Metainterfaces with mechanical, thermal, and active programming properties based on programmable orientation-distributed biometric architectonics

Abstract

Interfaces between different materials crucially determine the performance of multi-material systems, impacting a wide range of industries. Currently, precisely programming interfaces with distinct properties at different localized interface positions remains a challenge, leading to limited interface adaptability and unpredictable interface failures, thus hindering the development of next-generation materials and engineering systems with highly customizable multiphysical interface performances. Our research introduces programmable “metainterfaces” for the first time, featuring engineerable biometric architectonics that allows for mechanically, thermally, and actively programmed distribution of interfacial effects by its orientation, driven by artificial intelligence. Enabled by metainterfaces, we showcased improved mechanical properties of future composite metamaterials by programming interface resistance customized to the decoupling modes of distinct lattice topologies. Additionally, we demonstrate enhanced and programmable impact mechanics in fish scale assemblies equipped with pre-programmed metainterface sheets. The proposed metainterface also allows for coolant flow programming in thermal management systems, opening new avenues for development of highly customizable thermos-mechanical systems. Additionally, we introduce digitally controlled “metadisks” enabled by metainterfaces as novel solutions for actively programmable interface systems in robotics, offering real-time adaptive and intelligent interfacial mechanics. This research sets the foundation for next-generation multi-material systems with precisely programmed interfacial effects, offering broad applicability in areas such as smart materials, advanced thermal management, and intelligent robotics.

---

New concepts

We are excited to report that our study introduces a novel concept of “metainterfaces” inspired by honeybee stingers, which leverage artificial intelligence to first achieve programmable mechanical, thermodynamical, and active interfacial effects. We address the crucial challenge of limited and uncontrollable interfacial mechanics and thermodynamics in existing materials and structural interfaces. Through a comprehensive study, we demonstrate the efficacy of our approach across various mechanical and thermodynamical materials and structures. This includes the remarkable enhancement of mechanical properties of composite metamaterials and metastructures, as well as the ability to program coolant flow in thermal management systems, enabling the development of intelligent thermos-mechanical systems. Furthermore, we introduce metadisks as innovative solutions for programmable interface systems in robotics, providing real-time adaptive and customizable interfacial mechanics. Overall, this research paves the way for the development of advanced materials and intelligent systems with precisely programmed interfacial effects and wide-ranging applicability.

1. Introduction

Materials and structures with programmable mechanical, thermal, and active properties enable novel functional performances,^1–3 thereby facilitating development of next-generation engineering systems with complex structures and diverse functional needs. The maturing additive manufacturing (AM) technology provides unlimited design potential for creating complex architectures in materials and interfaces,⁴ offering the programmability to achieve advanced functional performances with intricate structures. For instance, it is reported that by inducing sidewall buckling in soft hollow pillars using low pressure, highly tunable dry adhesion can be achieved.⁵ In the materials domain, these complex architectures enable the development of metamaterials with specified design and manufacturing techniques to passively or actively program multiphysical properties. The mechanical responses of simple architectures are usually controlled by studying their geometrical design parameters through experimental and numerical methods.^6,7 Studies also utilize rational design of more complicated mechanostructures,^8,9 leveraging structure-induced mechanical features to program overall performance. These efforts involve creating metamaterials with controlled novel microstructures and unit cell topologies to exhibit targeted mechanical features, such as the development of perforated shellular structures for engineered multistable responses.¹⁰ Basic architectural units, including struts, shells, and cells, are designed with nature-inspired hierarchies like helices,¹¹ honeycombs,^12,13 or crystal-mimicking phase meta-structures^14,15 to achieve advanced deformation mechanics such as strain field control, failure mode engineering, and damage tolerance. Due to the complexity of these designs, machine learning (ML) is employed in some studies to assist architectural design, using ML-enabled data-driven approaches^16,17 or ML-based rapid inverse design.¹⁸ For thermal properties, programmable design strategies to engineer thermal conduction, radiation, and shape response have been proposed. Studies have investigated the design parameters of lattice structures affecting thermal properties such as heat conductivity.¹⁹ Programmed structural designs distribute thermal conductivity through carefully engineered material property distributions,^20,21 enabling novel properties such as thermal camouflage or thermal cloaking. Additionally, some studies have designed thermo-responsive structures^22,23 that can adapt their shape programmably under thermal stimuli. Active metamaterials are often created using advanced 4D printing methods, allowing them to exhibit desired responses to external stimuli or achieve controlled deformation through precise engineering. For example, studies have manipulated in situ shape programming in response to stimuli such as temperature,²⁴ ultraviolet light,²⁵ electrical,²⁶ magnetic field,^27,28 or chemical stimuli.²⁹ Innovative studies have also proposed transformable architectures using novel interlocking mechanisms, such as employing Taji gears.³⁰

Besides the design of material architectures, interfaces between different materials have critical mechanical and thermal interaction features. These interfaces significantly affect mechanical behaviours and thermal properties, playing a crucial role in engineering structures and systems by contributing substantially to mechanical bonding,^31,32 friction and wear resistance,^33,34 and thermal management.^35,36 It is reviewed by different studies^37,38 that the interface performances can be significantly affected by the variation of surface geometries caused by factors such as defects. Studies have also discovered that by manipulating the interface surface with pre-designed geometrical patterns, improved interface mechanical and thermal behaviours can be achieved. Studies reported that designing interlocking configurations combining brittle and stiff materials with soft tissue-like materials,^39,40 or incorporating specific patterns or structures,^41–43 can uniformly enhance the interface mechanical performances. Novel interface materials^44–47 or repetitive design patterns such as three-dimensional and vertically aligned carbon fiber (3D-CF) skeleton structures⁴⁸ or self-assembled cubic boron arsenide⁴⁹ are also developed to uniformly enhance or resist thermal conduction to improve thermal management. To further improve the interface behaviours, studies have mimicked the biological surface structures to develop functional interface designs with improved interface properties. It has been reported that by manipulating interface geometries with modifications inspired by biological structures, such as the stingers of honeybees, elytra of beetles, and stingers of parasites, anisotropic and improved interface mechanics can be achieved. By mimicking the crassula mucosa interface, researchers have also achieved functional structures capable of triggering selective directional liquid transport.⁵⁰ However, in terms of interface programmability, existing designs typically engineer interface properties uniformly across the entire surface by forming interface geometries with uniformly applied shape parameters, lacking the ability to customize interface properties at every localized region. This customization is essential for achieving novel characteristics, such as highly anisotropic behaviours that provide varied resistance to mechanical deformations in different areas or guiding thermodynamic fluids to specific cooling spots, thereby enhancing performance and functionality. In addition, existing designs often apply biomimetic or empirical modifications targeted towards specific geometries or functional uses with single-function capabilities, which do not have the generality needed for various engineering systems. Furthermore, existing biomimetic interface designs often feature highly simplified bioinspired modifications, which fail to replicate the full anisotropic capabilities of structures from nature, limiting the programmability and effectiveness of the interface units. Therefore, next-generation interfaces should exhibit locally programmable interface architectonics, capable of displaying distinguishable multifunctional properties across different interface surface units to address these issues effectively.

Here, we present the first development of metainterfaces (Fig. 1) with mechanically, thermally, and actively programmable and enhanced interfacial effects, achieved through orientation-distributed programmable architectonics replicated from honeybee stingers. We used X-ray computed tomography (XCT) measurement technology and a digital stinger rebuild algorithm to reconstruct the complicated geometry of our design unit with a highly anisotropic backward stinger barb and adapt it to a variety of complicated interface geometries (Fig. 1(a) and Fig. S1, also see Supplementary Note 1 for the design rationales, ESI†) and applied additive manufacturing (AM) to fabricate such interfaces with complex features. Fig. 1(b) highlights the introduction of highly programmable interface thermomechanical behaviours, achieving customizable properties at each design unit, defining the essence of a metainterface. This is evolutionary compared to existing interface designs with conventional modifications⁴¹ and biometric approaches^12,51–56 that exhibit uniform and unprogrammable interface design, enabling the development of next-generation multi-material engineering systems with customizable thermal, mechanical, and active programming properties (Fig. 1(c) and Fig. S2, ESI†). Our results showed that metainterfaces greatly improved thermal and mechanical properties, expanding the range of interface characteristics. The interface programmability also enabled development of new multi-material metamaterials with programmed interface resistance, enhancing modulus and specific energy absorption over traditional designs. Additionally, we applied artificial intelligence (AI) to optimize coolant flow in complex geometries through the metainterface, achieving targeted cooling and flow rates. We also provide novel design solutions in robotics enabling real-time, actively programmable interfacial mechanics, enhancing functionality across robotic systems and paving the way for development of advanced, intelligent robotics using metamaterials. Our studies encompass the programmability of interface behaviours, transcending the limitations of traditional interface designs and opening up new avenues for diverse next-generation materials and engineering applications with highly customizable interface properties.

