China. * Corresponding author. Email: [email protected] (X.L.); * Corresponding author. Email: [email protected] (Y.W.) † These authors contributed equally to this work. Roles TongTong Liu : Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Tao Sun : Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Ning Cao : Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - review & editing Yue Shen : Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Kailun Wang : Formal analysis, Investigation, Writing - review & editing Haichao Long : Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Validation, Writing - review & editing Yongbin Guo : Formal analysis, Resources, Validation Yang Zhang : Funding acquisition, Validation, Writing - review & editing Xiang Li : Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing - original draft, Writing - review & editing Ying Wu : Conceptualization, Data curation, Formal analysis, Funding acquisition, Project administration, Resources, Supervision, Validation, Writing - original draft, Writing - review & editing Received 2025 Oct 7; Accepted 2026 Mar 10; Collection date 2026 Apr 10. Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license , which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. PMC Copyright notice PMCID: PMC13068065  PMID: 41961926 Abstract Mechanical metamaterials derive unique properties from microarchitectures, yet most designs remain static once fabricated. Here, we propose a three-dimensional (3D) self-locking granular metamaterial composed of rigid ellipsoidal particles with flexible hook-like appendages inspired by Xanthium seed burs. The hooks interlock to form self-confined structures that fail via sequential stepwise unhooking under tension, greatly enhancing ductility. Under shear, the material transitions from an initially low-resistance, fluid-like state to a rigid, solid-like state once hooks engage, exhibiting a sliding-to-locking transition. In compression and impact, energy is dissipated through layer penetration and collapse of internal voids, with kinetic energy converted into heat via interhook friction, yielding superior energy absorption. Unlike foams, the structure can protect fragile payloads without external packaging. Because the hooks deform elastically rather than plastically, the units remain intact and reusable after loading. This work demonstrates the 3D self-locking granular metamaterial without external confinement, enabling adaptive and reusable protective materials. Xanthium -inspired 3D granules interlock without confinement, enabling robust and reconfigurable mechanical behavior. INTRODUCTION Mechanical metamaterials can achieve distinct, exotic properties through rational microstructural design ( 1 ). Various classes, such as periodic lattices ( 2 – 6 ), chiral networks ( 7 – 13 ), and origami-inspired folds ( 14 – 17 ), heavily rely on perfectly ordered unit cells. Traditionally, randomness was regarded as a flaw, but controlled randomness can actually bolster toughness and resilience ( 18 ). For instance, regular honeycombs tend to localize deformation into narrow shear abilities under stress, reducing energy absorption and service life. By contrast, introducing irregularity encourages multiple, diffuse shear paths and gradual strain hardening, suppressing a single catastrophic failure band ( 19 , 20 ). To harness this effect, researchers use topological optimization to explore random architectures within defined constraints ( 21 – 23 ), yielding structures for buffering ( 24 ), auxetic behavior ( 25 ), or adaptable lattices ( 26 , 27 )—many resemble natural forms ( 28 ). Alternatively, biomimicry directly translates strategies from nature ( 29 , 30 ) into artificial materials ( 31 , 32 ). Bone-inspired composites can pair high strength with toughness, which were thought incompatible ( 33 – 37 ). Likewise, foam- and honeycomb-inspired cellular designs leverage hierarchical, multiscale geometries to dissipate loads efficiently ( 38 – 43 ). Recent advances in additive manufacturing have enabled the realization of these biomimetic designs—ranging from hoof-like microstructures ( 44 ) to grapefruit-peel layers ( 45 ) and spider-web honeycombs ( 46 )—achieving record energy absorption, stiffness, and durability compared to conventional materials. Despite these advances, most mechanical metamaterials remain static once made: Their shape and mechanical responses are fixed. This limits their reusability and adaptability and even produces waste when repairs or reconfigurations are needed ( 43 , 47 ). To overcome these challenges, we turn to another natural strategy: self-locking hooks. Inspired by Xanthium seeds ( 48 ) that passively interlock using flexible barbs, we design metamaterial “granules” that lock together via hooks. Each unit cell is a hollow resin ellipsoid carrying multiple hyperelastic hooks on its surface ( Fig. 1 ). When packed, the hooks snap over neighbors and hold the particles together. Distinct from two-dimensional (2D) self-locking metamaterials ( 49 – 54 ) or other existing systems ( 55 – 57 ) that rely on boundary pressure, buckling, jamming, or chemical media, our 3D hooked particles achieve stability solely through intrinsic hook engagement without external confinement. This design supports multiaxial loading and offers quantifiable energy absorption, thereby markedly expanding design flexibility and enabling reusable, tunable architectures. Fig. 1. Prototype and design of the 3D self-locking granular metamaterials. Open in a new tab ( A ) Self-locking mechanisms of Xanthium seeds. ( B ) Self-locking configuration of the Xanthium -inspired metamaterials. ( C ) Single 3D self-locking unit cell consisting of an ellipsoidal body and uniformly distributed hook-like structures. ( D to F ) Geometric parameters of the unit cell. For the ellipsoid, the parameters include the major ( L = 29 mm ) and minor ( W = 16 mm ) axes, the thickness ( t = 4 mm ), the diameter of the through-holes ( Φ 1 = 2 mm ), and the diameter ( Φ 2 = 2.4 mm ) and depth ( l 1 = 2.7 mm ) of the hook insertion