Curved Architected Triboelectric Metamaterials: Auxeticity‐Enabled Enhanced Figure‐of‐Merit

Triboelectric generators are integrated into curved architected materials to realize triboelectric metamaterials that simultaneously harvest electricity from wasted mechanical energy and perform mechanical energy absorption. Novel triboelectric mechanical metamaterials (TMMs) of distance‐changing, angle‐changing, and mixed modes are designed, fabricated, and tested under a cyclic compressive load. The open‐circuit voltage and short‐circuit current of lightweight TMMs are found to be as high as 40 V and 10 nA. The introduced TMMs can effectively harvest energy under loadings from two distinctive directions. A theoretical model for predicting the energy harvesting properties of TMMs is developed, and the role of auxeticity on the energy harvesting figure‐of‐merit (FOMes) is elicited. The introduced TMMs exhibit enhanced FOMes enabled by a decrease in their negative Poisson's ratio and an increase in their resilience. The FOMes of curved architected TMMs surpasses by more than 16 times the FOMes of triboelectric materials with conventional architectures (i.e., triangular, quadrilateral, and hexagonal cell topologies). An intelligent skateboard with integrated TMMs is fabricated as a proof of concept to demonstrate motion sensing, shock‐absorbing, and energy harvesting functionalities of multimodal triboelectric metamaterials. The introduced design strategy for triboelectric metamaterials unlocks their applications in self‐powered and self‐monitoring sports equipment, smart soft robots, and large‐scale energy harvesters.


Introduction
With the rapid growth of the Internet of Things (IoTs) and portable devices, more attention has been given to the DOI: 10.1002/adfm.202306022development of mobile power sources and self-powered sensors.Ambient mechanical energy (AME) (e.g., hydrokinetic, [1] sound, [2] and biomechanical [3] energy), a clean and widely available form of energy, has been one of the most sought-after wasted energy resources to be harvested. [4]he triboelectric effect, also known as triboelectric charging, is a type of contact electrification on certain insulators after they are separated from a material they were contacted or rubbed (henceforth the tribo prefix, a Greek word means "rub," is referring to "friction" in triboelectricity).To convert AME into electricity with low cost and high efficiency, triboelectric effect and electrostatic induction (introduced in detail in Section S1 in the Supporting Information), two common phenomena in daily life, were first combined as generators, also named triboelectric generators (TEGs), in 2012. [5]Even though there are many variants of TEGs (introduced in detail in Section S1 in the Supporting Information), a TEG generally consists of insulators, which are called triboelectric layers, [6] as the source of triboelectric charging and conductors as electrodes.The insulators are electrified after separation from another component (insulator or conductor) with a work function difference. [7]The electrical charges at the far end of an electrode from the insulator, driven by the electrostatic induction and electromotive force, are transferred to another electrode and form an electric current when both are connected in a closed circuit.
By virtue of advanced micro/nano additive manufacturing, multifunctional metamaterials (M 2 s) constructed with rationally designed micro/nanostructures open new avenues for attaining programmable, interactable, and counterintuitive multiphysical properties (e.g., negative Poisson's ratio, [8] tunable electromagnetic permittivity, [9] structural multistability, [10] and electrochemical reconfigurability [11] ) that are inaccessible in naturally occurring or conventional synthetic materials.Among the diverse classes of M 2 s, curved architected mechanical metamaterials inspired by the wavy network microstructures found in soft biological tissues (such as an actin filament or a collagen fibril [12] ), typically feature impressive resilience. [13]The microstructures of this class of emerging mechanical metamaterial are also named horseshoe architectures. [14]Additionally, Poisson's ratio of horseshoe-architected materials can be precisely customized in a wide range, [14,15] which facilitates their potential applications in programmable flexible electronics. [14,15]onsidering the coexisting demands of load bearing, mechanical energy absorbing, energy converting, and autonomous sensing/actuating properties in IoTs, it is of great interest to develop the next generation of electromechanical metamaterials by integrating TEGs into M 2 s, and thereby realize triboelectric multifunctional metamaterials (TMMs).In the past few years, TMMs have been designed out of beam-array, [16] snapping, [17] honeycomb, [17] chiral, [18] or hierarchical [19] architectures as substrates, together with embedded, [16] inserted, [20] or attached [17,21] TEGs to demonstrate their energy harvesting, [22] sensing, [17a] vibration suppressing, [18] and load impact reducing [23] capabilities.Despite the recent efforts to create new architected triboelectric materials, it is yet to be uncovered if auxeticity can be capitalized to enhance the electrical performance of architected triboelectric metamaterials while providing remarkable mechanical properties.There is also a lack of analytical tools to quantify the efficiency of triboelectric metamaterials for the optimization of their electrical output, exclusively when multiple working modes of TEGs coexist due to the complex intrinsic deformation mechanisms of their underlying architecture.First, TMMs are required to be highly resilient and remarkable in energy absorption for a long life span under cyclic loadings. [24]Second, the electrical networking TEGs should be synchronized in yielding electric voltages or currents for the maximization of electric output. [24,25]Finally, TMMs should be able to harvest energy and sense external excitations from arbitrary directions. [26]This study introduces, for the first time, design, fabrication, and optimization strategies for the realization of auxetic TMMs with tailorable mechanical properties (i.e., stiffness, specific energy absorption, and maximum recoverable compressive strain) and efficient energy harvesting characteristics.The electromechanical properties including deformation modes, voltage, and current output of this new class of TMMs are examined through experiments and compared to the conventionally architected counterparts, namely regular triangular, quadrilateral, and hexagonal architectures.Theoretical models for electrical output and finite element models are developed to quantitatively investigate the influence of topological parameters of underlying architectures of TMMs on their energy harvesting figure-of-merit.The roles of auxeticity (i.e., negative Poisson's ratio, which leads to transverse contraction when the metamaterial is compressed longitudinally) in facilitating uniform deformation and synchronizing all TEGs connected in parallel are explored.This study sheds light on the engineering application schemes of TMMs as building blocks of intelligent load-bearing infrastructures, including micro/nanopower sources, [27] self-powered sensors, [28] and wearable electronic devices. [29] Methods

