Tetra-chiral structure-based flexoelectric metamaterial

Abstract

The invention discloses a flexoelectric metamaterial based on a four-chiral structure. A manufacturing method of the flexoelectric metamaterial comprises the following steps: constructing the four-chiral flexoelectric metamaterial of a curved ligament through the four-chiral structure; according to the four-chiral flexoelectric metamaterial of the curved ligament, constructing a theoretical model of the four-chiral flexoelectric metamaterial of the curved ligament; building a finite element model of the four-chiral flexoelectric metamaterial of the bent ligament of the A * B periodic array by utilizing simulation software; the four-chiral flexoelectric metamaterial of the bent ligament of the A * B periodic array is prepared, and the equivalent piezoelectric coefficient of the four-chiral flexoelectric metamaterial of the bent ligament of the A * B periodic array is measured through a flexoelectric metamaterial experimental device. The equivalent elastic modulus of the four-chiral flexoelectric metamaterial of the bent ligament is low, and under the same external load, the structural deformation of the four-chiral flexoelectric metamaterial is more sufficient, so that the bent ligament of the rotating unit generates larger bending deformation, and then a larger strain gradient is generated, and induced flexoelectric charges are enhanced.

Description

Technical Field

[0001] This invention relates to the field of metamaterial structure design technology, and more specifically, to a flexoelectric metamaterial based on a four-chiral structure. The invention may also be titled as a flexoelectric metamaterial based on a four-chiral structure and its fabrication method. Background Technology

[0002] The flexure electrical effect describes the coupling between strain gradient and polarization intensity in dielectric materials, and because it is not limited by crystal symmetry, it is widely present in any dielectric and semiconductor material. Furthermore, due to the size effect of the strain gradient, the flexure electrical effect plays a crucial role in microelectromechanical systems (MEMS) at the micro- and nano-scale. However, the flexure electrical effect in conventional bulk materials is too weak at the macroscopic scale to be practically applicable.

[0003] Flexoelectric metamaterials, through artificially designed periodic structures, can overcome the limitations of traditional bulk materials and enhance macroscopic flexoelectric response, providing an important approach to improving flexoelectric response. By collecting the flexural charge generated within the metamaterial's internal structure when it is subjected to pressure, flexoelectric metamaterials often exhibit excellent macroscopic equivalent piezoelectric properties, while also possessing advantages such as being unrestricted by crystal structure and resistant to extreme environments such as high frequency, high temperature, low temperature, and radiation. Combining the advantages of metamaterials and the flexoelectric effect, flexoelectric metamaterials hold promise for applications in various mechanoelectric coupling fields, including explosion-proof vibration reduction, sensors, flexible electronics, and aerospace.

[0004] Currently, research on flexoelectric metamaterials is limited, and existing flexoelectric metamaterial structures often struggle to balance excellent flexoelectric properties with structural stability. Pyramid array composite structures and periodically curved sheet multilayer composite structures exhibit relatively weak macroscopic performance, while gourd-shaped structures and quasi-zero stiffness structures based on curved beam designs are prone to torsion and instability under load. Although topology optimization methods have been used to optimize the structural layout of flexoelectric metamaterials, the resulting structures are often too complex for practical application.

[0005] Prior art 1 (application number: 2017103352491, application date: 2017.05.12) discloses a metallic glass metamaterial with a chiral microstructure. Figure 1 This is a schematic diagram of a metallic glass metamaterial with a chiral microstructure of four ligaments, as described in Existing Technology 1; see [link / reference]. Figure 1 As shown, the chiral microstructure is applied to metallic glass material, including multiple cylinders 01 made of metallic glass material and ligaments 02 connecting the cylinders 01; the core of this scheme is "the excellent electro-mechanical integration of chiral structure and metallic glass to obtain excellent mechanical properties". Its design concept and material selection are not compatible with the "mechanical-electric coupling" requirement in the field of flexoelectricity and cannot be applied to the field of flexoelectricity.

[0006] Prior art 2 (application number: 2025103403178, application date: 2025.03.21) discloses a method for fabricating a flexoelectric metamaterial based on an inverse trichiral structure. The method includes establishing a theoretical model of the inverse trichiral flexoelectric metamaterial, describing the deformation and flexoelectric response of the internal ligaments, and theoretically predicting the mechanical and flexoelectric properties of the inverse trichiral structure. The inverse trichiral structure comprises units arranged in an array along the x-axis and y-axis directions, perpendicular to each other. Each unit comprises six unit cells forming a hexagon. Each unit cell includes a solid cylinder and three ligaments tangentially connected to the solid cylinder. The solid cylinder and ligaments are made of the same material. The ligaments include one horizontal ligament and two oblique ligaments. The method verifies the inverse trichiral structure by performing finite element numerical simulation on the U×V array of the inverse trichiral structure. The mechanical properties of the flexoelectric metamaterial model were investigated. A U×V array inverse trichiral structure was fabricated, and the equivalent piezoelectric coefficient of the U×V array inverse trichiral flexoelectric metamaterial was measured using a flexoelectric metamaterial experimental setup. The equivalent piezoelectric coefficient was compared with that obtained from the theoretical model of the inverse trichiral flexoelectric metamaterial to verify the flexoelectric performance of the theoretical model. The inverse trichiral flexoelectric metamaterial exhibits a high equivalent elastic modulus due to its structural design (straight ligament), resulting in disadvantages such as high rigidity and difficulty in bending when applied to the flexoelectric field. Under external loads, the ligament bending deformation is small, making it difficult to generate the strain gradient required for the flexoelectric effect, thus leading to weak induced flexoelectric charge and a significantly low equivalent piezoelectric coefficient (e.g., the equivalent piezoelectric coefficient of the inverse trichiral structure in prior art 2 is only 1.8 pC / N).

[0007] Traditional flexoelectric metamaterials suffer from drawbacks such as high stiffness and limited deformation due to their structural design. Under external loads, the structural deformation is small, making it difficult to generate the strain gradient required for the flexoelectric effect, resulting in weak macroscopic equivalent piezoelectric properties. Therefore, solving these problems has become a pressing technical challenge in this field. Summary of the Invention

[0008] In view of this, the present invention provides a method for fabricating flexoelectric metamaterials based on a four-chiral structure, in order to solve the problems that traditional flexoelectric metamaterials have high stiffness and are not easy to deform, resulting in small structural deformation under external loads and difficulty in generating the strain gradient required for the flexoelectric effect, thus making their macroscopic equivalent piezoelectric properties weak.

[0009] In a first aspect, this application provides a method for fabricating a flexoelectric metamaterial based on a four-chiral structure, comprising:

[0010] A four-chiral flexural electric supermaterial for constructing flexural ligaments is generated through a four-chiral structure. The four-chiral structure comprises rotating units arranged in a periodic array along the horizontal and vertical directions, which are perpendicular to each other. Each rotating unit consists of four unit cells, each including a cylindrical node and four flexural ligaments tangentially connected to the cylindrical node. The flexural ligaments include two horizontal flexural ligaments and two vertical flexural ligaments, which are coplanar and rotate symmetrically distributed along the circumference within the same cross-section of the cylindrical node. The shapes of the horizontal and vertical flexural ligaments are either fan-shaped or semi-circular. When both the horizontal and vertical flexural ligaments are fan-shaped, the four cylindrical nodes in the four unit cells form symmetrical double-ring quadrilaterals with a portion of the horizontal and vertical flexural ligaments, respectively. When both the horizontal and vertical flexural ligaments are semi-circular, the four cylindrical nodes in the four unit cells form an X-shaped structure with a portion of the horizontal and vertical flexural ligaments, respectively.