opening; for the hook, the parameters include the diameter ( Φ 3 = 1.7 mm ), the protruding length of the end ( l 3 = 1.7 mm ), the axial radius of the curved section ( r = 1.7 mm ), the body length ( l 2 = 8 mm ), and the base diameter ( Φ 4 = 2.2 mm ). ( G ) Various structures like dense-solid, pyramid, and elephant, which can be assembled by the granular metamaterials. ( H and I ) Comparison between the packaging foams and the self-locked metamaterials. The foams can protect the sample only when they are put in a box with four sides. Once two sides are removed, the foams will collapse and lose the protection ability. The self-locked metamaterials can hold its original shape because of self-locked properties. Here, we show that these 3D self-locking granular metamaterials display unusually robust, yet reconfigurable, mechanical behavior. In the tensile and shear experiments and simulations on ordered assemblies, we validate the theoretical tensile stiffness of a two-hook pair, the consistent hook-body engagement, and structural stability. Under compression and impact, we quantify densification strain and energy absorbed per unit for both ordered and random packings; the dominant dissipation mechanisms are layer penetration and the progressive collapse of internal voids, which together produce high energy absorption efficiency. Because the hooks deform elastically rather than plastically breaking, particles can survive, and self-locked structures can be disassembled and reused after loading. Our concept bridges granular materials and architected metamaterials, pointing to a typical class of 3D reconfigurable metamaterials. We anticipate wide applications in impact mitigation, adaptive acoustic absorption, modular construction, and other areas where tunable, durable materials are needed. RESULTS Design and fabrication Inspired by the tetrapod structure used in bank protection ( 58 , 59 ) and the self-adhesion seen in Xanthium seeds (see Fig. 1A ) ( 48 ), we developed a reusable, self-locking granular metamaterial (see Fig. 1B ). The particles can be self-locked using elastic hooks that replicate natural mechanisms. Each unit cell is a hollow ellipsoid (with specified axis lengths) carrying multiple flexible hooks on its surface ( Fig. 1C ). The hooks are arranged so that every four hooks leave a small gap ( 60 ), which creates complementary cavities that neighboring particles can interpenetrate, thereby preventing sliding and enhancing self-locking. On the basis of the observations of the Xanthium seed structure, the geometric parameters are illustrated in Fig. 1 (D to F) . The ellipsoids were fabricated by photosensitive resin, while the soft hooks were made of thermoplastic polyurethane (TPU) with hyperelastic properties (see table S1). TPU was selected not merely for flexibility but for its specific mechanical profile: A tensile modulus of 4 to 14 MPa prevents buckling during engagement, while a recoverable strain of ≥ 100 % enables elastic recovery where resin or nylon would fracture. In addition, the hook-hook friction coefficient ( 0.49 to 0.55 ) is suitable to stabilize engagement without inducing irreversible locking. The mechanical properties of tensile specimens and hooks are provided in the Supplementary Materials and figs. S2 and S3. These two components were then bonded with adhesive. Like Xanthium seeds, these discrete unit cells can be self-locked to assemble both ordered and random arrangements for bearing load and protection, such as dense-solid, pyramid, and elephant-like structures ( Fig. 1G and movies S1 and S2). Furthermore, self-locking granules may offer a promising alternative to traditional foam packaging fillers. As shown in Fig. 1H , traditional foam inserts lose their protective function if even one side of a package is compromised: The foam shifts, and fragile items are exposed. In contrast, our self-locking granular metamaterials maintain a stable, interlocked structure with or without an enclosing box ( Fig. 1I ). Even if the package is punctured or torn, the material holds its shape and continues to shield fragile payloads during transit. In addition, the holes within the gaps reduce the overall density of the material, offering potential for applications such as sound absorption ( 61 ). Tensile behavior The Xanthium -inspired unit cell exhibits excellent self-locking performance because of its good tensile and shear properties of hooks. To quantify the effect of the number and spatial arrangement of unit cells on tensile properties of the self-locking structures, we divided them into two groups along the y and x directions, respectively. Each direction includes the line, plane, and solid structures (see Fig. 2A ). Ordered assemblies show strong anisotropy: Along the y axis, each cell engages four hooks with its neighbors, whereas along the x axis, only two hooks engage. Consequently, the y -direction samples have roughly double the stiffness and strength of the x -direction samples. In experiments, the samples are fixed at the bottom of the testing platform, with a vertically upward velocity boundary condition applied to the top layers. Fig. 2. Stepwise unhooking behavior under tensions. Open in a new tab ( A ) Tensile samples depicting line, plane, and solid structures arranged along both the x and y directions. ( B ) Stress-strain curves from experimental and simulated tensile specimens. The inset on the left depicts the experimental image, while the inset on the right illustrates the simulated model image along with dimensional annotations. ( C ) Stress-strain curves from theoretical, experimental, and simulated hook tests (using hyperelastic solid elements, elastic solid elements, and beam elements). The insets, from left to right, represent the experimental model, the solid element simulation model, and the beam element simulation model. ( D and E ) Experimental tensile force-displacement curves along the x and y directions, respectively. The solid lines represent average values, while the shaded regions indicate the standard deviation observed across multiple