Designs and Fabrication
In this study, the unit cells of TMMs were designed by capitalizing curved walls in triangular, quadrilateral, and hexagonal cellular architectures.The in-plane bending of the horseshoeshaped cell walls was expected to drive the opposite triboelectric surfaces to approach each other in a TMM under com-pression, and to facilitate the generation of electricity.Triangular, quadrilateral, and hexagonal cellular materials were selected as basic underlying architectures since they were the only solutions for the realization of regular tiling in an Euclidean plane. [30]As identified in a previous eigenmode analysis [31] on these polygonal cells, eight cellular architected designs with curved walls could be identified to demonstrate auxetic behaviors.A TEG contained in the TMMs was separated into two parts (named tribopairs, i.e., negative-charge-attractive layer/electrode and positive-charge-attractive layer/electrode) attached to adjacent cell walls that contacted each other under compression, as shown in Figure 1a.Polyester (PET) and polytetrafluoroethylene (PTFE) were selected from a wide range of potential insulator candidates as the positive-and negative-charge-attractive materials to form the integrated TEGs mainly due to their highest open-circuit voltage generation when were operated in a contactseparation mode, as shown in Section S4 (Supporting Information).Copper was used as the electrode materials.Polypropylene (PP) was selected as the parent material for the insulative cellular substrate of the TMMs since its flexibility provided TMMs with mechanical resilience and damage tolerance, extending their life span.Figure 1b briefly explained the role of auxeticity in driving the TEGs distributed in the x-direction when the TMM was under compression in the y-direction.To increase the chance of internal contact of every TEGs under cyclic compressive loadings, finite element method (FEM) simulations of the corresponding cellular substrate with the abovementioned architectures were first conducted under a multiaxial compression in order to optimize the positions of tribopairs in TMMs, as presented in Section S5 (Supporting Information).
According to the different working principles shown in Figure 1c of the integrated TEGs, eight TMM designs with curved cell walls were divided into three types, i.e., angle-changing, distance-changing, and mixed-type TMMs.A TEG in anglechanging TMMs featured two triboelectric surfaces sharing the same axis of rotation, while a TEG in distance-changing TMMs was composed of two triboelectric surfaces taking relative translational motion but without relative rotation.A TEG in the mixedtype TMMs took both kinds of motions for its working principle.Meanwhile, TMM designs with triangular, quadrilateral, and hexagonal architectures were selected to examine the electromechanical performance of the developed TMMs with underlying horseshoe architectures.All the TMM designs were named by the abbreviation of the substrate geometries and a specific number, as presented in Figure 1c.To simplify the modeling procedure without losing the generality, each curved cell wall was modeled as an arc with a central angle of Φ = 120°.Chamfers were introduced to avoid short circuit of two adjacent electrodes and local stress concentration leading to damage of the cellular substrates.For comparison of structural efficiency of electrical output, all the TMMs possessed the same triboelectric surface area for a single TEG.More information on the geometrical parameters of the unit cell design can be found in Section S2 (Supporting Information).The relative densities  r of all TMM designs could be theoretically determined, as presented in Section S2 (Supporting Information) and were controlled to be identical (i.e.,  r = 0.3) by adjusting the thickness of the cell walls t 0 .To evaluate if the electrical structural efficiency of the designed TMMs could surpass the conventional plate-like TEG structures [32] and  multilayered [33] TEG structures based on plate-like TEG structures, stacked TEG (ST) model was designed as a representative of the plate-like and multilayered TEG structures, as shown in Figure 2e.Moreover, stacked curved TEGs (SCTs) were proposed in Figure 2e as a conceptual combination of stacked TEGs and curved struts.TEGs in the ST and SCT designs were distributed to work only in the y-direction.Therefore, ST and SCT were not as capable as TMMs proposed in the current study in harvesting energy and bearing loads applied in multiple directions.Both ST and SCT possessed the same layer height l 0 and relative density  r as the Q2 design, but the adjacent layers were connected by spring-like structures to realize resilience in the structure.
The TMM samples were fabricated through the procedure shown in Figure 1d.First, the substrates of TEGs, namely the cellular material parts of TMMs, were fabricated through fused deposition modeling 3D printing out of PP polymers as the parent material.Then, the copper electrodes in the form of acrylic adhesive-back films (i.e., copper AABFs) with a dimension of 12.7 × 10 × 0.05 mm were attached to the designated positions of the cellular substrate.All electrodes in a TMM were connected in parallel with copper AABF ribbons of 2 mm width.Finally, PTFE and PET AABFs from McMaster-Carr with a dimension of 12.7 × 10 × 0.25 mm were attached to the electrodes.All the abovementioned AABFs were shaped by a Trotec Speedy 100 laser cutter.

Electromechanical Experiments
To investigate the mechanical and electrical behaviors of TMMs under cyclic loading, electromechanical experimentations were carried out on four alternative TMM samples made out of T1, Q2, H3, and Q0 architectures as representatives for the angle-changing, distance-changing, mixed-type, and conventional TMMs with 2 × 2 unit cells.These samples were adhesively connected to upper and lower fixtures, as shown in Figure S4a (Supporting Information).All cyclic loading tests were conducted on a universal mechanical test machine ADMET eXpert 7601 with a 250 lbf (1.11 kN) capacity load cell.A compressive strain sequence of 30 cycles ⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞ [0.25, 0, 0.25, ⋅ ⋅ ⋅, 0, 0.25, 0] was applied by moving the upper end of samples at a loading rate of 2 mm s −1 , while the lower end was clamped fixed to the test machine.The compressive strain of −0.25 was determined to guarantee that all the TMM samples could undergo the first inner contact before the end of compression.Open-circuit voltage output (V OC ) and short-circuit current output (I SC ) were measured using a Keithley 6517a electrometer, as shown in Figure S4b (Supporting Information).Short-circuit transferred charge amount (Q SC ) was cal- dt where t c is the ending time of a loading cycle.A LabVIEW-based program was developed to control electrometer measurements and to store readings in the host computer.At least three replicates were tested for each TMM architecture to ensure the repeatability of experimental results.In the first several loading cycles, the charge density on the triboelectric surface gradually reached a maximum value by contact electrification.In the following cycles, the TMMs presented repeated oscillation of reaction force-time, open-circuit voltage-time, and short-circuit current-time outputs until the tests were completed, as shown in Video S1 (Supporting Information), confirming their potential for serving as a cyclic load-bearable engineering materials for a prolonged life span.