[0011] Based on the four-chiral flexoelectric metamaterial of flexural ligaments, a theoretical model of the four-chiral flexoelectric metamaterial of flexural ligaments is constructed to describe the deformation and flexoelectric effect of the flexural ligament within the four-chiral flexoelectric metamaterial of flexural ligaments. The mechanical and flexoelectric properties of the four-chiral structure are theoretically predicted; including:

[0012] Treating the cylindrical node as a rigid body, when the four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the cylindrical node rotates around its own axis. Both the horizontal bending ligament and the vertical bending ligament bend along their thickness directions, generating strain gradients and inducing flexural polarization. The mechanical properties are characterized by the equivalent elastic modulus, and the flexural electrical properties are characterized by the equivalent piezoelectric coefficient. Specifically:

[0013] When the horizontal and vertical bending ligaments are fan-shaped, the equivalent elastic modulus and equivalent piezoelectric coefficient are expressed as follows:

[0014] ,

[0015] ,

[0016] When the horizontal and vertical bending ligaments are semi-circular in shape, the equivalent elastic modulus and equivalent piezoelectric coefficient are expressed as follows:

[0017] ,

[0018] ,

[0019] In the formula, The equivalent elastic modulus of the tetrachial flexural electric supermaterial representing the fan-shaped ligament. Indicates the stress on the structure. This represents the strain in a unit cell along the vertical direction. This indicates the thickness of horizontal and vertical flexural ligaments. This indicates the length of horizontal and vertical flexural ligaments. This represents the constant used in calculating arc length. Represents the radius of the cylindrical node; The equivalent elastic modulus of a tetrachiral flexural electric supermaterial representing a semicircular ligament. Indicates the elastic modulus of the substrate. This represents the angle between the diameter of the semicircle and the line connecting the centers of two adjacent nodes;

[0020] The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the fan-shaped ligament. Indicates the lateral flexural conductivity of the substrate. Indicates the elastic modulus of the substrate. This represents the number of unit cells contained in each row or column of a periodic array in a tetrachiral flexural electric supermaterial for flexural ligaments. The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the semicircular ligament;

[0021] A finite element model of a four-chiral flexoelectric metamaterial of a bending ligament in an A×B periodic array was constructed using simulation software. Finite element numerical simulations were performed on this model to analyze the deformation behavior and strain gradient distribution of the bending ligament. A and B are both positive integers greater than 2, where A represents the number of four-chiral flexoelectric metamaterials in the row direction and B represents the number of four-chiral flexoelectric metamaterials in the column direction.

[0022] A four-chiral flexoelectric supermaterial of a bending ligament with an A×B periodic array was prepared. The equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the bending ligament with an A×B periodic array was measured using a flexoelectric supermaterial experimental device. The equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the bending ligament with an A×B periodic array was compared with the equivalent piezoelectric coefficient obtained from the theoretical model of the four-chiral flexoelectric supermaterial to verify the flexoelectric properties of the theoretical model of the four-chiral flexoelectric supermaterial.

[0023] Optionally, the cylindrical node is considered a rigid body. When the four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the cylindrical node rotates about its own axis. Both the horizontal bending ligament along the thickness direction of the horizontal bending ligament and the vertical bending ligament along the thickness direction of the vertical bending ligament undergo bending, generating strain gradients and inducing flexural polarization. Its mechanical properties are characterized by the equivalent elastic modulus, and its flexural electrical properties are characterized by the equivalent piezoelectric coefficient, including:

[0024] When a four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the unknown forces and moments experienced by the horizontal and vertical bending ligaments under the load are analyzed. Based on the unknown forces and moments experienced by the horizontal and vertical bending ligaments under the load, the loads experienced by the horizontal and vertical bending ligaments in the unit cell are obtained. Based on the loads experienced by the horizontal and vertical bending ligaments in the unit cell, the strain energy of the unit cell is obtained.

[0025] When the horizontal and vertical flexural ligaments are fan-shaped, the loads on the horizontal and vertical flexural ligaments in the unit cell are expressed as follows:

[0026] ,

[0027] The strain energy of a single cell is expressed as:

[0028] ,

[0029] When the horizontal and vertical flexural ligaments are semi-circular in shape, the loads on the horizontal and vertical flexural ligaments in the unit cell are expressed as follows:

[0030] ;

[0031] The strain energy of a single cell is expressed as:

[0032] ,

[0033] In the formula, This represents the vertical forces acting on unit cell points A and B during uniaxial compression. This indicates the width of the horizontal and vertical flexural ligaments. This represents the bending moment experienced by unit cell points A and B of a vertically bent ligament under uniaxial compression. This represents the bending moment at unit cell points C and D corresponding to the horizontally bent ligament under uniaxial compression. Indicates the radius of horizontal and vertical flexural ligaments; Indicates a point on the horizontally curved ligament and The angle between the line connecting the x and x' axes. This represents the area of ​​the cross-section of horizontal and vertical flexural ligaments. The moment of inertia represents the cross-section of horizontally and vertically curved ligaments. This represents the angle between the semicircular diameter of a vertically curved ligament and the line connecting the centers of two adjacent cylindrical nodes.

[0034] Optionally, when the horizontal and vertical bending ligaments are fan-shaped, the equivalent elastic modulus analysis of the four-chiral flexure-electric supermaterial based on the fan-shaped ligaments reveals the strain gradient and flexure polarization of the bending ligaments under uniaxial loading. The strain gradient of the bending ligaments under uniaxial loading is expressed as:

[0035] ,

[0036] ,

[0037] The sum of the integrals of the flexural polarization on the horizontally and vertically curved ligaments yields the total flexural charge of the unit cell, which is expressed as:

[0038] ,

[0039] For a four-chiral flexoelectric supermaterial for a fan-shaped ligament composed of an n×n unit cell periodic array, the total flexural charge of the structure is expressed as:

[0040] ,

[0041] When both the horizontal and vertical bending ligaments are semi-circular in shape, the equivalent elastic modulus analysis of the four-chiral flexure-electric supermaterial based on the semi-circular ligaments reveals the strain gradient and flexure polarization of the bending ligament under uniaxial loading. The strain gradient of the bending ligament under uniaxial loading is expressed as:

[0042] ,

[0043] The sum of the integrals of the flexural polarization on the horizontally and vertically curved ligaments yields the total flexural charge of the unit cell, which is expressed as:

[0044] ,

[0045] For a tetrachiral flexoelectric supermaterial for a semicircular ligament composed of an n×n unit cell periodic array, the total flexural charge of the structure is expressed as:

[0046] ,

[0047] In the formula, and These are the transverse strain gradients of vertical and horizontal bending ligaments, respectively. This represents the total flexural charge of a unit cell. Indicates the opponent's score; Represents the total charge of the structure; This represents the total charge of the structure.