experimental groups. The dashed lines represent the simulation values. The inset shows the experimental setup. ( F ) Quasistatic tensile deformation processes of the solid- y structure, corresponding to positions marked by I, II, and III in (E). The color bar shows the values of von Mises stress. ( G ) Tensile energy absorption of various structures in (D) and (E). The inset figure presents the energy absorption per the number of interlocked hook pairs in the line, plane, and solid structures. ( H and I ) Tensile simulation force-displacement curves along the x and y directions, respectively. ( J ) Tensile stiffness of the structure in the x direction. First, we performed uniaxial tensile tests on the hook material ( Fig. 2B ) to extract its mechanical properties. Those parameters were then implemented in ABAQUS 2021 to simulate an identically shaped tensile specimen, yielding stress-strain curves that closely match the experimental data and validate the material model. Next, we built two finite-element hooks contacting models—one using solid elements and the other using beam elements—applying identical boundary conditions and loading. Both the solid- and beam-element simulations (and our experiments) predict a peak interhook force of ≈ 2 N ( Fig. 2C ) and similar stress-strain curves. The beam-model curve shows minor fluctuations after slip but matches the overall response. Thus, we select the beam-element approach in the following simulations, which provides a marked reduction in mesh size and computation time while retaining the accuracy of the solid element results. We theoretically analyze the stiffness curve for a pair of hooks (see the Supplementary Materials and figs. S4 and S5) by splitting deformation into two stages: a self-locking phase and a relative-sliding phase. The result closely matches experimental and simulated curves, particularly in the linear region, and thus clarifies the mechanics underlying the metamaterial’s self-locking behaviors. We then examine the tensile response of the four configurations from Fig. 2A under loading in both the x and y directions ( Fig. 2, D and E ). It can be observed that all the simulated curves show good agreements with the experimental results, verifying the accuracy of the finite element model of our samples. Focusing on the y direction, moving from the line 1 × 3 arrangement to the plane 3 × 3 arrangement leaves the fracture displacement essentially unchanged while tripling both the peak force and linear stiffness. Extending to the solid 3 × 3 × 3 structure again triples the peak force, but the fracture displacement grows markedly. This increase arises because hooks in the solid array detach gradually rather than simultaneously. Once the first hook reaches its failure load, the total force drops sharply, yet the remaining hooks continue to stretch and then fail in sequence. We term the sequential failure of individual hooks under tensile load “stepwise unhooking,” which allows the solid assembly to stretch much more than a single layer (movie S3). It explains why solid assemblies can sustain much larger overall displacements before complete fracture. Figure 2F compares experimental and simulated deformations at three key stages (I to III in Fig. 2E ). Stage I shows the peak-load configuration, with all hooks fully engaged. Stage II captures the onset of stepwise unhooking, as a single hook detaches while the remaining hooks stay connected. Stage III depicts complete fracture, with all hooks separated. Stepwise unhooking can further boost energy absorption of self-locked structures at tensile failure ( Fig. 2G ). Transitioning from line to plane assemblies roughly triples the absorbed energy, while the solid configuration delivers an even larger gain. We further normalized the energy absorption by the number of interlocked hook pairs (inset of Fig. 2G ). The solid configuration maintains a high energy absorption, demonstrating that the enhanced energy dissipation is an intrinsic feature of the self-locking structure rather than a consequence of increased unit number. Therefore, self-locking granular metamaterials combine highly normalized energy absorption with large fracture strains, allowing them to undergo greater deformation and dissipate more energy before complete failure, which represents the hallmarks of enhanced toughness and impact resistance. Next, we computed the force-displacement curves for the line, plane, and solid configurations under both x - and y -direction tension ( Fig. 2, H and I ). The results confirm that stepwise unhooking markedly extends the fracture displacement—in particular, the solid 4 × 4 × 4 array under y -axis loading shows a marked increase in failure displacement. Notably, the linear stiffness of these self-locking metamaterials depends directly on both the number of hooks and their spatial arrangement. We can evaluate each assembly’s effective stiffness along the x direction, defined by ∆ F = k ∆ x . For line structures, a single hook (line 1 × 1 ) carries force ∆ F and stretches by ∆ x , so k 0 = ∆ F / ∆ x . Adding hooks in series (e.g., line N × 1) still requires the same total force Δ F , but the total elongation is N ∆ x . The stiffness is k 0 / N . In a plane N × N , N hooks share the load in parallel, so the total force is N ∆ F , while each chain still elongates by N ∆ x . That gives k = ( N ∆ F ) / ( N ∆ x ) = k 0 , which is the same stiffness as a single hook. However, for a solid N × N × N , the parallel chains carry N 2 Δ F . Given that each chain’s deformation is N Δ x , the effective stiffness doubles to N k 0 . Figure 2J confirms that the computed stiffnesses align perfectly with these theoretical predictions. In addition, the normalized force-displacement curves by the number of engaged hook pairs for line, plane, and solid structures collapse onto a single trend, revealing that the mechanical response is governed by hook-level mechanics rather than specimen size (see the Supplementary Materials and fig. S6). Shear behavior To investigate the shear behavior of the self-locking granular