FEM Simulation
To develop a quantitative predictive model for exploring the multiphysical behaviors of alternative TMMs, electromechanical FEM simulation was utilized.COMSOL Multiphysics Version 6.0 was used as the FEM platform, in which the Structural Mechanics and AC/DC modules were combined to solve the electromechanical problem involving nonlinear geometric deformation, electric potential variation of deformed domains, and charge transfer in a circuit.Semidetailed computer-aided design (CAD) models of the TMM designs with 4 × 4 unit cells were imported into COMSOL Multiphysics software for 2D analysis with plane-strain approximations, in which the exact planar geometry of the PP cellular substrate was modeled, while the PTFE/PET layers and the adjacent electrodes were composited into an equivalent area, neglecting the effect of the 0.05 mm thin copper AABFs on the overall mechanical properties.Specifically, these equivalent areas were endued with mechanical properties of the corresponding composite layers from experiments.The surface charges, zero potential, and floating potential, were defined on the triboelectric layers, electrode layers beneath PET layers, and electrode layers beneath PTFE layers, respectively, as shown in Figure S8a (Supporting Information).All the above layers were perfectly bonded with sharing element nodes.Elastoplastic material properties of PP, PTFE-electrode composite layer, and PET-electrode composite layer were defined with the parameters shown in the Table S1 (Supporting Information).The bulk densities of the materials were measured through direct measurement of mass and apparent volume. [34]The mechanical properties (i.e., Young's modulus E and initial yield stress  y ) of PP and the two composite films (PTFE-copper and PET-copper) were obtained from the tensile tests, as shown in Section S4 (Supporting Information).Plasticity in all solids was considered with a perfectly plastic isotropic hardening model.The Poisson's ratios of the three materials (i.e., PP, PET-copper, and PET-copper) were assumed to be 0.38, while their relative permittivities were measured according to the procedure specified in Section S4 (Supporting Information).
After a mesh sensitivity analysis, each narrow area member (i.e., PTFE-electrode layer, PET-electrode layer, or PP strut area) was modeled by at least two shell elements in the thickness direction of TMMs, as shown in Figure S8a (Supporting Information).The moving mesh method was applied to the air domain to simulate the topological changes of underlying architectures induced by the deformation of solid materials while avoiding premature element distortion at the interface between gas and solids.The charge density on the surface of triboelectric layers, which was difficult to predict due to the complexity of contact electrification mechanisms, was the subject of manipulation as it linearly scaled the simulated electric output. [16]The simulated maximum opencircuit voltage could be close to the experimental values when the charge density  was specified as 2.52 The structural transient behavior of quasistatic was set, which meant there were no second-order time derivatives in the formula.Backward differentiation formula was used to solve this time-dependent nonlinear electrostatic-structural mechanics problem, which was an implicit method.The numerical study of electric output was conducted via a preset charge equilibrium strategy simulating the steady electric output of TMMs after several loading cycles, as described in Section S16 (Supporting Information) in detail.
To examine the auxetic behavior of the TMMs, the effective Poisson's ratio v eff was also measured by Overvelde's method. [35]he motions of the nine vertices of four central representative volume elements (RVEs) were monitored (shown in Figure S8a in the Supporting Information), as their motion response was clearly more uniform and less affected by the boundary conditions than the other RVEs.The resilience of TMMs was quantitatively evaluated by the maximum recoverable compressive strain ( yy,m ), which was defined as the compressive strain when the ratio of dissipated energy, due to the plasticity of base polymers, reached 10% of the total input mechanical energy. [36]Specific energy absorption (SEA) and maximum open-circuit voltage V OC,max of TMMs were also defined by the following equations

Theoretical Model
A theoretical model was established for the electric energy output of TMMs in a cycle for maximum energy output (CMEO) based on a previously reported model for contact-mode triboelectric materials. [37]The CMEO of the TMMs was obtained by alternating close-circuit/open-circuit conditions and alternating uniaxial strains applied to the TMMs, as shown in Figure 2a.
The theoretical upper bound of energy output E m could be calculated according to the following Equation (3a) when the resistance of external loading is approaching infinity; [38] TEG working modes observed in experiments and simulations, including angle-changing, distance-changing, and mixed mode contactseparation were considered in this theoretical model )) (3c) )) (3d) where N is the number of TEGs inside a TMM (values of N for the introduced TMM designs in Figure 1 can be found in Section S6 (Supporting Information));  is the charge density of the triboelectric surfaces; Q SC is the charge transfer between the two electrodes of each TEG; V OC and V ′ OC are the open-circuit voltage at stage three and stage one in a CMEO, respectively; l 0 and w are the length and width of the simplified triboelectric surfaces; C x is the capacitance between two triboelectric surfaces of a TEG that varies with the equivalent distance x between the triboelectric surfaces; C d1 and C d2 are the capacitances between negative/positive triboelectric surfaces and the attached electrodes, respectively.The detailed derivations can be found in Section S14 (Supporting Information).In the current theory, two curved triboelectric surfaces of a TEG were simplified by two flat planes (two red dashed lines in the 2D schematic graph of Figure 2c), defined as rigid bodies by the following rules: for angle-changing type TEGs, the ends of the two curved triboelectric surfaces ( ⌢ AB, ⌢ BC) served as the ends of the simplified planes (AB, BC); for distance-changing and mixed-type TEGs, the simplified planes met the curved triboelectric surfaces at the midpoint (E and F) and were parallel to the planes connecting the ends of the curved triboelectric surfaces ( ⌢ AB, ⌢ CD).The validity of the simplified model was examined by comparing the V OC of TEGs with curved triboelectric surfaces and those with the equivalent planes using FEM simulations, as shown in Figure S13 (Supporting Information).Considering the edge effect of a capacitor, the capacitances inside a TEG could be expressed by equations from previous research [39] C x =  0  r l 0 w x where  0 = 8.854 × 10 −12 F m −1 is the absolute permittivity of vacuum; x for arbitrary working modes could be derived by the following Equation ( 5)(a)-(d).By considering the strain vectors of the concerned area of a TMM in Figure 2b, the local coordination of the concerned area, and the detailed model of the local motion of a single TEG in Figure 2c x