[0048] Secondly, this application provides a flexoelectric supermaterial based on a four-chiral structure, which is fabricated according to the above-described method for fabricating a flexoelectric supermaterial based on a four-chiral structure.

[0049] Compared with the prior art, the flexoelectric metamaterial based on a four-chiral structure and its fabrication method provided by the present invention achieve at least the following beneficial effects:

[0050] First, the equivalent elastic modulus of the tetrachiral flexoelectric supermaterial of the flexural ligament is significantly lower than that of the inverse trichiral flexoelectric supermaterial in prior art 2. Due to the lower equivalent elastic modulus, the tetrachiral flexoelectric supermaterial of the flexural ligament undergoes more complete structural deformation under the same external load. This results in greater bending deformation of the horizontal and vertical flexural ligaments of the rotating unit, leading to a larger strain gradient and enhanced induced flexural charge. Consequently, the equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial of the flexural ligament can be increased to 16.87 pC / N, far exceeding the equivalent piezoelectric coefficient of the inverse trichiral structure in prior art 2. This solves the problem that traditional flexoelectric supermaterials suffer from high stiffness and difficulty in deformation, resulting in small structural deformation under external loads and a strain gradient required to generate the flexural effect, thus leading to weak macroscopic equivalent piezoelectric properties. Second, it has high sensitivity to small strain gradients, making it suitable for high-precision micro-force / deformation sensing and biomechanical signal (such as pulse and acoustic vibration) detection. It can also be adapted to flexible / low-frequency scenarios and reduce driving energy consumption. It has good low-frequency response and can cover the range of low-frequency mechanical signals that are difficult for traditional piezoelectric materials to adapt to.

[0051] Of course, any product implementing this invention does not necessarily need to achieve all of the above technical effects simultaneously.

[0052] Other features and advantages of the invention will become clear from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments of the invention and, together with their description, serve to explain the principles of the invention.

[0054] Figure 1 This is a schematic diagram of a metallic glass metamaterial with a chiral microstructure of four ligaments, as described in prior art 1.

[0055] Figure 2 This is a schematic flowchart of the fabrication method of the flexoelectric supermaterial based on a four-chiral structure provided by the present invention;

[0056] Figure 3This is a schematic diagram of the structure of the four-chiral flexure-electric supermaterial for flexural ligaments provided by the present invention, wherein (a) is a schematic diagram of the structure of the four-chiral flexure-electric supermaterial for fan-shaped ligaments, and (b) is a schematic diagram of the structure of the four-chiral flexure-electric supermaterial for semi-circular ligaments.

[0057] Figure 4 The present invention provides a finite element simulation of the bending deformation of a unit cell of a four-chiral flexoelectric supermaterial of a flexural ligament under compression, wherein (a) represents the bending deformation of a unit cell of a four-chiral flexoelectric supermaterial of a fan-shaped ligament under compression; (b) represents the bending deformation of a unit cell of a four-chiral flexoelectric supermaterial of a semi-circular ligament under compression; the red areas in (a) and (b) The blue area represents tensile strain. Indicates compressive strain;

[0058] Figure 5 This is a stress analysis of the four-chiral flexural electric supermaterial for fan-shaped ligaments provided by the present invention. (a1) shows a schematic diagram of the structure of the horizontal and vertical fan-shaped bending ligaments under uniform compressive load. x-cut represents a horizontal cutting line that is parallel to the horizontal direction x and defines the x-direction boundary of the rotation unit. y-cut represents a vertical cutting line that is parallel to the vertical direction y and defines the y-direction boundary of the rotation unit. Multiple horizontal cutting lines x-cut and multiple vertical cutting lines y-cut divide the four-chiral structure into multiple unit cells. (a1) represents the stress on the structure; (a2) represents the force analysis diagram of the unit cell and its corresponding local coordinate system;

[0059] Figure 6 This is a stress analysis of the four-chiral flexural supermaterial for semicircular ligaments provided by the present invention. (b1) shows a schematic diagram of the structure of the horizontal and vertical semicircular flexural ligaments under uniform compressive load; x-cut represents a horizontal cutting line, which is parallel to the horizontal direction x and defines the x-direction boundary of the rotation unit; y-cut represents a vertical cutting line, which is parallel to the vertical direction y and defines the y-direction boundary of the rotation unit; multiple horizontal cutting lines x-cut and multiple vertical cutting lines y-cut divide the four-chiral structure into multiple unit cells; (b1) represents the stress on the structure; (b2) represents the force analysis diagram of the unit cell and its corresponding local coordinate system;

[0060] Figure 7 The following are the finite element analysis results of the four-chiral flexural electric supermaterial of the fan-shaped ligament under vertical compression provided by this invention: (a10) Deformation distribution of the horizontal and vertical bending ligaments of the fan-shaped ligament, where GF is a gray frame representing the undeformed four-chiral structure; (a11) Strain gradient distribution of the horizontal and vertical bending ligaments in the four-chiral flexural electric supermaterial of the fan-shaped ligament. The black arrows indicate the direction of flexural polarization, and the blue coordinate axes represent the local coordinate system defined for each flexed ligament.

[0061] Figure 8 The following are the finite element analysis results of the four-chiral flexural electric supermaterial of the semicircular ligament under vertical y-compression provided by this invention: (b10) Deformation distribution of the horizontal and vertical bending ligaments of the semicircular ligament, where GF is a gray frame representing the undeformed four-chiral structure; (b11) Strain gradient distribution of the horizontal and vertical bending ligaments in the four-chiral flexural electric supermaterial of the semicircular ligament. The black arrows indicate the direction of flexural polarization, and the blue coordinate axes represent the local coordinate system defined for each flexed ligament.

[0062] Figure 9 This is a schematic diagram of the experimental apparatus and electrode configuration for the four-chiral flexural electric supermaterials of flexural ligaments (four-chiral flexural electric supermaterials of fan-shaped ligaments and four-chiral flexural electric supermaterials of semi-circular ligaments) provided by the present invention.

[0063] Figure 10 The equivalent piezoelectric properties characterization results of the four-chiral flexoelectric supermaterial of the flexural ligament provided by the present invention are shown in the charge-force relationship diagrams of the four-chiral flexoelectric supermaterial of the fan-shaped ligament and the four-chiral flexoelectric supermaterial of the semi-circular ligament. The linear slope represents the measured equivalent piezoelectric coefficient.