metamaterials, we also organized them into line, plane, and solid configurations along x and y directions ( Fig. 3A ). In each orientation, we vary the number of interlayers from 0 to 3, which is equivalent to adding hooks in series perpendicular to the shear force. Conversely, increasing the number of parallel hooks (layers in the shear plane) transforms a line assembly into a plane assembly and a plane assembly into a solid assembly. This systematic variation can help us understand how serial versus parallel hook arrangements control shear resistance. Fig. 3. Tunable shear properties and “sliding-to-locking” transition behavior. Open in a new tab ( A ) Shear samples depicting line, plane, and solid structures arranged along both the x and y directions. F s denotes the shearing force. ( B to D ) Experimental and simulated shear force-displacement curves for various structures. Blue, red, green, and orange regions indicate contact with zero-, one-, two-, and three-layer hooks, respectively. ( E ) Shearing stiffness of line, plane, and solid structures along the x and y directions versus the varying number of interlayers. The upper and lower bounds of each data point represent the corresponding values of the three kinds of structures. ( F and H ) Experimental curves of samples in the y direction (the average curve is taken here) with two and three interlayers, respectively. The gray part represents the fluid-like properties of the structure. ( G ) Experiments and simulations of the line- y 2 interlayers structure under different shearing displacements. The upper panels show the initial gaps between hooks (marked by blue and green). The middle panels capture the fully locked state, where all hooks are engaged. The bottom panels illustrate the fractured line structure after complete hook separation. The color bar shows the values of von Mises stress. ( I ) Number of interlocked hook pairs as the displacement increases. ( J ) von Mises stress of the line- y 2 interlayers for zero, one, three, and six hook pairs, corresponding to displacements of 25.7, 26.1, 29.3, and 32 mm, respectively. The experimental and simulated force-displacement curves for the above assemble structures are illustrated in Fig. 3 (B to D) . Figure 3B compares the shear force-displacement response from a direct two-cell interface (line- x 0 interlayer) through the line- x 3 interlayers with three extra cells. In all cases, the peak shear force remains at ~ 1.5 N , but each added cell extends the fracture displacement by roughly 25 mm —demonstrating that serially chaining cells boosts shear ductility without raising the failure load. Figure 3C shows the plane- x assemblies, which stack three parallel line- x layers in the shear plane. Here, the fracture displacement is unchanged from the single-line case, while the peak shear force increases to about 4.8 N —three times that of the line- x structures—confirming that parallel layering multiplies load capacity. Figure 3D presents the solid- x arrays, combining both serial and parallel stacking. As in the plane- x case, tripling the number of shear-plane layers again triples the peak force, with no change in fracture displacement. Furthermore, Fig. 3E presents the shearing stiffness of the line, plane, and solid structures along the x and y directions. For a fixed number of interlayers, the stiffness of the three structures is nearly identical in each direction, while increasing the number of interlayers leads to a pronounced reduction in stiffness. Given that the number of interlocked hook pairs in the y direction is twice that in the x direction, giving rise to the stiffness along y is approximately twice that along x . This consistent pattern highlights how arranging hooks in series boosts ductility with lower stiffness, while arranging them in parallel enhances strength. We observe an unexpected fluid-like response, which means that the structure cannot withstand shearing force, in certain shear assemblies under y -direction loading, as shown in Fig. 3 (F to H) . In the line- y 2 interlayers ( Fig. 3F ), the shear force remains nearly constant over an initial displacement range—indicating no resistance as the hooks slide until full contact is made (shaded region). This fluid-like behavior weakens in the plane- y 2 interlayers and vanishes entirely in the solid- y 2 interlayers. The initial fluid-like plateau (near-zero shear force) reflects sliding motion until hooks engage (top panel in Fig. 3G ). Only after a critical displacement (when gaps close; middle panel in Fig. 3G ) do hooks interlock, yielding a sharp increase in shear resistance (the solid-like response). We frame this behavior as a “sliding-to-locking” transition rather than classical granular shear jamming ( 55 , 62 ). If we continuously increase the shearing displacement, the structure will be fractured (bottom panel in Fig. 3G ). By varying the number of hooks in series and parallel, we can program structures to behave either as strong shear-resistant solids or as low-friction, fluid-like interfaces (see the Supplementary Materials and fig. S7). A similar pattern appears in the line- y 3 and plane- y 3 arrays ( Fig. 3H ) but again disappears once the structure is fully solidified. To further capture the mechanism underlying the “sliding-to-locking” transition behavior, we present the number of interlocked hook pairs in the line and plane structures as a function of displacement ( Fig. 3I ). For each structure, there exists an initial displacement at which the hooks begin to engage but are not yet fully locked. As the displacement increases, the number of hook pairs gradually increases until it reaches the maximum value allowed by the structural configuration. Beyond this displacement, the structure starts to sustain shear loading. Four representative cases of the line- y 2 interlayers—corresponding to zero, one, three, and six interlocked hook pairs—are shown in Fig. 3J . During this regime, the structure undergoes deformation while being unable to effectively resist shear forces. Compression behavior Through