⏟⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏟
angle-changing (5a) where d 1 and d 2 are the thicknesses of the two triboelectric layers (herein PTFE and PET layers), as shown in Figure S1 (Supporting Information);  1 and  2 are the relative permittivities of the two triboelectric layers; Δx 1 , Δx 2 , and  are the relative translational displacements along the s-and t-axes and rotation of the two simplified planes.For angle-changing type TEGs, )), x 20 = l 0 sin( 2 , l v0 = l 0 sin( 0 ), and Δ =   ; for distance-changing type TEGs, x 10 = 0, x 20 = constant, Δx 1 =   l v0 , Δ x 2 =  ⊥  l v0 , Δ = 0, l v0 = l 0 ; and for mixed type TEGs, x 10 = l 0 (1 − cos( ) −  0 , and l v0 = constant.The deformation of each layer of ST and SCT could be described by the theory of distancechanging type TEGs by considering x 10 = 0, x 20 = constant, Δx 1 =   l v0 , Δ x 2 =  ⊥  l v0 , Δ = 0, and l v0 = 4l 0 .The local strain vectors   and  ⊥  could be derived from the domain under a uniaxial compression in the y-direction in Figure 2b through the following expressions The definitions and values of the other geometric parameters (i.e., x 10 , x 20 ,  0 , , and l v0 ) can be found in Section S6 (Supporting Information) for the proposed TMM designs.When connected in parallel, the total open-circuit voltage output of multiple TEGs was assumed to be expressed by the following equation, verified in Figure S14 (Supporting Information) by comparing the results with the detailed finite element analysis predictions It was assumed that all the constitutive cells yielded voltage output equally for a TMM experiencing a uniform deformation.From Equations (3)(a)-(g) to (6)(a)-(c) for one unit cell, the TEGs with the same  or rotational symmetry possessed identical theoretical voltage output, as marked by the same number in Figure 2d, from which a representative TEG could be determined.Therefore, the open-circuit voltage output of a TMM was equal to the overall V OC of representative TEGs connected in parallel (Equation ( 7)).To quantitatively evaluate and compare the energy harvesting performance of TEGs with alternative underlying architecture, a dimensionless electrical-structural figure-ofmerit (FOM es ) was evaluated [38,40] FOM es = max where A and x are the area and the displacement of TMM in the loading direction.