Fig. 1 The programmable metainterface inspired by stingers of honeybees. (a) Design of a freeform metainterface based on XCT measurement of stingers of the honeybee, where the honeybee image is retrieved from ref. 57; see Fig. S30 (ESI†) for a fabricated freeform metainterface. (b) Metainterface with highly programmable localized properties, where P₁ to P₅ are abstract representations of different interface properties; the stimulus direction is defined as the direction of the external loads or thermal flows at the substrate, the plug-in direction is the reverse direction of the stimulus representing the relative motion of the stinger, and θ_s is the stinger angle defined as the adjacent angle between the reverse direction of the stimulus and the tip of the barb. (c) Application potentials including the thermos-mechanical metamaterials with programmed coolant flow, anti-impact metamaterials with programmed interface mechanical resisting directions, and advanced robotics equipped with actively programmable metadisks enabled by metainterfaces.

2. Materials and methods

2.1. Materials and experiments

2.1.1. Parent materials and post-processing conditions. In this study, the stereolithography (SLA) additive manufacturing technology was employed for fabricating metamaterials and metastructures due to its ability to achieve high precision and intricate geometries. The Form 3 printer served as the printing platform, utilizing Formlabs® standard clear resin and flexible 80A resin as parent materials. The clear resin was chosen for constructing metainterfaces due to its rigidity, stiffness, and transparency, enabling internal deformation observations of the substrates. The flexible 80A resin, known for its high elastic strain, was selected as the substrate material to provide mechanical compliance and effective energy absorption in composite metamaterials. Fig. S3 and Table S1 (ESI†) provide post-processing conditions for the parent materials with various experimental designs, ensuring consistent mechanical properties through suggested curing time and temperatures: 15 minutes at 60 °C for standard clear resin and 10 minutes at 60 °C for flexible 80A resin. Mechanical testing specimens of parent materials were prepared according to ASTM D638 standard configurations. The mechanical properties were evaluated using the ZwickRoell Z100 universal tensile test machine at a strain rate of 10⁻³ s⁻¹ to ensure quasi-static loading conditions. Table S2 (ESI†) summarizes the detailed specimen geometries and experimental mechanical properties of parent materials. Notably, the suggested curing conditions yielded an average modulus of 1662.43 MPa, an ultimate tensile stress of 48.52 MPa, and a fracture strain of 8.49% for standard clear resin, while the flexible 80A resin exhibited an average modulus of 4.44 MPa, an ultimate tensile stress of 3.79 MPa, and a fracture strain of 85.83%.

2.1.2. Experimental measurement of coupled interface energy. The shear and tensile test configurations were employed to assess the stress–strain response of the coupled specimens. The interface geometry was bonded to the substrate using a small amount of liquid resin to ensure coupled stress conditions. Fig. S4(a) (ESI†) illustrates the specimen preparation process, where the substrate materials were initially fabricated with matching features to the interface geometries and then bonded to the interface using surface resin. The as-printed interfaces underwent initial post-curing with 5 minutes of ultraviolet light irradiation at 60 °C. Subsequently, the glued configurations were further cured with the substrates for an additional 10 minutes to ensure complete curing of both the interface geometries and the substrate. The test configuration of the coupled shear interface specimens, shown in Fig. S4(b) (ESI†), featured shear regions and grip regions. The grip regions were designed with additional thickness to ensure that shearing forces were parallel to the shear regions, thereby establishing pure shearing stress conditions for the interface. For the tensile specimen, the test height (Fig. S4(a), ESI†) is set as the largest height of the interface modifications for the interface designs featured in this study. The specimens were evaluated using the ZwickRoell Z100 universal tensile test machine, applying a quasi-static shearing stress condition with a load rate of 1 mm per minute. The load–displacement curves were used to calculate the interface energies for the specimens, with fracture defined as a 95% drop in load. Based on the stress–strain curves (Fig. S5, ESI†), the total mechanical interface energy was calculated using the following method:where δ is the displacement, σ is the interface stress, δ_f is the displacement at the interface fracture, and S is the interface energy to be calculated. To generalize the experimental results for comparison purposes for future publications, we normalized the interface energies by the modulus of the substrate:

γ_coupled,1 = S/E₀ (2)

where E₀ is the modulus of the substrate and γ_coupled,1 is the normalized mechanical interface energy of specimens prepared under coupled stress conditions. For the Ashby chart comparison, the γ_coupled,1 is further normalized by the area of the contacting surface introduced by different interface designs, A_c, for fair comparison purposes.

2.1.3. Experimental measurement of uncoupled interface energy. The specimens designed for uncoupled stress conditions (Fig. S6(a), ESI†) were equipped with thicker grip portions to enable controlled compression using the fixtures of the tensile test machine. The additional displacement introduced by the extra portion of the grip is used to generate a desired amount of vertical stress, σ_v. To achieve precise control of the σ_v based on the extra thickness of the grip, compression experiments were conducted on both metainterfaces and interfaces without stingers using the configuration and data in Fig. S7 (ESI†). In this experiment, the load was applied vertically to the contact regions between the interfaces and substrates. These compression tests were performed at a load rate of 0.1 mm per minute to ensure quasi-static compression conditions, and the obtained data were used to design specimens with uncoupled stress conditions featuring controlled stimulated vertical stress. The results of the compression tests (Fig. S7, ESI†) guided the design of specimens to achieve a stimulated vertical stress of 0.5 MPa. The additional thickness of the grips (d_s) measurements yielded actual experimental stimulated vertical stresses of 0.46 MPa and 0.47 MPa for the metainterfaces and interfaces without stingers, respectively.

The experimental configuration of the specimens with uncoupled stress conditions is shown in Fig. S6(b) (ESI†), with stress–strain curves provided in Fig. S8 (ESI†). The test platform and load conditions were identical to those used for the specimens with coupled stress conditions. To facilitate comparison, the interface energy was further normalized with respect to the vertical stress in these specimens:

γ_uncoupled = S/(E₀σ_v) (3)

where σ_v is the vertical stress.