previous tensile and shear experiments, we have verified the self-locking performances of the 3D granular metamaterials, which enable us to actively program the force-displacement curves by assembling discrete unit cells into various geometric configurations. For example, we have obtained a range of 3D structures, such as pyramidal, random cubic, and dense cubic configurations ( Fig. 1G ). Constructing these structures would be challenging with other types of metamaterials with fixed geometries ( 63 , 64 ). However, because of the self-locking properties of unit cells, these 3D granular metamaterials can maintain their configurations even under external compressive loads. Therefore, it is essential to investigate compression, energy absorption, and reusable properties of these metamaterials. The dense-solid structure was built by stacking unit cells so that each upper layer nests into the voids of the layer below. During compression, samples were fixed at the base while a downward velocity was applied to the top surface. Figure 4A shows that the experimental and simulated stress-strain curves of the four-layer dense-solid structure agree closely, with a densification strain (black circles on the curves) of about 0.42, which can be used to quantify energy absorption per unit volume ( EAU ) (details in Materials and Methods) ( 65 ). Higher EAU values correspond to greater energy dissipation and larger deformation. As the structure enters its quasiplastic stage, the initially loose cells progressively compact under load, reducing volume and increasing density—a process termed densification ( 62 ). Figure 4B depicts the deformations of the dense-solid sample at successive compression stages. At a strain of ε = 0.22 , the second layer fully penetrates the voids of the first and third layers. By ε = 0.45 , the fourth layer is driven into the third’s voids, resulting in a compact, two-layered cube. This layer penetration mechanism postpones full densification, elevating the densification strain and thereby enhancing the material’s energy absorption capacity. Fig. 4. Layer penetration and void squeezing under compression boost the energy absorption capacity. Open in a new tab ( A , C , and E ) Stress-strain curves for the dense-solid, pyramid, and Random 125 structures, respectively. The black circles denote the positions of densification strains. The solid and dashed lines represent the experimental and simulated results, respectively. Insets illustrate the loading conditions. F N and F x , y , z denote the compressive forces for single-axial and multiaxial loading, respectively. ( B , D , and F ) Experimental (upper panels) and simulated (lower panels) deformations of the dense-solid, pyramid, and Random 125 structures at various strains, respectively. ( G ) Measured EAU and energy absorption efficiency during compressions of the five structures. ( H ) Cyclic loading stress-strain curves of the Random 125 structure with different compressive strains. The arrows denote the times of loading. The black squares denote the residual strains of each cycling. The insets show the initial and compressed structures. ( I ) Reusability of the Random 125 structure. The blue line denotes the 100th compression. The orange curve shows the average performance over 100 compression cycles. The layer penetration behavior can further improve the densification strains of pyramid structures. As illustrated in Fig. 4C , unit cells in the n th layer are arranged in an n × n configuration and were embedded into the voids of the ( n + 1 ) th layer. The stress-strain chart shows that as n increases, the elastic modulus decreases, primarily due to the increasing area of the bottom layer. Regardless of the number of layers, the pyramid structure will be ultimately compressed to a single layer ( ε = 0.72 ; Fig. 4D ). As the base size n grows to infinity, the densification strain approaches 100 % because additional layers must fully collapse for densification. In other words, larger pyramidal bases compress more before reaching full densification. This feature can also be attributed to the layer penetration behavior, where unit cells orderly insert from the upper layer into the voids of the lower layer during compression. It is important to note that the densification strain approaching 100 % in the pyramid configuration is a geometric design effect arising from its tapered architecture, not a universal material constant of the granular system. The deformed diagrams of the pyramid structure at different strains ( Fig. 4D and movie S4) confirm the phenomenon. Additional experiments and simulations of ordered structure compression are shown in the Supplementary Materials and fig. S8. Furthermore, we demonstrate that discrete unit cells can be assembled into a random, reusable block ( 66 , 67 ). Forty cells were poured into a 125-mm cube mold and then lightly compressed to interlock hooks. Once the container was removed, the cells remained intact (denoted as “Random 125”). The structure has a porosity of ϕ = V p / V m ≈ 70 ± 0.9 % , where V p and V m denote the volumes of the particles and the mold, respectively. As shown in Fig. 4E , both experimental and simulated stress-strain curves match closely and are similar to the rising trend observed in the dense-solid and pyramid structures. Notably, the Random 125 block achieves even higher densification strain and peak stress, confirming that this simple, reconfigurable assembly offers enhanced energy absorption and structural resilience. This is because the random assembly contains more internal voids than its ordered counterparts. During compression, these voids squeeze ( Fig. 4F ), delaying overall densification and substantially increasing both the densification strain and energy absorption capacity. As a result, the Random 125 configuration achieves the highest EAU compared to both the dense-solid and pyramid assemblies ( Fig. 4G ). It should be noted that the energy absorption efficiency η (see Materials and Methods) of the above five structures is ~ 20 % ( Fig. 4G ) because of the soft