Mechanical and Electrical Performance of TMMs
As shown in Figure 3a, all four types of TMMs (T1, Q2, H3, and Q0) present stable mechanical and electrical performance when subjected to a uniaxial cyclic load in the experiment.Compared to conventional architectures, TMMs with curved struts (i.e., T1, Q2, and H3) can realize more remarkable open-circuit voltage (V OC ) and short-circuit current (I SC ).In specific, experimental V OC and I SC of Q2 surpass the corresponding performance of the triboelectric design with the conventional architecture (Q0) by 53.3 and 55.1 times, respectively.The TMM with underlying Q2 architecture presents the highest V OC of ≈ 40 V and the highest I SC of around 10 nA.33c,41] As presented in Figure 3b,c, when loaded until a compressive strain of  yy = -0.25, the introduced TMMs with curved architectures undergo a uniform deformation through the bending of curved struts, driving all the integrated TEGs to generate electricity synchronously from the mechanical deformation.In the meantime, the stress-strain curve of curved architected TMMs features an initial increasing trend for stress followed by a gradual decline in the slope of stress-strain curves.Then, contact electrification occurs (black circles in the stress-strain curve in Figure 3c) at nearly all the triboelectric pairs for T1, Q2, and H3 designs before strain reaches  yy = −0.25.In comparison, the conventional architected triboelectric materials first experience a narrow elastic domain (  yy = 0 to −0.02) with the opposite triboelectric surfaces approaching each other in the compressive direction.Then, local buckling of cell walls in the conventional architectures triggers a layer-by-layer deformation in tandem with lateral separating motions of the triboelectric pairs at the deformed layer; the triboelectric pairs in the Q0 design hardly contact each other after buckling during the compression of triboelectric materials, resulting in a poor contact-electrified charge density.Consequently, as shown in Figure 3c, the open-circuit voltage of Q0 increases in the elastic domain, but the lateral separating motion triggered by the in-plane buckling of the square cells [42] reverses the increasing trend caused by approaching motion and decreases the generated voltage to negative values.Moreover, the Q2 design realizes a 19.3% improvement of SEA under a compressive strain  yy = −0.25 compared to the Q0 design, as shown in Table S1 (Supporting Information).In summary, resorting to the curved architecture design can lead to the realization of TMMs with combined excellent electric output and high energy absorption capacity.Moreover, ST and SCT are compared with Q2 and Q0 by experimentations, as shown in Section S11 (Supporting Information).The ST and SCT triboelectric exhibit uniform deformation and zero Poisson's ratio during compression until  yy = −0.25.The maximum generated V OC of ST and SCT designs are 0.8 and 9.8 V, respectively, much lower than the generated voltage by Q2 design, i.e., 40 V.The developed FEM method is also validated in Figure 3b,c where the developed numerical model can accurately predict the compressive stress-strain curves and match the trend of the V OC -strain curves found in experiments.The difference between FEM and experimental results in terms of V OC -strain curves is caused by the nonuniform distribution of charges on the triboelectric surfaces and the charge dissipation into the air. [43]n order to investigate the relation between curved architectures and electromechanical performance, a finite element analysis is performed on all eleven TMM designs made by 4 × 4 cells.By tailoring the architectural parameters and adopting FEM, Figure 4a shows how TMMs can occupy a large space in the SEA-stiffness- m triboelectric material selection chart; the 2D sub-charts of this 3D Ashby diagram can be found in Section S7 (Supporting Information).TMM designs with curved architectures can achieve much higher  yy,m (95.1% higher compared to T0 design) but lower stiffness than those triboelectric with conventional architectures.Specifically, the Q2 design exhibits the best resilience of  yy,m = −0.183.Generally, the resilience of angle-changing type TMMs is lower than the distance-changing types.The SEA of angle-changing type and mixed-type TMM designs with curved architectures is comparable to those with conventional architectures.The distance-changing type TMMs can deliver excellent SEA and resilience simultaneously, among which H2 possesses the highest SEA as of 1.27 J g −1 .
The detailed stress-strain curves and V OC -strain curves of all TMM designs from FEM analysis are presented in Section S8 (Supporting Information).The triboelectric material designs with conventional architectures (i.e., T0, Q0, and H0) feature a peak on the stress-strain curves and V OC -strain curves, caused by the local buckling of cell walls followed by the change of the mode of motion of triboelectric pairs.The maximum recoverable compressive strains  yy,m for T0, Q0, and H0 designs are close to the strains of the peak stress, which are much lower than the TMM designs with curved architectures.As output open-circuit voltage increases monotonically with the compressive strain, the resilient curved architectures impart greater electric output for a larger range of strain.Generally, by introducing curved architectures, localized deformation of triangular, quadrilateral, and hexagonal cellular architecture can be fully or partially eliminated, and the TMMs can benefit from a wider range of loading strain for the generation of electricity.The effective Poisson's ratios are measured for all TMM designs using FEM for a range of strains from  yy = 0 to  yy,m , as shown in Figure 4b.It is found that the TMM designs with conventional architectures exhibit positive  eff , while TMM designs with curved segments except H4 exhibit negative Poisson's ratio.Since there is no transverse deformation in ST and SCT designs, their Poisson's ratios are zero.
As compared in Figure 4c, the theoretical predictions for V OC at the maximum recoverable compressive strain  yy,m are consis-tent with the results of detailed finite element modeling.The Q2 design possesses the highest V OC among all the TMM designs with the same relative density.It is worthwhile mentioning that due to the uniform distance-changing and angle-changing deformation of T0, Q0, and H0 design before  yy,m as shown in Figure S8c (Supporting Information), these three designs can be, respectively, considered as angle-changing, distance-changing, and angle-changing types of TEGs in the theoretical analyses to predict their electrical output.Consequently, T0 and H0 share the same form of theoretical equations and geometrical parameters (x 20 , x 20 ,  0 , , and l v0 ) with T1 and H4, respectively, while x 20 is the only difference between Q0 and Q2, as shown in Section S6 (Supporting Information).