2.2. Design and modelling

In this section, we present the design and modeling process of the stingers for various applications, including freeform surfaces, composite mechanical metamaterials, metastructures inspired by fish scale assembly, and unit cells for the AI-driven thermal management system. The stinger designs are based on the slicing of XCT images captured at the Shanghai Synchrotron Radiation Facility BL16U2 beamline, with an acceleration voltage of 16 keV and a resolution of 325 nm. The raw XCT images undergo post-processing using phase retrieval and slicing operations through the PITRE software. An edge configuration algorithm is developed to detect stinger edges, based on predefined locations and a range of edge values for the pixels of the slicing images. These detected edge coordinates are then processed from the images and input into Rhino 6. To accurately reconstruct the stinger geometries and use them for subsequent analyses and applications, these points are scaled using the Scale3D function and connected with the AddCurve function using rhinopythonscript, following the method described by:where O is the geometrical center of the stinger base, O(h_stinger) is the geometrical center of the stinger pinpoint, O(h_{stinger_design}) is the geometrical center of the stinger pinpoint based on the design enlarging requirement, p_i,j represents the ith point of the jth stinger edges, where n and N are the resolutions of the stinger edge curve and the model geometry of stinger growth, represents the scaled control points of the stingers, C_j is the jth curve of the stinger edge, G is the grouping operations of selected objects, and S is the Scale3D operation, which scales the coordinates of the control points of the stingers. The size of the stingers is determined as 1 mm by the printability limit of the Form 3 machine, as indicated by surface finish comparison of the printability test results in Fig. S9 (ESI†). The detailed design information of samples in Fig. 4 is summarized in Tables S3 and S4 (ESI†). Specifically, the size of the unit cell for composite lattice structures presented in Fig. 4(a) is selected as 15 mm, while the struct diameter of lattice implants without metainterfaces is selected as 1 mm to ensure that a minimum sufficient design space can be reserved for the stingers of the metainterface on its struct geometry. Similarly, the size of the rigid sheets for fish scale assemblies is 20 × 20 mm with a thickness of 1 mm. To ensure identical relative densities among the samples for comparison purposes, the struct diameters or the sheet thicknesses of the samples with metainterfaces are designed with reduced values to balance the volume occupied by stingers. Experimental results confirmed that the relative densities of samples with and without metainterfaces exhibited a maximum deviation of 0.3%, ensuring the fair comparisons of the presented results. The cell size of the thermos-mechanical samples in Fig. 5 is 3 mm, being the minimum cell that enables the stinger within its cell volume to achieve most effective thermal management. Preliminary experiments are also conducted to design the load-bearing structures with diameters of 0.416 and 0.5 mm with and without metainterfaces (Fig. S10(a), ESI†), where the load-bearing structures are designed with supportive surfaces to ensure identical mechanical performances (Fig. S10(b), ESI†). The results of duplicate experiments (Table S5, ESI†) confirm that the samples in this study possess an identical relative density of 27% and normalized moduli of 0.17 to 0.18 MPa MPa⁻¹.

The theoretical design relations for active programming of metadisks can be achieved through:

{t₁,t₂,…,t_N} = {f_E→t(E₁,m₁),f_E→t(E₂,m₂),…,f_E→t(E_N,m_N)} (6)

f_E→t(E_i,m_i) =R(E_n,mi⁻¹(E_i,θ_stress),θ_g,pi)T/2π (7)

where t_1−N represents the signal duration for the motor of the 1−N^th metadisk, f_E→t(E_i,m_i) is the energy-signal conversion function derived based on the period of the motor, T is the angle of the previous disk state θ_g,pi, the desired grasp angle θ_g,i derived from the inverse function of the experimentally established relationships between the stinger angle and interface energy E_n,mi⁻¹(E_i), where E_i represents the desired normalized interface energy of the ith metadisk and m_i represents the interface mode (coupled or uncoupled), θ_stress is the orientation of potential stress, and R(θ₁,θ₂) is the angle required to rotate the MDMs from θ₂ to θ₁.

In addition, we also propose a multidisciplinary design theory that could innovatively achieve pre-designed interfacial energies on N different stress angles based on solving the following M sets of equations:

where is the equivalent interface energy on sth stress orientation θ_stress,s with interface mode m_s and E_n,ms(θ_g,i,θ_{stress,s=1,2,…,M}) represents the interface energy with interface mode m_s, stress orientation θ_{stress,s=1,2,…,M}, and grasp angle θ_g,i.

2.3. Machine learning aided programming of thermodynamical behaviours of metainterfaces

In this study, machine learning techniques⁵⁸ are employed to understand and facilitate the programming of thermodynamical behaviours in metainterfaces based on the tensorflow.⁵⁹ The overall procedure consists of three main parts: (a) training data generation, (b) training of the Fully Connected Neural Networks (FCNN), and (c) AI-driven thermodynamical programming, as depicted in Fig. S11 (ESI†). To develop the simulation model, the inlet flow rate and stinger angle are utilized (Fig. S12(a) and (b), ESI†). The flow simulation⁶⁰ in SolidWorks is applied as the simulation tool in this study. The simulation includes both laminar and turbulent flow types of water through complex stinger geometries, with the stinger interface subjected to adiabatic wall conditions. The external analysis is employed, excluding cavities and internal spaces. The fluid temperature is set at 293.2 K, representing room temperature. Heat conduction in solids is disabled during flow velocity simulation to reduce computational costs. For heat exchange rate simulation, temperatures ranging from 543.2 K to 1293.2 K are applied to the stinger, resulting in a temperature difference of 250 K to 1000 K between the stinger and the fluid. It should be noted that the results of the simulations are independent of the parent materials for the truss structures, where the temperature gradient is preserved. At the end of the simulation, data slices are extracted from different surfaces of the computational domain for various flow velocities and fluid temperatures, which are then processed using flow rate and heat exchange rate image processing algorithms. Example input images for flow rate and heat exchange rate calculations are shown in Fig. S12(c) and (d) (ESI†).

For the prediction of flow velocity, the training inputs consist of the inlet flow rate, stinger angle, and outlet face, while the calculated outlet velocity perpendicular to the outlet surface is the output. Regarding heat exchange rate, the training inputs include the inlet flow rate, stinger angle, and temperature difference, with the calculated heat exchange rate as the output. The distribution of training data for flow rate and heat exchange rate prediction is presented in Fig. S13(a)–(d) (ESI†), respectively. The training data are uniformly distributed across the entire range of training inputs to ensure the quality of training. The amount of training data is progressively increased until the test errors of the model reduce to acceptable and converged levels (0.14 m s⁻¹ for velocity prediction and 2.4 K for temperature prediction), as demonstrated in Fig. S14 (ESI†). The detailed design hyperparameters of the fully connected neural networks (FCNNs) are outlined in Table S6 (ESI†). The FCNNs, featuring two hidden layers, are trained using optimized hyperparameters determined through preliminary tests of models, such as the number of neurons per layer and the number of training epochs, as detailed in Fig. S15 (ESI†). The rectified linear activation unit (ReLU) is chosen as the activation function due to its ability to address vanishing gradient issues,⁶¹ supported by comparative analysis among different activation functions shown in Fig. S16 (ESI†), confirming that FCNNs with ReLU activation demonstrate a more effective decay in loss.

With the trained FCNNs, flow rate programming (Fig. S17(a), ESI†) and heat exchange rate programming algorithms (Fig. S17(b), ESI†) are developed to program the thermodynamical behaviour of the metainterface. Due to the fact that the mechanical requirements vary upon the different engineering environments of the load-bearing systems, the parent materials are not specified to improve the generality of this research, where the normalized mechanical data ensure that the designs with and without metainterfaces would result in identical relative densities and mechanical responses (Table S5 and Fig. S10, ESI†). The working temperatures of the thermos-mechanical metamaterials should be selected such that there is no significant geometrical variation to replicate the thermal behaviours of this study. For each thermodynamical outlet spot, potential inlet flow contributions and temperature differences along desired outlet directions are identified from neighboring top and side stingers and cells. Additionally, each velocity is adjusted by a negative contribution from the surrounding metamaterial structures (v_surrounding) to enhance thermodynamical predictions’ accuracy. The actual stinger angles are determined based on the directions of different inlets and stinger orientations. To achieve a desired outlet flow rate (v) and heat exchange rate (q), the random-generation-modified (RGM) deep search algorithm, proposed in our previous work, is utilized. The RGM algorithm randomly generates n different stinger angles, utilizes the FCNNs for rapid thermodynamical property predictions, and iterates to obtain the optimal combination of stinger angles {θ_s,c1,θ_s,c2,θ_s,c3,θ_s,c4}_optimal that satisfy the desired thermodynamical properties.