hooks. Such energy dissipation is largely absent in previously reported self-locking metamaterials with hard contacts ( 55 ). In addition, compared to 2D self-locking metamaterials ( 49 – 54 ), our granular metamaterial is capable of bearing multiaxial loading. As illustrated in Fig. 4E , we performed triaxial compression simulations on the Random 125 structure. The corresponding stress-strain curves along the three orthogonal directions nearly overlap, indicating that the structure exhibits isotropic compressive behavior. The orientation vector of the long axis of individual ellipsoidal particle is represented by ( Δ x , Δ y , Δ z ). The sums of these absolute components ∑ ∣ ∆ x n ∣ ≈ ∑ ∣ ∆ y n ∣ ≈ ∑ ∣ ∆ z n ∣ are nearly identical, indicating the isotropic property of random block (see figs. S9 and S10). Therefore, although a single particle is anisotropic, such unit-cell anisotropy is effectively averaged out in the random structure when a large number of granules become self-locked, leading to an overall isotropic mechanical response. We also provide the stress-strain curves for four cycles of loading on the Random 125 structure ( Fig. 4H ). The first cyclic loading involves compressing the sample to a strain of ε 1 = 0.16 , followed by unloading to a residual strain of ε 1 r = 0.04 . In subsequent cycles, the sample is compressed to ε 2 = 0.32 , ε 3 = 0.48 , and ε 4 = 0.64 , with corresponding residual strains of ε 2 r = 0.13 , ε 3 r = 0.24 , and ε 4 r = 0.36 . Here, the rebound ratio is defined as ( ε peak − ε r ) / ε peak , and its decrease ( 0.75 → 0.44 ) indicates growing plastic compaction. Meanwhile, the increase in peak stress (to 5.5 kPa ) suggests that the assembly becomes stiffer under repeated loading. The cyclic loading curves of one hook and other structures (table S2) are provided in figs. S3 and S11, respectively. Moreover, the structure shows minimal damage and maintains a nearly consistent stress-strain curve ( Fig. 4I ) after 100 cycles of loading with compressive strain up to ε = 0.7 . These findings highlight the improvements in mechanical properties achieved by random structures, demonstrating the reusability and durability of the self-locking unit cell. Impact protection Now, we conduct impact experiments of the random structures and foams to evaluate the protective efficiency, as shown in Fig. 5A . A steel sphere of mass m serves as the impact source, released from a height h to impact the metamaterial sample. The impact energy is given by E im = mgh , where g is the gravitational acceleration. The sample is placed on a square impact platform, with an acceleration sensor positioned at the center of the platform’s back. This sensor allows real-time monitoring and recording of the acceleration throughout the entire impact process. In addition, a high-speed camera is set up in front of the metamaterial to capture its deformation and dynamic responses at a high frame rate. The impact energy of the platform can be expressed as E p = 1 2 ρ t ∬ ( v sin π x a sin π y a ) 2 dxdy , where ρ , t , and a denote the density, thickness, and side length of the platform, respectively, and v is the velocity obtained by integrating the acceleration of the impact platform. The energy absorption efficiency is calculated by η = 1 − E p / E im . Fig. 5. Impact protection and potential applications of the 3D self-locking granular metamaterials. Open in a new tab ( A ) Experimental setup for the free-fall impact of a steel ball onto the sample. Red markers indicate the two acceleration sensors. The platform has a side length of a = 0.5 m , and the steel ball drop height is h = 0.5 m . ( B ) Schematic illustration of Random 125 and conventional foams under two confinement conditions. Top: Random 125 self-locking cells. Bottom: Foam material. Left column: Material confined in a four-sided container. Right column: Material placed in a three-sided container. ( C ) Measured platform accelerations of various structures under impact from balls with masses of 0.4 kg . The snapshots at times of 160 and 400 ms are captured by a high-speed camera. ( D ) Measured impacted acceleration attenuations of the five cases in (C). ( E and F ) Steel ball accelerations and platform kinetic energy versus the number of impacts. ( G ) Damaged and undamaged foams and granular metamaterial after 80 and 120 impacts, respectively. Enlarged figures on the left show the typical broken units highlighted by red dashed circles. ( H ) Snapshots showing that the Random 125 structure effectively protects a fragile egg from impact without damage. ( I ) Potential applications of self-locking metamaterials across various length scales, from body armor to bank protection, and from ordered to random structures. These metamaterials can be tailored using different materials and sizes to achieve specific performance targets. In Fig. 5B , we first filled a four-sided container with granular unit cells to form a random assembly. After removing one wall, the structure remained self-locked and intact. In parallel tests, conventional foams were poured into both four- and three-sided enclosures. Comparative tests were conducted under strictly standardized benchmarks: identical impact energy and matched containment geometry ( 125 -mm box) for both the metamaterial and commercial foams to ensure fair evaluation. Figure 5C shows the measured acceleration curves of the impact platform with various structures subjected to impacts from steel spheres with a mass of 0.4 kg . For the random structure and foams with four sides impacted by a steel sphere, the acceleration curves exhibit a single peak at 2.5 g , with the entire impact duration lasting 280 ms . When one side was removed, the foams expelled and lost the protective function (producing a 140 g peak), which represents a typical packaging failure during transit. However, in the random structure with three sides and even with zero sides, the maximum accelerations remain at 2.5 g . This performance stems from elastic deformation of hooks (movies S5 and S6): Upon impact, unit cells interlock, crack