Effect of Topological Parameters
To derive generalized conclusions on the relationship between FOM es and alternative architecture designs, the following assumptions have been made to generalize the theoretical model: 1) by varying the shape, curvature, and thickness of the TMM cell walls while keeping the position of nodes connecting the struts unchanged, a group of TMM variants with a wide range of v eff from −1 to 0.5 can be realized and can bear  yy,m from 0 to −0.25; 2) the length of the triboelectric surface l 0 is equal to a for Q0 and Q2 designs, and it is a/2 for the other TMMs when the chamfers of the adjacent cell walls and the volume of strut nodes are neglected.As shown in Figure 4d, theoretical analyses verified by FEM unravel the effects of Poisson's ratio on the generated voltage of TMM designs with T1, Q2, and H3 architectures.For Q2 design, V OC decreases with the increase of v eff from −1 to 0.33 and grows slowly for architectures with higher  eff = 0.33; for T1 and H3 designs, V OC shows a monotonic decreasing trend with Poisson's ratio.An example of achieving a wide range of  eff by changing the architectural parameters is presented in Figure 4e for Q2 design that shows a variation of Poisson's ratio between −0.12 and −0.98; a theoretical model [15] for predicting  eff for Q2 design with arbitrary t 0 and Φ parameters is presented in Section S10 (Supporting Information). [15]For the sake of comparison,  eff for four variants of Q2 designs, based on theoretical modeling and FEM, is presented in Figure 4f.For other TMMs, similar analytical modeling can be developed to investigate the influence of geometric parameters on  eff .
The electrical-structural figure-of-merit for eight TMM groups with curved struts under a uniaxial strain  yy = −0.21are calculated by utilizing the developed theoretical model and compared in Figure 5a where the effects of v eff on the FOM es are also explored.The FOM es values for the majority of architectural groups are significantly enhanced by their auxeticity.The Q2 architecture exhibits the highest FOM es for the whole range of Poisson's ratio, reaching the maximum value of 0.339 for FOM es at the lowest v eff .The T1, H1, and H3 architectures also show FOM es values close to that of Q2 architecture.As T1 has the highest area of triboelectric surfaces per volume (shown in Figure S3b in the Supporting Information), its FOM es is not less than 50% of that of Q2 TMM, as shown in Figure 5a, even though its V OC is only 15.4% of V OC of Q2 TMM, as depicted in Figure 4c.In comparison, the FOM es of conventional plate-like and multilayered TEGs ST and SCT are only 25.0% and 21.6% of the Q2 architecture when  yy = −0.21and v eff = 0; hence, FOM es of Q2 design can surpass those of stacked triboelectric devices by at least 3 times; ST and SCT need to be compressed much greater to be able to offer comparable V OC to the Q2 architecture, as shown in Figure 5b.This figure also reveals that the generated V OC is highly dependent on the average Δx/x 0 of the TEGs forming the triboelectric metamaterials.Considering the variable values of  yy , Figure 5c compares the performance of Q0, Q2, ST, and SCT designs with the same l 0 = 12 mm when v eff = −1to 0.5 and  yy = 0 to −0.25; in this condition the Q2 designs can realize a FOM es as high as 0.635 when  yy = −0.25 and v eff = −1, which is 16.4 times higher than the maximum FOM es that is achievable by Q0 design.Compared to Q0 group, ST, and SCT, and Q2 designs show the highest FOM es throughout a wide range of compressive strain  yy = 0 to −0.25.It is worth mentioning that even though a wide range of compres-sive strain is presented for the Q0 design, this design tends to fail by local buckling at a small compressive strain, as demonstrated by numerical simulation in Figure 5b.Consequently, Q2 architecture is the optimal choice for TMMs considering its remarkable FOM es , high resilience, and wide range of v eff .
Selecting Q2 and T1 architectures as representatives of distance-changing and angle-changing TMMs, the effects of critical geometric parameters on the FOM es can be evaluated by conducting a theoretical analysis.For Q2 design, critical parameters, including the effective distance between the opposite triboelectric surfaces x 0 and the length of cell wall l 0 are considered, while the angle between the opposite triboelectric surfaces  0 and l 0 are considered for the T1 architecture.The analytical results impart design strategies for these two categories of TMMs, as shown in Figure 5d.To realize the maximum FOM es for the Q2 architecture, l 0 should be small that indicates decreasing the unit cell size is beneficial for attaining a higher electrical and structural efficiency.Meanwhile, x 0 /l 0 for Q2 design should be as small as possible.As a result, Q0 with x 0 /l 0 = 1 is anticipated to possess lower FOM es than the Q2 design with x 0 /l 0 = 0.272.For reaching the maximum FOM es in T1 design, l 0 should be small while  0 should be as large as possible.Figure 5d also reveals that variation of  eff affects the maximum values of FOM es but does not affect the abovementioned conclusions.The anisotropy of FOM es of T1 and Q2 TMMs is also investigated, as shown in Figure 5d where the variation of FOM es with the loading direction  is also determined.Both T1 and Q2 architectures exhibit a more isotropic behavior for FOM es when  eff decreases.
To understand the underlying mechanisms leading to the variation of FOM es with Poisson's ratio, the correlation among FOM es , V OC of each TEG, and deformation vectors of each TEG is investigated for various  eff .Figure 6 shows theoretical predictions for the relationships between five parameters (Δx 1 , Δx 2 , Δ, Δx, and V OC ) of TEGs for alternative orientations and  eff .For the Q2 design, the V OC of TEG 1 remains constant when  eff increases, while the V OC of TEG 2 decreases, resulting in a decreasing trend for the overall V OC in Figure 4d.As a distancechanging mode TMM, it is assumed that the distance-related vectors (Δx 1 , Δx 2 ) play critical roles in the electrical output; V OC is also highly dependent on the equivalent displacements Δx.Therefore, the following trending chain is assumed for TEG 2 of Q2 design:  eff ↓ → Δx 2 ↑ → Δx↑ → V OC ↑ and demonstrated in Figure 6; identical trends of  eff , Δx 2 , Δx, and V OC versus various  eff are observed for the associated TEG 1.For an anglechanging mode TMM (for example, T1 design), both TEG 1 and TEG 2 show little variation of V OC for alternative  eff .The decreasing trend of the overall V OC with  eff is highly consistent with the trend of TEG 3 with  = 240 • , the orientation of which is the closest to the loading direction among all three orientations of TEGs in the T1 design.By observing the relationship among the abovementioned parameters, the dominant mechanisms are concluded as follows for the T1 design where Δ↑ → Δx↑is a unique dominant mechanism distinguished from the distance-changing mode TMMs (for example, Q2 design).For mixed-mode TMMs, both the dominating  lowest V OC among all the TEGs that drop the total generated output voltage of the TMMs.These findings indicate that the relationship between the overall V OC and  eff is strongly dependent on the corresponding behavior of TEGs with angle orientation close to the loading direction.Furthermore, for all three modes of TMMs, a higher Δx/x 0 results in a higher V OC , which is consistent with the conclusion from Figure 5b.