[0064] Figure 11 The equivalent piezoelectric properties characterization results of the four-chiral flexure-electric supermaterials for flexural ligaments provided by this invention are shown in the graphs. The relationship between the equivalent piezoelectric coefficients of the four-chiral flexure-electric supermaterials for fan-shaped ligaments and the four-chiral flexure-electric supermaterials for semi-circular ligaments and the length of the flexural ligaments is shown in the graphs. The dashed lines represent the theoretical predicted values. Detailed Implementation

[0065] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0066] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0067] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0068] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0069] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0070] Example 1

[0071] Reference Figure 2 and Figure 3 As shown, this embodiment provides a flexural electric hypermaterial based on a four-chiral structure, specifically a four-chiral flexural electric hypermaterial for flexural ligaments, such as a four-chiral flexural electric hypermaterial for fan-shaped ligaments. Figure 3 As shown in (a), and the four-chiral flexure-electric supermaterial of the semicircular ligament [as shown in (a)]. Figure 3 [As shown in (b)]. Introducing the bending ligament 1111 into the four-chiral flexoelectric supermaterial can effectively improve the structural flexibility, thereby enhancing the strain gradient and flexoelectric polarization of the four-chiral flexoelectric supermaterial, and achieving a significant improvement in the equivalent piezoelectric properties of the four-chiral flexoelectric supermaterial.

[0072] Four-chiral flexoelectric metamaterials based on flexural ligaments. First, theoretical models of mechanical-flexoelectric coupling were established for four-chiral flexoelectric metamaterials based on fan-shaped ligaments and semi-circular ligaments, respectively, and the relationship between their equivalent piezoelectric coefficients and geometric parameters was derived. It should be noted that the theoretical model of mechanical-flexoelectric coupling is the core foundation and analytical tool supporting the construction of the theoretical model of four-chiral flexoelectric metamaterials.

[0073] Secondly, refer to Figure 4 As shown, the deformation behavior and strain gradient distribution of the flexural ligaments 1111 [such as (a) fan-shaped flexural ligaments, or (b) semi-circular flexural ligaments] in the tetrachiral structure 1 flexural electric supermaterial were analyzed using the finite element method, verifying the correctness of the theoretical model of the tetrachiral structure flexural electric supermaterial; finally, unpolarized lead zirconate titanate [P b (Zr 1-x Ti x Using O3 and PZT ceramic materials as the matrix, metamaterial samples were prepared using laser micromachining technology, such as a four-chiral flexoelectric metamaterial for a fan-shaped ligament and a four-chiral flexoelectric metamaterial for a semi-circular ligament; (Continue to refer to...) Figure 9As shown, the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament were experimentally verified using a flexoelectric supermaterial experimental device. The experimental results show that the equivalent piezoelectric coefficients of the four-chiral flexoelectric supermaterial samples of the fan-shaped ligament and the semi-circular ligament can reach up to 16.87 pC / N, verifying the effectiveness and feasibility of the flexural ligament reinforcement strategy.

[0074] Reference Figures 2 to 11 As shown, the fabrication method of this flexoelectric supermaterial based on a four-chiral structure includes the following specific steps:

[0075] Step S1: Construct a four-chiral flexural electric supermaterial for flexural ligaments using a four-chiral structure 1. The four-chiral structure 1 includes rotating units 11 arranged in a periodic array along the horizontal direction x and the vertical direction y, with the horizontal direction x and the vertical direction y being perpendicular. Each rotating unit 11 consists of four unit cells 110. Each unit cell 110 includes a cylindrical node 1101 and four flexural ligaments 1111 tangentially connected to the cylindrical node 1101. The flexural ligaments 1111 include two horizontal flexural ligaments 1111a and two vertical flexural ligaments 1111b. The two horizontal flexural ligaments 1111a and the two vertical flexural ligaments 1111b are coplanar and all lie within the same cross-section of the cylindrical node 1101 along a circular arc. The circumferential distribution is rotationally symmetrical; the horizontal bending ligaments 1111a and vertical bending ligaments 1111b are both fan-shaped or semi-circular; when the horizontal bending ligaments 1111a and vertical bending ligaments 1111b are both fan-shaped, the four cylindrical nodes 1101 in the four unit cells 110 respectively form symmetrical double-ring quadrilaterals with a portion of the horizontal bending ligaments 1111a and a portion of the vertical bending ligaments 1111b; when the horizontal bending ligaments 1111a and vertical bending ligaments 1111b are both semi-circular, the four cylindrical nodes 1101 in the four unit cells 110 respectively form X-shaped structures with a portion of the horizontal bending ligaments 1111a and a portion of the vertical bending ligaments 1111b.

[0076] Specifically, in combination Figure 3 and Figure 5 As shown, a four-chiral flexure-electric supermaterial for flexural ligaments is constructed using a four-chiral structure 1. This four-chiral flexure-electric supermaterial for flexural ligaments can also be a four-chiral flexure-electric supermaterial for fan-shaped ligaments [e.g.] Figure 3 As shown in (a), and the four-chiral flexure-electric supermaterial of the semicircular ligament [as shown in (a)]. Figure 3 As shown in (b), the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament are both unpolarized piezoelectric materials. Their chirality comes from the crystal structure itself, and a large strain gradient is generated by the bending deformation of the ligament during structural deformation, which induces strong flexoelectric polarization.

[0077] Figure 3 Figures (a) and (b) illustrate the design pathway for tetrachiral flexoelectric metamaterials for flexural ligaments. Specifically, Figure 3 (a) illustrates the design pathway of a four-chiral flexoelectric metamaterial for fan-shaped ligaments. Figure 3 (b) illustrates the design pathway for a four-chiral flexoelectric metamaterial for a semicircular ligament. Combined with... Figure 3 (a) and (b) Figure 5 (a1) and (a2) Figure 6 As shown in (b1) and (b2), the four-chiral flexoelectric supermaterial of the flexural ligament acts as a rotating unit 11. When the four-chiral flexoelectric supermaterial of the flexural ligament is subjected to uniaxial (e.g., vertical y-direction) compression, the rigid rotation of the cylindrical node 1101 will cause bending deformation of the horizontal flexural ligament 1111a and the vertical flexural ligament 1111b. The strain gradient along the thickness direction of the flexural ligament 1111 (e.g., the transverse strain gradient along the thickness direction of the horizontal flexural ligament 1111a and the vertical flexural ligament 1111b) will induce flexoelectric polarization along the thickness direction of the flexural ligament 1111 due to the flexoelectric effect. If the flexural charges generated in the horizontal flexural ligament 1111a and the vertical flexural ligament 1111b are effectively collected, the four-chiral flexoelectric supermaterial of the flexural ligament can exhibit an equivalent piezoelectric effect under uniaxial compression on a macroscopic scale. Based on this, a design was made... Figure 3 (a) and Figure 5The four-chiral flexure-electric supermaterial of the fan-shaped ligament shown in (a1) and (a2) is constructed by a four-chiral structure 1. The four-chiral structure 1 includes rotating units 11 arranged in a periodic array along the horizontal x-direction and the vertical y-direction. Each rotating unit 11 consists of four unit cells 110. Each unit cell 110 includes a cylindrical node 1101 and four flexural ligaments 1111 tangentially connected to the cylindrical node 1101. The flexural ligaments 1111 include two horizontal flexural ligaments 1111a and two vertical flexural ligaments 1111b. The two horizontal flexural ligaments 1111a and the two vertical flexural ligaments 1111b are coplanar and all are coplanar with the same cylindrical node 1101. The cross-section exhibits rotational symmetry along the circumferential direction, with both horizontally curved ligaments 1111a and two vertically curved ligaments 1111b being fan-shaped. When multiple unit cells 110 form a rotating unit 11, one end of each fan-shaped horizontally curved ligament 1111a and vertically curved ligament 1111b in a unit cell 110 is connected to its own cylindrical node 1101, and the other end is connected to the cylindrical node 1101 of an adjacent unit cell 110, thus forming a rotating unit 11 interconnected with multiple unit cells 110. The four cylindrical nodes 1101 in four adjacent unit cells 110 respectively form approximately symmetrical double-ring quadrilaterals with a portion of the horizontally curved ligaments 1111a and a portion of the vertically curved ligaments 1111b. By combining the structural characteristics and flexoelectric effect of the four-chiral flexoelectric metamaterial with fan-shaped ligaments, this embodiment can achieve a macroscopic equivalent piezoelectric response in any dielectric material, providing a new structural design approach for electromechanical coupling in unpolarized media.