2.4. Numerical simulations

Finite element analysis (FEA) is utilized to evaluate interfacial stresses in metainterfaces. Two simulation configurations, namely uncoupled and coupled stress conditions, are illustrated in Fig. S18(a) and (b) (ESI†), respectively. For the uncoupled stress condition, a flexible substrate is placed on top of the metainterface and the interface without stingers. A uniform stress is initiated at step 1 of the simulation on the top surface of the substrates. At step 2, the same velocity as in the shear experiment is applied to the substrate to replicate and analyze the uncoupled interfacial stresses. The interfaces are considered as rigid bodies with a fixed boundary condition. In the coupled stress condition, a tied interface condition is applied between the connections of the flexible substrates and the interfaces without applied stresses. Velocities are applied to simulate the shear process of the coupled stress condition, while a fixed boundary condition is employed on the rigid interface structures. The C3D4 mesh type is selected to simulate the complex geometry of the metainterface, whereas the C3D8R mesh type is chosen for the interface without stingers and the flexible substrates. During the simulation, the stresses at different locations of the interfaces are recorded to analyze and compare the deformation and failure processes of metainterfaces and interfaces without stingers. The calculation of the stress at a certain interface depth is defined in Fig. S18(c) (ESI†). A plane of two-dimensional stress data is first extracted from the simulation at a given interface depth, where the stresses are averaged to provide the data presented in Fig. 2(c).

Fig. 2 The mechanical and thermodynamical performances of the metainterface. (a) The interface energy of the metainterface with different stinger angles θ_s under coupled and uncoupled stress conditions, where σ_v is the vertical stress for the uncoupled stress condition. (b) and (c) The maximum interfacial stress and the internal stress distribution of the metainterface and conventional interface without stingers, respectively. Here the plug-in direction results in θ_s = 0°. (d) The heat exchange rate of the metainterface and conventional interface without stingers for different inlet flow rates and 500 K temperature difference. Here the plug-in direction results in θ_s = 180°. (e) and (f) The ML-predicted flow rate and heat exchange rate for the metainterface, respectively, with different stinger angles, inlet flow rate, and interface temperatures.

2.5. XCT experiments

In this study, XCT experiments were conducted at the BL16U beamline of the Shanghai Synchrotron Radiation Facility (SSRF) and using the ZEISS Xradia 520 Versa X-ray microscope at the Instrumental Analysis Center of SJTU. The purpose of these experiments was to reconstruct the stinger geometries and examine the fracture surfaces of the proposed metastructures. During the XCT scanning of the stinger (Fig. S19(a), ESI†), an acceleration voltage of 16 keV was applied, resulting in a spatial resolution of 325 nm. A total of 1200 scanning images were generated, and the slicing images were used to reconstruct the stinger geometries. To achieve different stinger geometries, a freedom metainterface design algorithm was developed, as depicted in Fig. S20 (ESI†). The slicing images of the stinger were processed using an edge detection program that extracted edge data based on the differences in gray scale values. For the height values within the mapping region, the following equation was applied to smoothly adjust the edge control points and achieve the desired freeform geometry, as illustrated in Fig. S20 (ESI†):

l_i = l_i(d_trans + d_stinger − d_total)/d_trans (9)

where l_i is the distance to adjust the ith control points of the edge from the original position p_o,i to the desired position p_i towards its closest control points of the geometrical edge of the freeform surfaces, p_s,i, i.e., l_i is the distance from p_o,i to p_s,i and d_trans, d_stinger, and d_total represent the depths of the transition zone, the current layer of stinger, and the whole stinger, respectively. The control points of each edge are then connected to construct the layer geometry of the stinger, where the loft function in Rhino 6⁶² is used to create the surfaces between each layer.

To examine the crack interface morphologies of different samples, XCT experiments were performed using the ZEISS Xradia 520 Versa X-ray microscope at the Instrumental Analysis Center of SJTU. The experimental process is outlined in Fig. S19(b) (ESI†). During the experiments, a resolution of 15.31 to 29.203 μm was used, and the size of the vision field was 30.62 × 30.62 mm. Cube-shaped samples with a side length of approximately 2.5 mm were positioned in the center of the X-ray zone. The X-ray microscope operated at an energy of 80 kV, with an X-ray power of 7 W and an LE2 filter. Each sample underwent a complete 360° rotation, and a total of 1201 projection images were captured during the scanning process, with an exposure time of 1 second. After adjusting for center shift, beam hardening, and rotation angle, the projection images were reconstructed using the Control System Reconstructor software based on slice images. The interface morphologies were analyzed using the TXM 3D Viewer Software, and the projection images were transformed into slices using the XMC Controller software. This allowed for further examination and analysis of the crack interface morphologies in the samples. The processed internal fracture surfaces of metamaterials with different interface designs are provided in Fig. 4(d), Fig. S21, and Supplementary movies Movies S1–S6 (ESI†).

3. Results and discussion

3.1. Mechanical and thermodynamical behaviours of metainterfaces

To validate the efficacy of strong interface coupling and establish a theoretical model for highly anisotropic interface energy programming, we conducted experiments to measure the mechanical interface energy of a stinger-inspired metainterface with 4 × 4 stingers. The programmability of the metainterface is achieved through engineering the stinger angle, θ_s, of each XCT-rebuild stinger, where the stinger angle is defined as the adjacent angle between the reverse direction of the stimulus and the tip of the barb. We varied the stinger angle θ_s from 0° to 180° and used the specimen designs detailed in Section 2.1 in Methods and Fig. S4 and S6 (ESI†), where the stinger angle is defined in Fig. 1(b) and 2(a). Fig. 2(a) defines the coupled and uncoupled stress conditions of the metainterfaces. The coupled interfacial conditions refer to fully glued interfaces between the metainterface and substrates. On the other hand, the uncoupled interface represents separated interfaces, where the interfacial energies are introduced under vertical stress. Note that the materials at the uncoupled interface are compressed together with an additional vertical stress, σ_v, that is, vertical to the direction of the applied load F, which acts to simulate the compressions at interfaces for applications with uncoupled stress conditions such as climbing or gripping (see Section 2.1.3 in Methods for details). For generality and fair comparison, the interface energy for the coupled stress condition is calculated as the amount of mechanical energy absorbed per unit area of the interface normalized by the modulus of the soft substrate E₀ as shown in eqn (2). The interface energy for uncoupled stress condition is derived similarly, by normalizing the mechanical energy by σ_v and E₀, as shown in eqn (3). Our results demonstrate a significant improvement in the interface energy introduced by stinger-inspired metainterfaces compared to the conventional ones without stingers. The interface energy of the uncoupled metainterface at θ_s = 20° was 207% higher than that of the conventional interface without stingers, while the coupled metainterface at θ_s = 0° exhibited a 155% improvement in interface energy compared to the conventional interface without stingers (Fig. 2(a)). We also observed that the interfacial energies of the coupled metainterface exhibit an exponential decay as the stinger angles increase from 0° to 180°. In contrast, we observed trigonometric curves for the interfacial energies of the uncoupled metainterfaces. These results suggest that stinger-inspired metainterfaces offer a promising route for designing programmable materials with tunable and significantly enhanced anisotropic interface properties.

In order to understand the ultrahigh coupling energy of metainterfaces observed experimentally, we conducted finite element analysis (FEA) using Abaqus CAE⁶³ to quantify and compare the stress distributions within metainterfaces and conventional interfaces. Our simulation results in Fig. 2(b) show that metainterfaces with θ_s = 0° exhibit a maximum interface stress that is significantly higher than conventional interfaces without stingers, under a range of σ_v, which is defined in Fig. 2(a). This amplified interfacial stress results in the ultrahigh uncoupled interface energies observed experimentally, indicating the effective geometries of the stingers, where the plug-in direction is defined as the direction opposite to the external stimulus representing the relative motion of the stinger (Fig. 2(b)). Our simulation results in Fig. 2(c) provide a summary of the stresses at different depths of the interface during the interface failures of metainterfaces and interfaces without stingers. The interface depths represent the distance between the substrate plane and the interfaces, where the stresses are calculated by averaging the simulated stress at the substrate plane (refer to Section 2.4 in Methods for details). We found that while interfaces without stingers exhibit significant stress concentrations at the contacting surfaces between the interfaces and substrate, metainterfaces reduce this stress concentration by sharing the stress to a larger depth of the substrate through the plug-ins of stingers. These phenomena delay the interface failures of metainterfaces, resulting in their ultrahigh interface energies. For the uncoupled metainterface, we observed that the experimentally measured interface energy exhibits a trigonometric pattern, proportional to the interacting area of its stingers facing the matrix motion. Consequently, we interpreted and modeled the uncoupled interface energy based on the size of the interacting area, incorporating a normalization factor to align with the experimental data. For the coupled metainterface, we used an exponential decay function to model the interface energy with respect to the stinger angles (Fig. 2(a)), as the energy quickly decays when the stinger angle deviates from the ideal angles, which makes pull-out more difficult and resembles what is observed in nature. The least squares method is applied to minimize the mean squared errors between the interpretation curves and the experimental data, and the mean squared errors for the uncoupled interface energy curve and coupled interface energy curve are 7.11 × 10⁻³ (mJ MPa⁻² mm⁻²)² and 3.15 × 10⁻³ (mJ MPa⁻² mm⁻²)², respectively, indicating a good alignment between the experimental measurements and the interpretation curves. The modelling of the stinger-inspired metainterface allows us to fully utilize the power of nature to program its selective interface coupling and opens up the potential for developing the next-generation artificial materials with programmable interfaces.