Daily-Life Application of TMMs
To demonstrate the advantages of TMMs including the simultaneous high energy absorption and sensing capabilities for detecting and scavenging energy from small deformation, a dailylife application of TMMs in the form of an intelligent skateboard is fabricated out of Q2 architecture, as shown in Figure 7a (schematic graph) and Figure S16 (Supporting Information) (photograph of fabricated machine) and experimentally tested under various skateboarding motions; Q2 design has been selected for fabrication since the design has been demonstrated (Figure 4a) to possess combined excellent mechanical properties (i.e., stiffness, resilience, and SEA) and the maximum electricalstructural figure-of-merit (also the highest power density) among the designs of architected triboelectrics explored in this study.Two groups of TMMs, each containing six triboelectrics of Q2 architecture are connected as presented in Figure 7b and are integrated into the front and rear skateboard trucks separately.The output voltage of the left (TMMs 1-3) and right (TMMs 4-6) TMM subgroups at the front of the skateboard differ from each other, reflecting the fact that the compressive displacements of these subgroups also differ when the skateboard is turned left or right; the rear group of TMMs outputs the summation of voltages of TMMs 7-12, presenting the loading amplitude in the zdirection.A wireless voltmeter Hantek IDSO 1070A is used to remotely transfer the open-circuit voltage outputs to a receiver.The TMMs in the front and rear trucks can independently generate voltage outputs regarding the roll and compression of the skateboard, which can sense human motions, including skating, turning left, and turning right, when their V OC -time curves are combined.As shown in Figure 7c and Video S2 (Supporting Information), when a skateboarder rider pushes on the skateboard to move it forward, the exerted force results in simultaneous deformation of the front and rear TMM groups.Both TMM groups undergo compression and a subsequent rebound from the compression in the z-direction, resulting in a sharp peak and valley of the voltage outputs for the rear group, while the front group presents no voltage fluctuation since the voltage output difference of TMMs 1-3 and 4-6 is zero.When the skateboarder turns left, there is a rotation of the skateboard around the x-axis, and both the front and rear TMM groups undergo a tilt around the xaxis.The difference in compressive deformation between TMMs 1-3 and 4-6 results in a valley followed by a peak on the V OCtime curve.Note that the TMMs 7-12 still generate V OC signals during turning but are not as significant as those from TMMs 7-12, as the rear TMMs experience weaker compression and rebound compared to skating forward.The fabricated intelligent skateboard shows great shock absorption capability in tandem with motion detection.The shock absorption feature of TMMs is evaluated by the maximum accel-eration in the z-direction (a z ) when the skateboard passes a washboard road with a velocity of 0.5 m s −1 .As shown in Figure 7d, the intelligent skateboard can reduce a z by 59.5% compared to a design without the utilization of TMMs.The shock energy is dissipated by the viscous and plastic characteristics of TMMs, as presented in Figure S2 and Table S1 (Supporting Information).As a demonstration of the energy harvesting capability, the intelligent skateboard is loaded by continuously stepping on to first charging a capacitor and then lightening up 20 LEDs.As shown in Figure 7e

Conclusion
In summary, a new triboelectric mechanical metamaterial with horseshoe underlying architectures is presented.By distributing a tribopair on two opposite surfaces within a unit cell, the introduced TMMs harvest electricity from the local-strain-induced mechanical energy.Exploring the local motions of tribopairs integrated in the cellular architectures, three working modes of TMMs (i.e., angle-changing, distance-changing, and mixed mode) are identified.TMM samples are fabricated by utilizing additive manufacturing and film adhesion techniques.FEM models are developed to study the underlying mechanisms associated with the remarkable electromechanical performance of TMMs.Experimental and numerical results unravel the role of curved struts in facilitating contact electrification and resisting nonuniform deformation, as well as realizing a remarkable combination of high resilience, SEA, and auxeticity.Moreover, the developed TMMs exhibit significantly higher V OC and I SC compared to the conventionally architected triboelectric materials and stacked TEGs with flat or curved structures.The Q2 design of TMM shows extremely high V OC and I SC among all the designed TMMs, 53.3 times and 55.1 times higher than those for the Q0 design, respectively.By tailoring the topological design, a wide space for the stiffness, resilience, SEA, and Poisson's ratio of triboelectric metamaterials can be achieved.The distance-changing type TMMs can achieve remarkable SEA and resilience simultaneously.Moreover, the developed TMMs effectively harvest energy under compressive loads exerted along multiple directions.
A theoretical model for the energy harvesting characteristics of TMMs is established to elicit the influence of Poisson's ratio, critical geometric parameters, and loading strains on the electricalstructural figure-of-merit.The theory, for the first time, renders a reliable strategy for analyzing the electric output of TMMs by taking into account alternative working modes of triboelectrics, simplifying the shape of curved struts, and discovering the relationship between the overall energy harvesting straits of the TMMs and the generated voltage/current of constitutive tribopairs that may possess distinctive displacements.Based on the theory, the  The lower negative Poisson's ratio leads to enhanced local deformations and higher V OC of these TEGs, resulting in a higher overall V OC of the TMM.The overall FOM es is affected by the TMM working modes, TEG orientations, and the area of triboelectric surfaces (or the number of TEGs) per volume that are determined by the topology of TMMs.Design strategies for the geometric parameters are proposed for distance-changing and angle-changing TMMs.A daily-life application is demonstrated for utilizing the shock-absorbing and load-bearing capabilities of TMMs to realize a multifunctional intelligent skateboard that converts the wasted mechanical energy into electrical sensing signals associated with the skateboard motion modes and into electricity for lightening 20 LEDs mounted on the board.Nevertheless, the electrical performance of TMMs can be further improved when advanced material modification technologies are introduced into the current architecture design in future studies.The potential technologies include physical, chemical, biological, or hybrid modification of triboelectric surfaces, [44] artificial injection of ions, [45] and surface polarization from ferroelectric materials. [46]The benefits of structural optimization accomplished in this study will be magnified by the material improvements to better contribute to overall electrical performance.In future research, humidity-resistant curved architected TMMs can be developed by combining the current topology and TEG distributing designs and recently reported humidity-resistant design strategies including packaging technique, [47] triboelectric surface morphology modification, [48] or special architectural design of TEGs.This research imparts a framework for developing the next generation of lightweight architected triboelectrics serving as self-powered sensors, [49] selfsensing materials, [50] and multifunctional energy harvesters. [51]

Figure 1 .
Figure 1.Triboelectric mechanical metamaterial design.a) Composition of a TMM and a sectional view of the attached TEGs, b) the role of auxetic behavior in driving the TEGs distributed in the x-and y-directions when the TMM is loaded in the y-direction, and c) out-of-plane views of unit cell designs including four angle-changing type TMMs, two distance-changing type TMMs, two mixed-type TMMs, and three conventional triboelectric materials as baselines.The working principles (also named working modes) are illustrated by the displacement of the tribopairs and the generated electric potential changes at electrodes.The design bases, including triangular, quadrilateral, and hexagonal cells, are presented with gray dashed lines.The vectors for 2D tessellation directions (td 1 and td 2 ) for these unit cells to form metamaterials are shown.d) Fabrication procedure of TMMs and fabricated TMM samples with Q0, Q2, T1, and H3 architectures.