[0078] Optionally, refer to Figure 3 (b) Figure 6 As shown in (b1) and (b2), a four-chiral flexural electric supermaterial with semi-circular ligaments is constructed by a four-chiral structure 1. The two horizontally curved ligaments 1111a and the two vertically curved ligaments 1111b in the four-chiral structure 1 are all semi-circular. When multiple unit cells 110 form a rotating unit 11, one end of the semi-circular horizontally curved ligaments 1111a and vertically curved ligaments 1111b in the unit cell 110 is connected to its own cylindrical node 1101, and the other end is connected to the fixed cylinder of the adjacent unit cell 110, thereby forming a rotating unit 11 interconnected between multiple unit cells 110. The four cylindrical nodes 1101 in four adjacent unit cells 110 respectively form an approximate X-shaped structure with part of the horizontally curved ligaments 1111a and part of the vertically curved ligaments 1111b.

[0079] like Figure 3As shown in (a), the introduction of the fan-shaped bending ligament 1111 can significantly reduce the elastic modulus of the structure, allowing the structure to undergo greater deformation under uniaxial load, thereby enhancing the strain gradient and flexural charge within the bending ligament 1111, and thus significantly improving the equivalent piezoelectric properties of the structure. Figure 4 (a) and (b) show the deformation of the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament under compression in finite element simulations. It can be seen that tensile deformation occurs on both sides of the curved ligaments 1111 (horizontal curved ligament 1111a and vertical curved ligament 1111b). and compression deformation It exhibits obvious bending characteristics.

[0080] Step S2: Based on the four-chiral flexoelectric metamaterial of the flexural ligament, construct a theoretical model of the four-chiral flexoelectric metamaterial of the flexural ligament to describe the deformation and flexoelectric effect of the flexural ligament 1111 inside the four-chiral flexoelectric metamaterial of the flexural ligament, and theoretically predict the mechanical and flexoelectric properties of the four-chiral structure 1; which includes:

[0081] Treating the cylindrical node 1101 as a rigid body, when the four-chiral structure 1 is subjected to a uniform compressive load in a uniaxial direction, the cylindrical node 1101 rotates around its own axis. The horizontal bending ligament 1111a along its thickness direction and the vertical bending ligament 1111b along its thickness direction both bend, generating strain gradients and inducing flexural polarization. Its mechanical properties are characterized by the equivalent elastic modulus, and its flexural electrical properties are characterized by the equivalent piezoelectric coefficient. Specifically:

[0082] When the horizontally curved ligament 1111a and the vertically curved ligament 1111b are fan-shaped, the equivalent elastic modulus and equivalent piezoelectric coefficient are expressed as follows:

[0083] ,

[0084] In the formula, The equivalent elastic modulus of the tetrachial flexural electric supermaterial representing the fan-shaped ligament. Indicates the stress on the structure. This represents the strain of a unit cell along the vertical direction y. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the constant used in calculating arc length. This represents the radius of cylindrical node 1101;

[0085] ,

[0086] In the formula, The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the fan-shaped ligament. Indicates the lateral flexural conductivity of the substrate. Indicates the elastic modulus of the substrate. This represents the number of unit cells contained in each row or column of a periodic array in a four-chiral flexural electric metamaterial representing a flexural ligament. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the constant used in calculating arc length. This represents the radius of cylindrical node 1101;

[0087] When the horizontally curved ligament 1111a and the vertically curved ligament 1111b are semi-circular in shape, the equivalent elastic modulus and equivalent piezoelectric coefficient are expressed as follows:

[0088] ,

[0089] In the formula, The equivalent elastic modulus of a tetrachiral flexural electric supermaterial representing a semicircular ligament. Indicates the elastic modulus of the substrate. This represents the angle between the diameter of the semicircle and the line connecting the centers of two adjacent nodes. This represents the constant used in calculating arc length. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the radius of cylindrical node 1101;

[0090] ,

[0091] In the formula, The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the semicircular ligament. Indicates the lateral flexural conductivity of the substrate. Indicates the elastic modulus of the substrate. This represents the number of unit cells contained in each row or column of a periodic array in a four-chiral flexural electric metamaterial representing a flexural ligament. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the constant used in calculating arc length. This represents the radius of cylindrical node 1101;

[0092] 1. Four-chiral flexural supermaterials for fan-shaped ligaments;

[0093] Figure 3 (a) and Figure 5 Figures (a1) and (a2) illustrate the lattice structure and unit cell stress analysis of the four-chiral flexoelectric supermaterial of the fan-shaped ligaments. The length, thickness, and radius of the cylindrical node 1101 of the curved ligaments 1111 (the horizontal curved ligament 1111a and the vertical curved ligament 1111b) are represented by L, t, and r, respectively. Since both the horizontal and vertical curved ligaments 1111a and 1111b are fan-shaped, the central angle corresponding to their curved edges is π / 3. For simplicity, the cylindrical node 1101 is considered a rigid body, and it is assumed that the deformation of the horizontal and vertical curved ligaments 1111a and 1111b satisfies the small deformation assumption while maintaining periodic symmetry.