In nature, stingers of honeybees are evolved to possess anisotropic dragging of the substrates to ensure their effective plug-ins and difficult pull-out into biological tissues with a mixture of solid (e.g. skin) and liquid (e.g. body fluid, blood) materials. The various plug-in directions of the stinger allow a significant increase of the contacting surface area with programmable dragging, which is ideal for advanced engineering applications with improved and programmable heat exchanges. To validate, we conducted thermodynamical simulations with different flow rates to compare the heat exchange rate of the metainterface with θ_s = 180° and the conventional interface without stingers (see Section 2.3 in Methods for simulation details). The temperature difference between the coolant and the interface in Fig. 2(d) is set to 500 K for comparison purposes, and our results indicate that the heat exchange rate of metainterfaces with θ_s = 180° is doubled compared to the interface without stingers.

To better understand and control the highly anisotropic thermodynamic properties of the metainterface, we have developed fully connected neural networks (FCNNs) to analyze the complex thermodynamic behaviours of stingers, considering a large number of input parameters such as stinger angles, outlet directions, inlet flow rate, and temperature differences. To train the FCNNs, we generated 1040 training data points based on numerical simulations, and randomly selected 10% of them for testing. Our results demonstrate an average prediction error of 0.15 m s⁻¹ and 2.4 K for output velocity and temperature, respectively, using optimized hyperparameters such as the number of hidden layers, number of neurons, type of activation functions, and training epochs (see Section 2.3 in Methods for the detailed training process of the neural network). These findings underscore the accuracy and reliability of the trained FCNNs.

Using the thermodynamic calculations in eqn (10), we derived the heat exchange rate based on the predicted fluid velocity and temperature variations. Specifically, the heat exchange rate (q) is an integrated and averaged function of the fluid density (ρ), specific heat capacity (c), inlet and outlet velocities (v₁ and v₂), and inlet and outlet temperatures (T₁ and T₂) at different positions (x,y) at the inlet and outlet slices with a total area A, respectively (see Section 2.3 in Methods for details of the simulation data processing). By utilizing the trained neural networks, we successfully predicted the anisotropic thermodynamic properties of stingers, including fluid velocity (Fig. 2(e)) and the heat exchange rate (Fig. 2(f)). These results demonstrate the effective heat exchange of the metainterface and provide a robust digital design database for novel thermal management applications, where the fluid can be programmed to desired cooling locations with pre-engineered heat-exchange rates. This method not only provides a better understanding of the complex thermodynamic behaviours of a single stinger, but also enables the design of more complicated and efficient heat exchangers for various thermal management applications.

We also compared the fundamental properties of metainterfaces with existing two distinct categories of interface designs reconstructed from the literature (Fig. 3): (1) empirical interfaces, characterized by rectangular, triangular, and wavy geometries and (2) biometric interfaces, inspired by the elytra of beetles,^42,64 parasite stingers,⁶⁵ and honeybee stingers⁶⁶ (see Fig. S22, ESI† for fabricated samples). An equivalent volume of interface modifications is preserved for these samples to ensure fair comparison, where the detailed design data are presented in Table S7 (ESI†). We conducted coupled shear and tensile experiments, as illustrated in Fig. S4 (ESI†), to quantify the mechanical properties, including modulus, strength, and interface energies of these specimens. We also employed flow simulations with the configuration depicted in Fig. S12(a) (ESI†) to determine the heat exchange rates of these designs. The results are normalized by the modulus of the substrate materials E₀ and the contact areas introduced by different interface designs A_c to ensure the generality and fair comparisons of this study. Fig. 3(a) reveals that the metainterfaces with θ_s = 0° demonstrate a substantial improvement, with up to 413% and 240% higher normalized interface shear strength and modulus (refer to Fig. S23, ESI† for tensile comparisons). The results (Fig. 3(c)) indicate that the metainterface exhibits an up to five-fold (θ_s = 180°) and 14% to 727% (θ_s = 0°) higher heat exchange rate and normalized shear interface energy, as per contact interface area. The metainterface also enables the selection of interface configurations with desired combinations of thermal and mechanical properties, allowing for a balance between thermal and mechanical application demands at varying levels. Per interface contact, our results (Fig. 3(d)) reveal that the anisotropic designable ranges of the heat exchange rate and normalized interface energy for metainterfaces are 18% to 389% and 8% to 1162% higher than those of existing designs. The detailed XCT experiments and fracture simulations explaining the underlying theories and fracture mechanisms of the presented results are provided in Supplementary Note 1 (ESI†). The results obtained from these Ashby charts present a systematic analysis and comparison thermomechanical database of state-of-the-art interface designs, confirming that metainterfaces with XCT-rebuild geometries are more effective in enhancing interface mechanics, thermal properties, and designable anisotropic programmable potentials compared to existing designs.

Fig. 3 Ashby charts comparing the thermal, mechanical, and anisotropic properties of metainterfaces and existing interface designs including the flat interface, interface modified by empirical conventional rectangular, triangular, and wave shapes,⁴¹ inspired by stingers of honeybees⁶⁶ and parasites,⁶⁵ and elytra of beetles with trapezium⁶⁴ or ellipse⁴² simplifications. (a) Shear strength σ_s and shear modulus E_s for different interfaces normalized by the modulus of the Formlabs® flexible 80A substrate material E₀, where the pentagon represents the metainterface with the highest shear strength and modulus. (b) Heat exchange rate q normalized by the area of interfacial contact A_c and surface mechanical energy absorption S normalized by the area of interface contact A_c and E₀ for different interfaces, where the pentagon represents the metainterface with the highest normalized heat exchange rate. (c) Anisotropic designable ranges of q/A_c and S/(E₀A_c) for different interfaces.