Figure 2 .
Figure 2. Theoretical model for analyzing the electric output of TMMs.a) A cycle for the maximized energy output of TMMs.The yellow area denotes the theoretical upper threshold of the energy output of a TMM, while the blue dashed curves denote the possible CMEO voltage-charge cycles with finite external resistances.The energy output associated with a working mode with any finite external resistances R is lower than that from a CMEO with infinite R. b) The homogenized medium of the TMM under compression and the local coordination of the concerned TEG area.c) The simplified model of angle-changing, distance-changing, and mixed mode TEGs.The red dashed lines denote the simplified planes of the curved triboelectric surfaces.d) Categorization of TEGs in each type of TMMs based on the orientation of TEGs; in the figure, TEGs with the same number yield identical electric output in the theoretical model.e) Schematic graphs for the theoretical models of Q2, SCT, Q0, and ST.The red dashed lines denote the simplified planes identifying the curved triboelectric surfaces.

Figure 3 .
Figure 3. Experimental and FEM simulation results for electromechanical performance of four alternative curved and conventionally architected TMMs.a) Time histories for the generated open-circuit voltages, short-circuit currents, reaction forces, and displacements of TMMs subjected to cyclic and uniaxial compression experimentations.b) Contour of electric potential (FEM simulation) and the deformation modes (Experiment) at a compressive strain −0.25 (scale bar: 10 mm).c) Comparisons of open-circuit voltage/stress-strain curves obtained by FEM and experimentations (Exp.).Black circles refer to the points where inner contacts occur.

Figure 4 .
Figure 4. Numerical and analytical results for the mechanical and electrical performance of TMMs.a) TMM mechanical properties chart (compressions in the x-and y-directions have been considered).b) The variation of effective Poisson's ratio for all introduced TMMs experiencing strains from  yy = 0 to  yy =  yy,m ; circles denote  eff at  yy,m .c) V OC of all TMMs at  yy =  yy,m determined by theoretical analysis and numerical simulation.d) Relationship between V OC and  eff for three representatives of TMM working modes (T1, Q2, and H3) using numerical simulation and theoretical analysis.e) Relationship between  eff and the geometric parameters (Φ and t lig ) of the Q2-based TMM design.f) Comparison between the theoretical and numerical simulation results for  eff of Q2 and its three variants.

Figure 5 .
Figure 5. Critical parameters and their effects on the electrical performance of TMMs.a) Effects of effective Poisson's ratio on FOM es of eight groups of TMMs with curved architectures when  yy = −0.21(FOM es of ST and SCT at  yy = −0.21are also presented) based on the theory of energy harvesting.b) Comparison of V OC and failure modes of Q2, Q0, ST, and SCT between the theoretical and numerical results.c) Effect of effective Poisson's ratio and the maximum recoverable compressive strain on the FOM es of TMMs with Q2 group architecture and the baselines (Q0 group, ST, and SCT) with the same volume.d) Effects of geometric parameters (l 0 , x 0 , and  0 ) and the loading directions on the FOM es of Q2 group and T1 group when  yy = −0.21.The gray areas in the contour plots denote geometric parameters not accessible for TMM design.

Figure 6 .
Figure 6.Theoretical results for the three displacement vectors (Δx 1 , Δx 2 , and ΔΨ), equivalent displacement Δx, and open-circuit voltages V OC for each representative TEGs based on Q2, T1, and H3 topologies versus  eff at a compressive strain of  yy = −0.21(star symbols show the initial values of the abovementioned parameters (x 10 , x 20 , Ψ 0 , x 0 , and V OC0 ) before compression, while gray dashed lines show the zero values of the above parameters).
, with three different capacitances, the voltage across the capacitor increases nonlinearly with the loading time, and the speed of charging decreases gradually until it reaches the voltage threshold of 3.0 V.As shown in Video S3 (Supporting Information), a 1 μF capacitor can be charged to the voltage threshold in 4 min to lighten up 20 LEDs.The damage-tolerant mechanical performance and the stability of electrical output of Q2 TMMs during a long service life are demonstrated by the stable amplitudes of electrical (i.e., open-circuit voltage) and mechanical (i.e., reaction force) responses after conducting an 8 h continuous cyclic loading experiment, as shown in Figure 7f.

Figure 7 .
Figure 7.A daily-life application of the introduced TMMs for developing an intelligent skateboard.a) Schematic graph of the fabricated intelligent skateboard.b) The circuit connecting TMMs to sense the skateboard's motions.c) Open-circuit voltage output of the front and rear groups of TMMs during skating forward, turning left, and turning right experiments.The characteristic curves are shown for different skateboard's motions.d) Comparison of z-acceleration between a conventional skateboard without TMM and an intelligent skateboard with TMM made from Q2 design (the geometry of the washboard road is presented in Figure S15 in the Supporting Information).e) Energy harvesting capacity of the intelligent skateboard: scavenging mechanical energy of stepping on the skateboard to charge a capacitor in a rectifier circuit for lighting up 20 light-emitting diodes (LEDs).Open-circuit voltage versus time curves of the charging process for three different capacitances of the capacitor C 0 is presented.f) Open-circuit voltage and reaction force output of Q2 TMMs in 8 h (i.e., 2400 cycles) continuously cyclic loading tests.

FOM
es of TMMs can be accurately tailored given that the relationship among geometric parameters, Poisson's ratio, and FOM es is quantitatively uncovered.The theoretical analysis reveals how the uniform deformation and auxetic behavior of cellular architecture enhance the electrical output through synchronizing the open-circuit voltage of different TEGs.It is found that the overall open-circuit voltage of TMMs is governed by the deformation mode and auxeticity of TEGs oriented in the loading directions.