progressively, and envelop the sphere, dissipating most kinetic energy and preserving both the payload and the metamaterials. After impact, the assembly can be reformed thanks to its self-locking and reusable design. The acceleration attenuations of the five cases are illustrated in Fig. 5D , which shows that except for foams with three walls, all tested configurations achieve roughly 30-dB attenuation. To further compare the impact-mitigation performance of the granular metamaterial and foams, repeated steel-ball impact tests were conducted (movies S7 and S8). The accelerations of the steel ball as functions of impact number are shown in Fig. 5E . At the beginning, both materials exhibit nearly identical acceleration values for the steel ball. With increasing impact cycles, the foam undergoes progressive softening ( 68 ), which temporarily reduces the accelerations. However, continued impacts lead to foam densification and structural degradation, ultimately diminishing its protective capability. After 80 impacts, the accelerations of the steel ball rise sharply from 10 g to 35 g . In contrast, the granular metamaterial, fabricated from hyperelastic TPU, maintains stable acceleration responses ( ≈ 15 g ) throughout repeated impacts. This degradation of foams is further reflected in the platform energy response (see Fig. 5F ): At the 80th impact, the foam-protected platform reaches an energy of ~ 36 mJ compared with about 16 mJ for the granule-protected platform even after 120 impacts. In addition, images of damaged and undamaged foams and granular metamaterials after cyclic impacts are shown in Fig. 5G . A total of 60 foam samples were filled in the box, of which 39 failed after 80 impact cycles, corresponding to a failure rate of 39 / 60 = 65 % ( > 50 % ). Many of the failed foams are visibly crushed or fractured, resulting in a loss of protection. In comparison, only 11 granules are damaged, corresponding to a damage ratio of 11 / 40 = 27.5 % ( < 50 % ). Despite these localized damages, the granular metamaterial retains its overall protective performance. Notably, some granule failures originate from insufficient adhesive strength, which in turn leads to the detachment of hooks and allows the steel ball to directly impact the internal rigid core, thereby increasing the acceleration. Last, to demonstrate the dual protection, an egg is dropped onto the random metamaterial, where the structure effectively protects the fragile egg from damage ( Fig. 5H and movie S9). Together, these results indicate that the 3D self-locking granular metamaterial provides impact energy absorption comparable to that of conventional foams placed in an intact box. However, when packaging integrity is compromised or under repeated impacts (Supplementary Materials and fig. S12), granular metamaterials exhibit better protective performance with a lower damage ratio. DISCUSSION We have introduced a typical class of 3D metamaterial that combines the discreteness of granular media with the programmability of architected materials. With consistent theoretical, experimental, and simulated results, we have shown that the elastic hook design yields strong interlocking in 3D and enables exotic phenomena, such as stepwise unhooking, sliding-to-locking transition behavior, layer penetrations, and void squeezing. The mechanism is reversible: After a large strain event, the hooks recover and allow complete reassembly. Compared to conventional foams without self-locking capability, our structure demonstrates better cyclic impact and dual-protection performance. Whereas 2D self-locking metamaterials are typically planar or require external pressure to hold a 3D shape, our 3D self-locking granules can form stable blocks of arbitrary shape and sustain multiaxial loads without any enclosing frame. In addition, this scale-invariant self-locking principle enables the creation of discrete (see the Supplementary Materials, tables S3 and S4, and fig. S15), adaptive architectures, a property that could be exploited in adaptable protective materials. Looking ahead, advances in additive manufacturing will enable the precise fabrication of such interlocking units at various scales. One can imagine tailor-making unit sizes and stiffnesses for specific performance. Potential applications span impact protection (e.g., reusable body armor or packaging; see Fig. 5I ), adaptive vibration damping, and even wave and sound management. Concepts similar to ours may be applied in vibration mitigation ( 69 ), wave manipulation ( 70 ), and sound absorption (fig. S13) ( 71 , 72 ) by exploiting the energy dissipation of the hooked network. Furthermore, their exceptional energy-absorbing characteristics make them ideal for protective applications, such as impact-resistant layers for automotive ( 73 ) or aerospace industries ( 74 ). While the current system relies on passive elasticity, future iterations could incorporate active reversibility. We have demonstrated the feasibility of a thermally triggered “lock-to-unlock” transition using shape memory alloy hooks, enabling programmable disassembly (fig. S16 and movie S10). Nature provides further inspiration (fig. S14): Other burs and hook-bearing plants (e.g., burdock and Velcro) suggest new geometries for self-locking architectures. In summary, our Xanthium -inspired metamaterial introduces reconfigurability and sustainability into mechanical metamaterials, opening routes to resilient materials that can be assembled, tuned, and recycled for diverse industrial and environmental challenges. MATERIALS AND METHODS Experiments The ellipsoids and hooks components are fabricated using commercial 3D printing technology. The ellipsoidal parts are produced via stereolithography with high-detail resin, ensuring smooth surfaces and intricate details, resulting in a gray appearance. The hook components and tensile specimen are made using selective laser sintering with TPU. The properties of the two materials are listed in table S1. The final assembly of these components is shown in fig. S1. To evaluate the mechanical