[0094] When the four-chiral structure 1 is subjected to a uniform compressive load in the uniaxial direction, the unknown forces and moments experienced by the horizontal bending ligaments 1111a and 1111b under the load are analyzed. Based on these unknown forces and moments, the loads experienced by the horizontal bending ligaments 1111a and 1111b in the unit cell 110 are obtained. Based on these loads, the strain energy of the unit cell is also obtained. Specifically, to obtain the deformation process of the bending ligaments 1111 inside the four-chiral structure 1, it is assumed that the structure is subjected to the following... Figure 5 The vertical direction y is uniformly compressed under load as shown in diagram (a2), and the unknown forces and moments experienced by the horizontal bending ligaments 1111a and 1111b under the load are analyzed. First, since there is no macroscopic force in the horizontal direction x, there is no horizontal force at each cutting point along the horizontal cutting line x-cut. According to the vertical cutting line y-cut, there should be a vertical force at unit cell points A and B to balance the external force. Furthermore, due to the 180° symmetry of the structure, any two opposite cutting points in unit cell 110 should experience the same force and moment. Therefore, there is a pair of equal-sized and opposite vertical forces F and bending moments M at unit cell points A and B. Since there is no macroscopic shearing effect on the structure, there is only one bending moment at unit cell points C and D. There is no vertical force. Therefore, as Figure 5 As shown in a2, according to the force balance relationship, the loads on each horizontal bending ligament 1111a and vertical bending ligament 1111b in unit cell 110 are expressed as follows:

[0095] ,

[0096] In the formula, This represents the vertical forces acting on unit cell points A and B during uniaxial compression. Indicates the stress on the structure. This indicates the width of the horizontal flexor ligament 1111a and the vertical flexor ligament 1111b. This represents the bending moment experienced by unit cell points A and B corresponding to the vertically bent ligament 1111b under uniaxial compression. This represents the bending moment experienced by unit cell points C and D corresponding to the horizontally bent ligament 1111a under uniaxial compression. This represents the radius of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. This represents the radius of cylindrical node 1101; These are the radii of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. To analyze the deformation of the horizontally curved ligament 1111a and the vertically curved ligament 1111b, a local polar coordinate system is defined for each of these ligaments, such as... Figure 5 As shown in (a2). Among them, point... θ is the center of the fan-shaped horizontal flexure ligament 1111a. θ is a point on the horizontal flexure ligament 1111a intersecting the line... The connection, and The angle between the axes, θ, obviously ranges from 0 to... Therefore, neglecting shear strain energy, the strain energy of a unit cell is expressed as:

[0097] ,

[0098] In the formula, This represents the strain energy of a single cell. This indicates a point on the horizontally curved ligament 1111a and... The connection, and The included angle of the axis, Indicates the elastic modulus of the substrate. This represents the area of ​​the cross-section of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This represents the radius of the fan-shaped horizontal flexural ligament 1111a and the vertical flexural ligament 1111b. The moment of inertia represents the cross-section of the horizontally curved ligament 1111a and the vertically curved ligament 1111b; , ,and This refers to the widths of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. Furthermore, due to the mirror symmetry of two adjacent unit cells 110, the rotation angle at any endpoint of unit cell 110 should always remain 0, i.e.:

[0099] ,

[0100] Combining the above formulas (1) to (3), the bending moments at unit cell points A and B corresponding to the vertically bent ligament 1111b under uniaxial compression are... And the bending moments at unit cell points C and D corresponding to the horizontally bent ligament 1111a under uniaxial compression. Represented as:

[0101] ,

[0102] Then, using Karl von Krones' theorem, the total displacement of the unit cell along the vertical y-direction is expressed as: Then the strain of the unit cell along the vertical direction y is expressed as:

[0103] ,

[0104] In the formula, This represents the total displacement of the unit cell along the vertical y-direction. This indicates the lengths of the horizontally curved ligament 1111a and the vertically curved ligament 1111b.

[0105] Obviously, after substituting the obtained values ​​of the unknown bending moments M and M1 into the equation for the strain energy of the unit cell in formula (2), the equivalent elastic modulus of the structure is determined by the ratio of the stress on the structure to the strain of the unit cell, as follows:

[0106]

[0107] In the formula, The equivalent elastic modulus of the tetrachial flexural electric supermaterial representing the fan-shaped ligament. The ε-strain represents the stress on the structure, specifically the strain of a unit cell along the vertical y-direction. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the constant used in calculating arc length. This represents the radius of cylindrical node 1101;

[0108] Next, based on the equivalent elastic modulus of the four-chiral flexoelectric supermaterial with fan-shaped ligaments, the strain gradient and flexural polarization of the horizontally bent ligament 1111a and the vertically bent ligament 1111b under uniaxial loading are analyzed. According to the Euler-Bernoulli beam model (a classical theory in mechanics of materials and elasticity), the transverse strain gradient of the horizontally bent ligament 1111a and the vertically bent ligament 1111b during bending is expressed as:

[0109] ,

[0110] in, and These are the transverse strain gradients of the vertically curved ligament 1111b and the horizontally curved ligament 1111a, respectively. It is important to emphasize that the gradient direction always points radially in polar coordinates, i.e., the thickness direction of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. The total flexural charge of the unit cell is obtained by summing the integrals of the flexural polarization on each curved ligament 1111:

[0111] ,

[0112] Where μ is the transverse flexural electrical coefficient of the substrate. For a four-chiral flexural electrical metamaterial of a fan-shaped ligament composed of an n×n unit cell array, the total flexural charge of this structure is obviously:

[0113] ,

[0114] In the formula, R is entirely represented by L. Under uniaxial compressive load, the total pressure on the structure is expressed as:

[0115] ,

[0116] Therefore, the equivalent piezoelectric coefficient of the four-chiral flexure-electric metamaterial of the fan-shaped ligament can be calculated from the derivative of the total charge of the structure with respect to pressure:

[0117] ,

[0118] In the formula, The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the fan-shaped ligament. Indicates the lateral flexural conductivity of the substrate. Indicates the elastic modulus of the substrate. This represents the number of unit cells contained in each row or column of a periodic array in a four-chiral flexural electric metamaterial representing a flexural ligament. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the constant used in calculating arc length. This represents the radius of cylindrical node 1101.

[0119] 2. Quadrichiral flexural supermaterials for semicircular ligaments;

[0120] Figure 3 (b) Figure 6 Figures (b1) and (b2) show the lattice structure and unit cell stress analysis of the tetrachiral flexoelectric supermaterial of the semicircular ligament. Since the only applied stress is along the vertical direction y, all endpoints except unit cell points A and B are unstressed, while unit cell points A and B bear a pair of perpendicular forces F in opposite directions. Furthermore, due to the 180° rotational symmetry of the tetrachiral structure 1, the forces and moments at the two opposite endpoints are centrally symmetric. Moreover, since the lines of unit cell points A and B coincide with the applied force F, moment balance requires all endpoints to remain without moment. Therefore, as... Figure 6 As shown in (b2), according to the force balance relationship, the loads on each horizontal bending ligament 1111a and vertical bending ligament 1111b in unit cell 110 are expressed as follows:

[0121] ,

[0122] In the formula, This represents the vertical forces acting on unit cell points A and B during uniaxial compression. Indicates the stress on the structure. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This indicates the width of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b.

[0123] Figure 6 (b2) summarizes the forces and torques acting on unit cell 110, where F can be expressed as: F=σL. Figure 6 (b2) also shows the center (point) of the horizontally curved ligament 1111a in a semicircle. A local polar coordinate system is established for each horizontally flexed ligament 1111a and vertically flexed ligament 1111b. (Angle) Points and points defined on the horizontally flexed ligament 1111a The angle between the line connecting the x-axis and the x'-axis ranges from 0 to π. Using these local coordinate systems, the strain energy of the unit cell can be expressed as:

[0124] ,

[0125] In the formula, This represents the strain energy of a single cell. This indicates a point on the horizontally curved ligament 1111a and... The angle between the line connecting the x and x' axes. Indicates the elastic modulus of the substrate. This represents the area of ​​the cross-section of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This represents the radius corresponding to the horizontally curved ligament 1111a and the vertically curved ligament 1111b. , The moment of inertia represents the cross-section of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. The angle between the semicircular diameter of the vertically curved ligament 1111b and the line connecting the centers of the two adjacent cylindrical nodes 1101 is represented.