3.2. Composite metamaterials with mechanical programming metainterfaces

Composite metamaterials, merging rigid lattice structures with a soft matrix, exploit interface interactions to achieve high specific energy absorption (SEA) while balancing compliance and stiffness, unlike the pure lattice structures that rely on parent materials with either high compliance or brittle fractures and high stiffness. In this section, we introduce innovative composite metamaterials containing implanted lattices with metainterfaces programmed to resist various decoupling modes of different lattice topologies (Fig. 4(a)). In addition, we have applied the metainterface concept to fish scale assemblies (Fig. 4(b)), exemplary metamaterials with unique composition of stiff and soft materials, enabling efficient stress distribution for exceptional anti-penetration and impact resistance. By incorporating a metainterface with pre-programmed interfacial resistances into the stiff sheets, we have introduced customizable and enhanced interface reactions, thereby achieving programmable and improved anti-impact mechanical behaviours that are not achieved in the existing literature. Fig. 4(c) presents specific energy absorptions (SEAs) of pure lattices, pure matrices, composite metamaterials without metainterfaces, and composite metamaterials with programmed metainterfaces (see Fig. S24, ESI† for detailed normalized stress–strain curves). We maintained identical weights for lattice implants with or without metainterfaces in each topology, where the composite metamaterials also exhibited comparable weights, with negligible deviations (Table S3, ESI†). It is observed that composite metamaterials exhibit significantly higher compliance in comparison to the brittle fracture behaviour of pure lattices. This leads to a notable enhancement in SEAs, ranging from 3.5 to 7.2 times and 2.1 to 3.8 times compared to pure lattices and matrices, respectively. The inclusion of metainterfaces with programmed resistance into interface decoupling results in elevated stress–strain curves when compared to composite metamaterials without metainterfaces, while achieving a maximum 18% improvement in the SEA. The result in Fig. 3(c) confirms the effectiveness of programming the topologically optimized interface resistances, while the detailed discussion of its effects on bending- and stretch-dominated structural designs is provided in Supplementary Note 2 (ESI†). For fish scale assembly samples, the thicknesses of the rigid sheets and the channel thickness of the flexible matrices are designed with different values for samples with and without metainterfaces to ensure the identical volume of rigid and soft materials (see Table S4, ESI† for detailed design information). The experimental results are also normalized by the density of the samples to further ensure fair comparisons. Fig. 3(d) suggests that the metainterfaces offer a 291% (θ_s = 0°) and 122% (θ_s = 90°) improvement of the compression modulus and specific energy absorption, respectively. The experimental results of fish scale assembly samples with metainterfaces also demonstrate a linear programmable compression stiffness at different θ_s values. These findings hold the potential to enhance and program impact energies and the modulus for composite metastructures through the use of metainterfaces with pre-engineered interfacial orientations.

Fig. 4 Mechanical programming in composite metamaterials enabled by metainterfaces. (a) The designs of composite body-centered-cubic (BCC), face-centered-cubic (FCC), tesseract, vintiles, and spherical hollow structure (SHS) metamaterials with and without programmed resistances from metainterfaces. (b) The designs of fish scale assemblies with and without metainterfaces with programmed orientations. (c) SEAs of composite metamaterials with and without programmable metainterfaces, pure lattice structures fabricated using the clear V4 resin, and pure matrix materials prepared using the flexible 80A resin. (d) The programmed modulus and SEA values for the fish scale assembly samples with metainterfaces at different stinger angles θ_s, compared to the results for samples without metainterfaces. (e) The interface fractures of FCC composite metamaterials with and without programmed interface resistance captured by XCT scanning. (f) The interface fractures of the fish scale assembly samples without programmed metainterfaces and with metainterfaces at θ_s = 0°. Note that the samples are designed with identical relative densities or sheet-to-matrix volume ratios with and without metainterfaces, please refer to Tables S3 and S4 (ESI†) for detailed sample information.

To interpret the results, we examined the fracture surfaces of the samples, as depicted in Fig. 4(e) and (f) (see Fig. S25, S21 and Movie S2–S6 (ESI†) for detailed XCT results for different topologies of metamaterials). The internal fractures within the composite metamaterials were visualized utilizing high-resolution XCT employing ZEISS Xradia 520 Versa X-ray microscopic equipment, with a resolution of 15.31 μm (refer to Section 5 in Methods and Fig. S19(b) (ESI†) for a comprehensive outline of the experimental procedure). In contrast to the limited interface resistance of the material decoupling observed in conventional composite metamaterials, the notable presence of enhanced interface resistance to deformation was observed in the metamaterials incorporating metainterfaces (Fig. 4(e)). Under identical compressive deformation conditions, the materials interfaces within the samples featuring metainterfaces exhibited more severe interface fractures, consequently resulting in a significantly improved interface energy and subsequently yielding a higher modulus and specific energy absorption (SEA). The fracture surfaces of the fish scale assemblies (Fig. 4(f)) implied an augmented utilization of materials interfaces in those incorporating metainterfaces, wherein stronger interfacial effects were necessitated for achieving complete structural failure, thereby contributing to the higher modulus and SEA observed in the metastructure. The innovation of this work lies in the integration of the programmable metainterface, which enables us to achieve highly controllable superior mechanical performance of artificial composite materials. Moreover, our proposed approach is not limited to the stated types of metamaterials, which offers broad potential in a wide range of mechanical applications for multi-material systems, where a programmable amplification of the interfacial effects is desired.

3.3. Thermos-mechanical structures with thermal programming metainterfaces

Aerospace lightweight components, such as turbine blades and thermal management systems in satellites, require the design of thermos-mechanical integrated structures to reduce weight and increase mechanical and heat management efficiency. However, the existing load-bearing structures often lack thermal control over the complicated geometries. Therefore, we utilized the contribution of this work to transform the conventional interface of load-bearing lattices to metainterfaces that are capable of programming the thermodynamical properties of the system without significantly varying their original mechanical performance (Fig. 5(a)). We implemented stingers on the complicated inner surface of the FCC unit cells to control the thermodynamic properties of fluid based on our machine learning results, while it should be noted that this strategy is not limited to this topology. We provide evidence for AI-driven programming of the thermodynamic properties of fluid by programming and concentrating the coolant flow to achieve prioritized cooling and selective flow rate patterns in certain areas with complex geometries (see Section 2.3 in Methods, Table S5 and Fig. S10, ESI† for detailed designs and methodologies).

Fig. 5 AI-driven thermal programming thermos-mechanical metamaterials. (a) The design of the unit cells for thermos-mechanical metamaterials with metainterfaces. (b) The design schematics and simulation results of prioritized programmable cooling, where the regions except the “SJTU” logo exhibits a lower heat exchange rate. (c) The design schematics and simulation results of programmed cooling patterns, where the regions except the “AI” logo exhibit a decelerated coolant velocity, while the regions within the “AI” logo possess an accelerated coolant velocity.

We programmed the coolant through the metamaterials to prioritize cooling on the surface except for cells located within the logo of Shanghai Jiao Tong University (SJTU), where the average outlet temperature of cells outside the logo was set to 300 K, and the region within the logo was set to 295 K (Fig. 5(b)). The results confirmed our expectations, with distinct temperatures for coolants inside and outside the logo region, with a variation of below 1 K for over 95% of the regions compared to design intuition, indicating a programmable heat exchange. To further demonstrate the novelty and effectiveness of our results, we applied the machine learning model with the thermodynamic programming algorithm to achieve controllable coolant velocity for a complex geometry. We designed retard cells and acceleration cells, where the estimated velocities of these cells were 4 m s⁻¹ and 8 m s⁻¹, respectively, with the inlet velocity of 6 m s⁻¹, and assembled them to form an accelerating “AI” logo and decelerating surroundings. The results in Fig. 5(c) demonstrate clear success in controlling the coolant velocity, with a deviation from the simulation results and programming intuition of below 0.3 m s⁻¹ for over 92% of the tested regions.

Our results suggest that the proposed method can be widely applicable to the thermos-mechanical design of engineering components or smart cooling metamaterials with highly controllable cooling sequences of desired regions for an optimized cooling result or concentrating the coolant resources to regions with higher cooling requirements, such as the surfaces of turbine blades where large amounts of high-temperature air flow through. In addition, our results open up a wide range of applications for smart thermal management systems, where the flow rate of coolant or the input fluid can be programmed to be accelerated or decelerated as desired, such as accelerating the coolant to locations in the satellite where a higher amount of heat is generated and decelerating it over the coolant recycling regions where a slow motion of coolant is desired to reduce the coolant temperature from surroundings.

3.4. Active programming in interfaces of intelligent robotic systems

In high-value applications such as wearable robotics, prosthetic limbs, and robot tracks, there is a preference for interfaces that can respond in an active and programmable manner to changing environmental conditions. However, this remains a significant challenge due to the difficulty in finding materials that can exhibit actively programmable and anisotropic interface performances that are generally applicable to various robotic systems. Here, we further validate the effectiveness of the programmable metainterfaces by presenting novel design solutions for actively programmable interface systems in robotics based on the utilization of metadisks enabled by metainterfaces (Fig. 6(a)). These systems can be widely implemented in different robotics applications, providing real-time adaptive and programmable interfacial mechanics. The fundamental unit of such a system is a motor-driven metadisk (MDM) with stingers controlled by digital signals. The programming of the interface mechanics relies on the relationship between the grasp angles and the experimentally measured normalized coupled and uncoupled interface energies (E_n,coupled and E_n,uncoupled), which are further normalized by the modulus of the parent materials. The grasp angles are defined as the angles between the symmetric lines of the metadisk systems and the orientation of each metadisk (Fig. 6(a)). By combining multiple MDMs, novel mechanical system features can be achieved, including in situ functional mode designs and interfaces that can satisfy pre-programmed mechanical interface properties in real-time for multiple stress orientations.