properties of the self-locking particles, we use a 5 kN –rated LD24 series computer-controlled electronic universal testing machine (Litest, Shanghai Scientific Instrument Co., Ltd.) for tensile and compressive tests (Supplementary Materials and fig. S2). The machine is equipped with a computer control terminal, specialized tensile fixtures, compression indenters, and dual force sensors with 10-kN and 100-N capacities. During testing, the samples are securely mounted on the machine’s fixtures. Using Litest testing software, we configure essential parameters such as the test type, displacement control mode, and stop conditions. In addition, a high-resolution EOS 6D Mark II camera captures specimen deformation at regular intervals to document the testing process. Simulations We adopt a simplification approach, modeling the hook barbs as beam elements and the ellipsoidal components as homogeneous shell elements. Using the Explicit module of ABAQUS 2021, we conduct finite element simulations of the structure. The beam element models are discretized into three-node linear beams (B31) with a mesh size of 0.7 mm, and the material properties include a density of 1.2 × 10 − 9 tonne/mm 3 , an elastic modulus of 14 MPa, and Poisson’s ratio of 0.4 . The shell models have a mesh size of 1.1 mm using four-node quadrilateral shell elements (S4R) with material properties of an elastic modulus of 60 MPa and Poisson’s ratio of 0.3 . During model construction, the shell and beam elements are combined using node merging techniques to replicate the actual geometry of the components. We perform the simulations using the Dynamic, Explicit analysis step, setting a mass scaling target of 1 × 10 − 6 . For contact settings, we use General Contact, select “Hard” Contact for Normal Behavior, and set a friction coefficient of 0.3 for Tangential Behavior to ensure accurate and realistic results. The validity of these settings is confirmed through simulations of tensile components and hook tension (fig. S3). Results from the tensile, shearing, and compressive simulations are provided in figs. S6 to S8. In simulating the random cube structures, we replicate the experimental setup while incorporating necessary adjustments. The finite element software generates particles that are spaced to prevent overlaps, requiring a larger container to accommodate the same number of particles as used in the experiments. This ensures accurate representation without particle penetrations. The simulation process involves two key steps. First, we fix the container’s bottom and apply displacement loads to compress the peripheral and top rigid plates, aligning the simulated container’s dimensions with those of the experimental setup. Second, we remove these constraints and apply a downward velocity load to the top plate, completing the simulation of the random structure. The stress-strain curves from our simulations closely match those obtained experimentally, demonstrating the fidelity of our approach (Supplementary Materials and fig. S9). Energy absorption per unit volume EAU is a key metric for assessing the energy absorption capacity of materials or structures under compressive loads. Higher EAU values indicate a greater ability to absorb energy and undergo substantial deformation when subjected to compressive stress. Densification strain is a fundamental concept in plastic deformation, describing the process by which a material’s internal structure becomes more compact. During plastic deformation, the initially loose particles or grains rearrange under external loads, forming a denser and more ordered structure. This leads to a reduction in volume and an increase in density, referred to as densification. On the energy absorption efficiency curve, densification strain corresponds to the final local maximum, marking the transition from gradual deformation to densification. It also represents the peak energy absorption efficiency. By measuring densification strain, we can gain valuable insights into the micromechanisms at play during plastic deformation and their influence on energy dissipation. The energy absorption efficiency is calculated by dividing the unit volume energy absorption by the nominal stress, as expressed in the following equation E ( ε ) = ∫ 0 ε σ ( ε ) d ε σ ( ε ) (1) where σ ( ε ) represents the nominal stress, and ε denotes strain. The densification strain ε d is defined as the last local maximum point on the energy absorption efficiency curve and is expressed as follows dE ( ε ) d ε ∣ ε = ε d = 0 (2) The energy absorption efficiency η is selected as the last local maximum point on the energy absorption efficiency curve. During compression, we use EAU to assess the energy absorption characteristics of the metamaterial, defined as EAU = ∫ 0 D d FdD N (3) where F is the compression force, D is the compression displacement, D d denotes the densification displacement corresponding to ε d , and N represents the total number of the unit cells. Therefore, we have obtained the expression of EAU . Acknowledgments We thank Y. Lu from The University of Hong Kong and F. Li from Beijing Institute of Technology for helpful discussions. Funding: We acknowledge the support from the National Nature Science Foundation of China under grant nos. 12302112 (to Y.W.), 12102193 (to X.L.), and 12232012 (to Y.G.) and the Fundamental Research Funds for the Central Universities under grant no. 30923010207 (to Y.W.). Author contributions: Y.W. and X.L. initiated the project and guided the research. Y.W., X.L., T.L., and T.S. established the theory. T.L., T.S., Y.S., K.W., and N.C. performed the numerical calculations and designed and performed the experiments. All authors contributed to the discussions of the results and the manuscript preparation. Y.W., X.L., T.L., and T.S. wrote the manuscript and the Supplementary Materials. Competing interests: The authors declare that they have no competing interests. Data, code, and materials availability: All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. 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