[0126] According to Karl von Krones' theorem, the equivalent elastic modulus of the four-chiral flexural electric supermaterial of the semicircular ligament is calculated as follows:

[0127] ,

[0128] In the formula, The equivalent elastic modulus of a tetrachiral flexural electric supermaterial representing a semicircular ligament. Indicates the elastic modulus of the substrate. This represents the angle between the diameter of the semicircle and the line connecting the centers of two adjacent nodes. This represents the constant used in calculating arc length. This indicates the thickness of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b. This indicates the lengths of the horizontal flexure ligament 1111a and the vertical flexure ligament 1111b. This represents the radius of cylindrical node 1101;

[0129] Next, the strain gradient and flexural polarization of the semicircular ligaments are analyzed. Based on the Euler-Bernoulli beam model, the transverse strain gradients of the horizontally bent ligament 1111a and the vertically bent ligament 1111b during bending are expressed as follows:

[0130] ,

[0131] in, It consists of the vertical bending ligament 1111b and the transverse strain gradient. Indicates the elastic modulus of the substrate. This represents the bending moment experienced by unit cell points A and B corresponding to the vertically bent ligament 1111b under uniaxial compression. Let represent the moments of inertia of the cross sections of the horizontally curved ligament 1111a and the vertically curved ligament 1111b. It is important to emphasize that the gradient direction always points radially in polar coordinates, i.e., along the thickness direction (y) of the horizontally curved ligament 1111a. Next, the total flexural charge of the unit cell is obtained by summing the integrals of the flexural polarizations on each of the horizontally curved ligament 1111a and the vertically curved ligament 1111b:

[0132] ,

[0133] In the formula, This represents the total flexural charge of a unit cell. Indicates the lateral flexural conductivity of the substrate. Let the integral be the cross-sectional area. For a tetrachiral flexural electric supermaterial consisting of a semicircular ligament composed of an n×n unit cell array, the total flexural charge of this structure is obviously expressed as:

[0134] ,

[0135] In the formula, This represents the magnitude of the total charge on the structure. This represents the number of unit cells contained in each row (or column) of a periodic array in a tetrachiral flexural electric supermaterial of a semicircular ligament.

[0136] Finally, the equivalent piezoelectric coefficient of the tetrachiral flexure-electric hypermaterial of the semicircular ligament can be calculated from the derivative of its total structural charge with respect to the total pressure:

[0137] ,

[0138] In the formula, The equivalent piezoelectric coefficient of the tetrachiral flexure-electric supermaterial of the semicircular ligament is represented.

[0139] It should be noted that the four-chiral flexure-electric metamaterials of the fan-shaped ligament and the semi-circular ligament have identical geometric dimensions in each unit cell 110, which is a fundamental rule for metamaterial composition. To satisfy the assumption that the cylinder is considered a rigid body, the thicknesses of the horizontally curved ligaments 1111a and 1111b are less than the radius of the cylindrical node 1101. To satisfy the assumption that the ligament beam primarily undergoes bending deformation, the ratio between the lengths of the horizontally curved ligaments 1111a and 1111b and the radius of the cylindrical node 1101 is greater than 4. To satisfy the beam bending model, the ratio between the lengths of the horizontally curved ligaments 1111a and 1111b and their thicknesses is greater than 8. The width of the horizontal flexor ligament 1111a and the vertical flexor ligament 1111b can be the same as the thickness of the horizontal flexor ligament 1111a and the vertical flexor ligament 1111b. Optionally, for ease of experimentation, the width of the horizontal flexor ligament 1111a and the vertical flexor ligament 1111b is designed to range from 1 mm to 5 mm.

[0140] Step S3: Construct a finite element model of the four-chiral flexoelectric metamaterial of the bending ligament in an A×B periodic array using simulation software. Perform finite element numerical simulation on the finite element model of the four-chiral flexoelectric metamaterial of the bending ligament in an A×B periodic array to analyze the deformation behavior and strain gradient distribution of the bending ligament. A and B are both positive integers greater than 2. A represents the number of four-chiral flexoelectric metamaterials in the row direction of the bending ligament; B represents the number of four-chiral flexoelectric metamaterials in the column direction of the bending ligament.

[0141] Specifically, continue to refer to Figure 7 (a10) and (a11) Figure 8As shown in (b10) and (b11), finite element models of tetrachiral flexoelectric metamaterials with 4×4 unit cell arrays of fan-shaped ligaments and semi-circular ligaments were constructed using COMSOL Multiphysics. The substrate was unpolarized PZT-5H, with its flexoelectric coefficient and Young's modulus set to 1 μC / m and 70 GPa, respectively. The width h of the horizontally curved ligament 1111a and the vertically curved ligament 1111b was 1 mm. The length L and thickness t of the horizontally curved ligament 1111a and the vertically curved ligament 1111b were set to 12 mm and 1 mm, respectively. The radius r of the cylindrical node 1101 was set to 1.5 mm. The mesh type was tetrahedral elements. The tetrahedral elements on the horizontally curved ligament 1111a and the vertically curved ligament 1111b were appropriately refined to better study the distribution of strain gradients on the horizontally curved ligament 1111a and the vertically curved ligament 1111b. A top pad 2 and a bottom pad 3 are installed at the top and bottom of the structure to simulate real compression conditions. A displacement load of 30 μm is applied to the surface of the top pad 2, while the bottom pad 3 is fixed.

[0142] The aforementioned COMSOL Multiphysics is a multiphysics simulation software. Its core function is to simulate the behavior of different physical fields (such as structural mechanics, electromagnetism, fluid mechanics, heat transfer, etc.) and the coupling effects between multiple physical fields through numerical calculations (finite element method, finite volume method, etc.).