Fig. 6 Using metainterfaces to achieve intelligent active programming in robotics systems. (a) The design of a wearable intelligent exoskeleton achieved through programmable motor-driven metadisks (MDMs), where θ_g is the grasp angle defined as the adjacent angle between the symmetric dashed line and the sting tip. (b) Different real-time functional modes and programmable multidirectional interface mechanics achieved by an intelligent exoskeleton.

To illustrate these concepts, we provide experimental results of a novel intelligent exoskeleton that incorporates four MDMs, conforming metasurfaces, and a control unit based on the Arduino uno R3 board (Fig. 6(a)). Different functional modes (Fig. 6(b)), such as climb, resist, or traction, can be switched in real-time based on electronic signals sent from the programmable control unit based on eqn (6)–(8). This novelty is firmly supported by Fig. 6(b) and Movie S7 (ESI†), where we present compelling evidence of our achievements. We showcase two examples that demonstrate the attainment of distinct coupled or uncoupled stress responses across four different directions. These experimental results establish a direct correlation between the mechanical theories of the metainterface and the integration of programmable digital inputs. The linkage of experimental observations with theoretical foundations paves the way for the development of future metastructures capable of real-time programmable mechanical responses tailored to a wide range of environmental mechanical situations. Furthermore, our design theories offer immense potential for adaptation across various robotics systems employing multiple MDMs. By incorporating our innovative approach, it becomes possible to create highly customized functional modes and engineer anisotropic systems with multi-directionally tailored interface energies. It should also be noted that the scope of the proposed metainterface extends beyond the cases presented in this study. The combination of these elements introduces an unprecedented level of versatility and control in robotics applications (see Supplementary Note 3 and Fig. S26, ESI† for an additional case study of an amphibious robotic feet), opening doors to new avenues of exploration and possibilities for programmable mechanical responses in diverse environmental contexts.

4. Conclusion

In conclusion, our study introduces the concept of metainterfaces achieving the mechanically, thermally, and actively programmable interfacial effects that are not reported before, leading to development of advanced composite mechanical metamaterials, thermomechanical systems, and intelligent robotic components with highly programmable localized interface properties (Fig. 1). Unlike conventional biometric interfaces with simplified geometries and restricted application types, our design strategy allows the construction of XCT-rebuild stingers into freeform geometries, resulting in ultrahigh and programmable mechanical and thermodynamical interface properties (Fig. 2 and 3). Enabled by metainterfaces, we report substantial enhancement of specific energy absorption (SEA) enabled by the programmed interface resistance of composite metamaterials customized to different lattice topologies and the programable modulus and significantly improved SEA of fish scale assemblies (Fig. 4). In addition, the AI-driven thermal programming is utilized innovatively to design and concentrate coolant flow by the metainterface, leading to the prioritization of cooling and selective flow patterns within complex geometries (Fig. 5). This pioneering approach has the potential to propel complicated thermos-mechanical systems forward, enabling highly controlled cooling sequences for optimized heat exchange and efficient coolant resource management. Furthermore, our introduction of metadisks, empowered by digitally controlled programmable metainterfaces, enables active and highly customizable interfacial mechanics and flow controls in robotics (Fig. 6).

This work also paves the way for several innovative and interdisciplinary research directions. Future investigations can explore the integration of metainterfaces into intricate metamaterial designs, enabling the programmed manipulation of interfacial reactions and the creation of novel properties such as programmed materials failures. Additionally, researchers can delve into programming various modes of interface resistance and engineering these patterns into diverse materials and engineering systems to study the effects of pre-designed interface properties. Furthermore, there is potential to uncover additional functionalities that can be programmed through metainterfaces, expanding the horizons of what can be achieved in this realm.

Data availability

The datasets related to this study are available from the corresponding authors upon reasonable request.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

Yi Wu acknowledge the financial support from National Key Research and Development Program of China (No. 2023YFB3712001). Zhenyang Gao acknowledges the support from the National Natural Science Foundation of China 523B2048. Hongze Wang acknowledges the support from the National Natural Science Foundation of China 52075327, National Natural Science Foundation of China 52004160, Shanghai Sailing Program 20YF1419200, Natural Science Foundation of Shanghai 20ZR1427500, SJTU Global Strategic Partnership Fund 2023 SJTU-CORNELL, innovation foundation of Commercial Aircraft Manufacturing Engineering center of China No. 3-0410300-031, and University Synergy Innovation Program of Anhui Province GXXT-2022-086. Yang Lu acknowledges the support from the Research Grants Council of the Hong Kong Special Administrative Region, China, under RFS2021-1S05; Hong Kong RGC general research fund #11200623; and RGC Hong Kong under the CRF project C7074-23GF. The authors also thank the facility access to the BL16U2 beamline of Shanghai Synchrotron Radiation Facility (SSRF) and staff support.

References

1. A. Farzaneh, N. Pawar, C. M. Portela and J. B. Hopkins, Nat. Commun., 2022, 13, 1041.
2. A. E. Forte, D. Melancon, M. Zanati, M. De Giorgi and K. Bertoldi, Adv. Funct. Mater., 2023, 2214897.
3. X. Huang, W. Guo, S. Liu, Y. Li, Y. Qiu, H. Fang, G. Yang, K. Zhu, Z. Yin and Z. Li, Adv. Funct. Mater., 2022, 32, 2109109.
4. J. Fan, L. Zhang, S. Wei, Z. Zhang, S.-K. Choi, B. Song and Y. Shi, Mater. Today, 2021, 50, 303–328.
5. G. Wan, Y. Tang, K. T. Turner, T. Zhang and W. Shan, Adv. Funct. Mater., 2023, 33, 2209905.
6. D. W. Abueidda, M. Elhebeary, C.-S. A. Shiang, S. Pang, R. K. A. Al-Rub and I. M. Jasiuk, Mater. Des., 2019, 165, 107597.
7. X. Fan, Q. Tang, Q. Feng, S. Ma, J. Song, M. Jin, F. Guo and P. Jin, Int. J. Mech. Sci., 2021, 204, 106586.
8. W. Wu, R. Xia, G. Qian, Z. Liu, J. Razavi, F. Berto and H. Gao, Prog. Mater. Sci., 2022, 101021.
9. P. Cai, C. Wang, H. Gao and X. Chen, Adv. Mater., 2021, 33, 2007977.
10. J. Shi, H. Mofatteh, A. Mirabolghasemi, G. Desharnais and A. Akbarzadeh, Adv. Mater., 2021, 33, 2102423.
11. W. P. Moestopo, A. J. Mateos, R. M. Fuller, J. R. Greer and C. M. Portela, Adv. Sci., 2020, 7, 2001271.
12. Z. Gao, H. Wang, H. Sun, T. Sun, Y. Wu, C. L. A. Leung and H. Wang, Composites, Part B, 2022, 247, 110345.
13. Y. Zhang, Y. Lin, Y. Li and X. Li, Thin Wall Struct., 2021, 164, 107795.
14. C. Liu, J. Lertthanasarn and M.-S. Pham, Nat. Commun., 2021, 12, 4600.
15. C. Liu and M. S. Pham, Adv. Mater., 2023, 2305846.
16. Z. Gao, P. Ren, H. Wang, Z. Tang, Y. Wu and H. Wang, Int. J. Mach. Tools Manuf., 2023, 104101.
17. T. Xue, A. Beatson, M. Chiaramonte, G. Roeder, J. T. Ash, Y. Menguc, S. Adriaenssens, R. P. Adams and S. Mao, Soft Matter, 2020, 16, 7524–7534.
18. C. S. Ha, D. Yao, Z. Xu, C. Liu, H. Liu, D. Elkins, M. Kile, V. Deshpande, Z. Kong and M. Bauchy, Nat. Commun., 2023, 14, 5765.
19. R. R. Sélo, S. Catchpole-Smith, I. Maskery, I. Ashcroft and C. Tuck, Addit. Manuf., 2020, 34, 101214.
20. N. Lee, J.-S. Lim, I. Chang, D. Lee and H. H. Cho, Int. J. Heat Mass Transfer, 2021, 173, 121173.
21. Y. Li, W. Li, T. Han, X. Zheng, J. Li, B. Li, S. Fan and C.-W. Qiu, Nat. Rev. Mater., 2021, 6, 488–507.
22. L. M. Korpas, R. Yin, H. Yasuda and J. R. Raney, ACS Appl. Mater. Interfaces, 2021, 13, 31163–31170.
23. P. Jiao, T. Chen and Y. Xie, Compos. Struct., 2021, 256, 113053.
24. H. Yang, N. D'Ambrosio, P. Liu, D. Pasini and L. Ma, Mater. Today, 2023, 66, 36–49.
25. A. Nain, S. Chakraborty, N. Jain, S. Choudhury, S. Chattopadhyay, K. Chatterjee and S. Debnath, Biomater. Sci., 2024, 3241–3472.
26. X. Wang, J. Sparkman and J. Gou, Compos. Sci. Technol., 2017, 141, 8–15.
27. H. Zhu, Y. He, Y. Wang, Y. Zhao and C. Jiang, Adv. Intell. Syst., 2022, 4, 2100137.
28. H. Zhu, Y. Wang, Y. Ge, Y. Zhao and C. Jiang, Adv. Sci., 2022, 9, 2203711.
29. T. J. Hinton, Q. Jallerat, R. N. Palchesko, J. H. Park, M. S. Grodzicki, H.-J. Shue, M. H. Ramadan, A. R. Hudson and A. W. Feinberg, Sci. Adv., 2015, 1, e1500758.
30. X. Fang, J. Wen, L. Cheng, D. Yu, H. Zhang and P. Gumbsch, Nat. Mater., 2022, 21, 869–876.
31. L. Yang, B. Zhou, L. Ma, G. Liu, S. Qian, Z. Xu, E. Liu, X. Zhang, C. He and N. Zhao, Carbon, 2021, 183, 685–701.
32. S. Zeng, T. Zhang, M. Nie, G. Fei and Q. Wang, Composites, Part B, 2021, 216, 108868.
33. A. Rout, P. Pandey, E. F. Oliveira, P. A. da Silva Autreto, A. Gumaste, A. Singh, D. S. Galvao, A. Arora and C. S. Tiwary, Polymer, 2019, 169, 148–153.
34. P. G. Grutzmacher, S. Suarez, A. Tolosa, C. Gachot, G. Song, B. Wang, V. Presser, F. Mücklich, B. Anasori and A. Rosenkranz, ACS Nano, 2021, 15, 8216–8224.
35. J. Li, Y. Fu, J. Zhou, K. Yao, X. Ma, S. Gao, Z. Wang, J.-G. Dai, D. Lei and X. Yu, Sci. Adv., 2023, 9, eadg1837.
36. A. Giri and P. E. Hopkins, Adv. Funct. Mater., 2020, 30, 1903857.
37. S. Wang, J. Ning, L. Zhu, Z. Yang, W. Yan, Y. Dun, P. Xue, P. Xu, S. Bose and A. Bandyopadhyay, Mater. Today, 2022, 59, 133–160.
38. A. Nazir, O. Gokcekaya, K. M. M. Billah, O. Ertugrul, J. Jiang, J. Sun and S. Hussain, Mater. Des., 2023, 226, 111661.
39. Z. Yin, F. Hannard and F. Barthelat, Science, 2019, 364, 1260–1263.
40. A. Melaibari, A. Wagih, M. Basha, A. Kabeel, G. Lubineau and M. Eltaher, Composites, Part A, 2021, 144, 106362.
41. L. Wang, Y. Liu, Y. Yang, Y. Li and M. Bai, Addit. Manuf., 2021, 42, 101992.
42. J. Rivera, M. S. Hosseini, D. Restrepo, S. Murata, D. Vasile, D. Y. Parkinson, H. S. Barnard, A. Arakaki, P. Zavattieri and D. Kisailus, Nature, 2020, 586, 543–548.
43. M. Zhu, F. Zhang and X. Chen, Small Struct., 2020, 1, 2000045.
44. R. W. Style, R. Tutika, J. Y. Kim and M. D. Bartlett, Adv. Funct. Mater., 2021, 31, 2005804.
45. G. Chen, Nat. Rev. Phys., 2021, 3, 555–569.
46. H. Yu, Y. Feng, C. Chen, Z. Zhang, Y. Cai, M. Qin and W. Feng, Carbon, 2021, 179, 348–357.
47. W. Dai, T. Ma, Q. Yan, J. Gao, X. Tan, L. Lv, H. Hou, Q. Wei, J. Yu and J. Wu, ACS Nano, 2019, 13, 11561–11571.
48. J. Ma, T. Shang, L. Ren, Y. Yao, T. Zhang, J. Xie, B. Zhang, X. Zeng, R. Sun and J.-B. Xu, Chem. Eng. J., 2020, 380, 122550.
49. Y. Cui, Z. Qin, H. Wu, M. Li and Y. Hu, Nat. Commun., 2021, 12, 1284.
50. L. Yang, W. Li, J. Lian, H. Zhu, Q. Deng, Y. Zhang, J. Li, X. Yin and L. Wang, Science, 2024, 384, 1344–1349.
51. H. Cheng, X. Zhu, X. Cheng, P. Cai, J. Liu, H. Yao, L. Zhang and J. Duan, Nat. Commun., 2023, 14, 1243.
52. C. Zhang, A. Akbarzadeh, W. Kang, J. Wang and A. Mirabolghasemi, Carbon, 2018, 131, 38–46.
53. C. Bonatti and D. Mohr, Int. J. Plast., 2017, 92, 122–147.
54. A. Parisien, M. S. ElSayed and H. Frei, Mater. Today Commun., 2022, 33, 104315.
55. K. M. Abate, A. Nazir and J.-Y. Jeng, Int. J. Adv. Manuf. Technol., 2021, 112, 2037–2050.
56. Y. Stylianos, M. Orestes, R. A. Votsis and F. P. Brennan, Mech. Res. Commun., 2018, S0093641318301587.
57. T. E. O. E. Britannica, Honeybee, https://www.britannica.com/animal/honeybee, accessed June 22, 2023.
58. K. P. Murphy, Machine learning: a probabilistic perspective, MIT Press, 2012.
59. M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean and M. Devin, arXiv, 2016, preprint, arXiv:1603.04467.
60. J. Matsson, An Introduction to SOLIDWORKS Flow Simulation 2023, SDC Publications, 2023.
61. S. Hochreiter, Int. J. Uncertain. Fuzz. Knowl.-Based Syst., 1998, 6, 107–116.
62. R. McNeel, Rhinoceros 3D, Version 6.0, Robert McNeel & Associates, Seattle, WA, USA, 2010.
63. D. Hibbitt, B. Karlsson and P. Sorensen, ABAQUS user-manual release 6.14, Dassault Systèmes Simulia Corp., Providence, RI, 2014.
64. Y. Ni, H. Bai, Z. Wang, H. Liao and W. Wu, Compos. Struct., 2023, 117220.
65. S. Y. Yang, E. D. O'Cearbhaill, G. C. Sisk, K. M. Park, W. K. Cho, M. Villiger, B. E. Bouma, B. Pomahac and J. M. Karp, Nat. Commun., 2013, 4, 1702.
66. D. Han, R. S. Morde, S. Mariani, A. A. La Mattina, E. Vignali, C. Yang, G. Barillaro and H. Lee, Adv. Funct. Mater., 2020, 30, 1909197.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4mh00570h

---