[0143] like Figure 7 (a10), (a11) and Figure 8 As shown in (b10) and (b11), the displacement deformation distribution results of the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament under uniform compression conditions indicate that after the four-chiral structure 1 is compressed, each cylindrical node 1101 undergoes rigid rotation, thereby causing significant bending deformation of the horizontally bent ligament 1111a and the vertically bent ligament 1111b. This feature verifies that the rotation unit 11 designed in this embodiment can effectively realize the transmission mechanism from external compressive load to internal bending deformation. Figure 7 (a10), (a11) and Figure 8 Figures (b10) and (b11) illustrate the strain gradient distribution and induced flexural polarization directions of typical horizontally curved ligaments 1111a and vertically curved ligaments 1111b in each structure. The strain gradient calculation is based on the local coordinate system of the horizontally curved ligaments 1111a and vertically curved ligaments 1111b; therefore, only a few representative horizontally curved ligaments 1111a and vertically curved ligaments 1111b are shown. Their specific locations are [not specified in the original text]. Figure 7 (a10) and Figure 8(b10) is marked with a blue dashed line d and a red dashed line c. Results show: Refer to... Figure 7 As shown in (a10) and (a11), in the four-chiral structure 1 corresponding to the four-chiral flexure-electric supermaterial of the fan-shaped ligament, the strain gradient distribution of the horizontal bending ligament 1111a corresponding to the blue dashed line d is still relatively uniform, but the strain gradient of the vertical bending ligament 1111b corresponding to the red dashed line c is obviously concentrated in the middle of the vertical bending ligament 1111b. This distribution characteristic is similar to... Figure 4 The bending moment distribution pattern caused by the concentration of force points in the unit cell shown in (a) is consistent with that in the figure; refer to Figure 8 As shown in (b10) and (b11), in the four-chiral structure 1 corresponding to the four-chiral flexure-electric supermaterial of the semicircular ligament, the strain gradient of the vertically curved ligament 1111b corresponding to the red dashed line c is significantly higher than that of the horizontally curved ligament 1111a corresponding to the blue dashed line d, and a slight concentration trend appears at the midpoint of the semicircle. This distribution characteristic is consistent with... Figure 4 The bending moment distribution caused by the concentration of stress points in the unit cell shown in Figure (b) is consistent with the trend. In summary, the finite element simulation results show that the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament proposed in this invention both exhibit bending deformation as the dominant deformation mode, and their strain gradient distribution is highly consistent with the theoretical model prediction results, thus verifying the accuracy and effectiveness of the theoretical analysis method in this embodiment.

[0144] Step S4: Prepare a four-chiral flexoelectric metamaterial of a bending ligament with an A×B periodic array. Measure the equivalent piezoelectric coefficient of the four-chiral flexoelectric metamaterial of the bending ligament with an A×B periodic array using a flexoelectric metamaterial experimental device. Compare the equivalent piezoelectric coefficient of the four-chiral flexoelectric metamaterial of the bending ligament with the equivalent piezoelectric coefficient obtained from the theoretical model of the four-chiral structure flexoelectric metamaterial to verify the flexoelectric properties of the theoretical model of the four-chiral structure flexoelectric metamaterial.

[0145] Specifically, to evaluate the actual performance of the designed flexoelectric metamaterials, laser cutting technology was used to prepare metamaterial samples, such as a four-chiral flexoelectric metamaterial for a fan-shaped ligament and a four-chiral flexoelectric metamaterial for a semi-circular ligament, using unpolarized PZT ceramic with a flexoelectric coefficient of 0.21 μC / m. For the four-chiral flexoelectric metamaterials for the fan-shaped ligament and the semi-circular ligament, samples with three different lengths (i.e., L = 10 mm, 12 mm, and 14 mm) of horizontally bent ligament 1111a and vertically bent ligament 1111b were prepared; the radius r of the cylindrical node 1101 and the thickness t of the horizontally bent ligament 1111a and vertically bent ligament 1111b were set to 1.5 mm and 1 mm, respectively. All metamaterial samples consisted of a 4×4 unit array.

[0146] Figure 9 Experimental setups and electrode configurations were demonstrated in four-chiral flexoelectric supermaterials for fan-shaped ligaments and semi-circular ligaments. Figure 9 In the diagram, FS represents the fixed end, used to fix the four-chiral flexure-electroelectric metamaterials of the fan-shaped ligament and the semi-circular ligament during testing. FE represents the free end, the loading end used to apply displacement loads to the metamaterial samples. CP represents the connection point. DAQ represents the data collector, used to collect the voltage signal from force sensor 6 and convert it into a digital signal for computer processing and analysis. The piezoelectric actuator 4 (model PhysikInstrumente, P-841) is driven by function generator 5 (Tektronix, model AFG31000) to apply oscillatory loads to the four-chiral flexure-electroelectric metamaterials of the fan-shaped and semi-circular ligaments. The forces acting on the four-chiral flexure-electroelectric metamaterials of the fan-shaped and semi-circular ligaments are monitored by force sensor 6 (such as a Spartau SBT641 5kg range pressure sensor) mounted above the piezoelectric actuator 4. A low-noise preamplifier 7 (Stanford Research Systems, model SR570) was used to measure the output current. Real-time current and force waveforms were measured using an oscilloscope 8 (Tektronix, model TBS2000B). Both sides of all horizontal bending ligaments 1111a and vertical bending ligaments 1111b were coated with silver paste to form electrodes. The electrodes on the tensioned surfaces were defined as positive electrodes (e.g., ...). Figure 9 (Marked in red in the middle), the electrode on the pressure surface is defined as the negative electrode (marked in blue). To prevent the flexural charges from canceling each other out, the positive and negative electrodes on each horizontal flexural ligament 1111a and vertical flexural ligament 1111b are insulated from each other. To effectively collect the flexural charges generated in the horizontal flexural ligaments 1111a and vertical flexural ligaments 1111b, all positive electrodes are interconnected using silver paste on adjacent cylindrical nodes 1101, such as... Figure 9 The connection point CP is shown in the diagram. Conversely, all negative electrodes are connected via cylindrical nodes 1101 on the back side. For the tetrachiral flexure-electro-hypermaterial of the semicircular ligament, an additional connection point CP is added to connect the positive (or negative) electrodes on two adjacent semicircular horizontal flexure ligaments 1111a and vertical flexure ligaments 1111b. Two connection points CP are selected on the front and back sides of the tetrachiral flexure-electro-hypermaterial of the semicircular ligament, and then connected to an electrical measurement system (which may be a preamplifier 7 and an oscilloscope 8) using two copper wires (shown in red and blue).

[0147] Therefore, the equivalent piezoelectric coefficients of the four-chiral flexoelectric supermaterials of the fan-shaped ligament and the semi-circular ligament, as measured experimentally, can be calculated using the following formula:

[0148] ,

[0149] In the formula, The experimentally measured equivalent piezoelectric coefficient represents the four-chiral flexoelectric metamaterial of a bending ligament in an A×B periodic array. This represents the amplitude of the total charge on the structure during measurement using the flexoelectric metamaterial experimental setup. The amplitude of the compressive force applied to the flexoelectric metamaterial experimental device; denoted as , where is the amplitude of the total structural current, and f is the loading frequency of the load.

[0150] See Figure 10 As shown, blue circles represent the four-chiral flexoelectric supermaterial of the fan-shaped ligament, green triangles represent the four-chiral flexoelectric supermaterial of the semi-circular ligament, and Semi represents the fitted line obtained by linearly fitting the experimental data points in the four-chiral flexoelectric supermaterial of the fan-shaped ligament, with its slope corresponding to the equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the fan-shaped ligament; Arc represents the fitted line obtained by linearly fitting the experimental data points in the four-chiral flexoelectric supermaterial of the semi-circular ligament, with its slope corresponding to the equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the semi-circular ligament; see also Figure 11 As shown, blue circles represent the four-chiral flexoelectric supermaterial of the fan-shaped ligament, and green triangles represent the four-chiral flexoelectric supermaterial of the semi-circular ligament. Each blue circle and green triangle corresponds to an error bar, which represents the standard deviation of multiple parallel test data, used to characterize the dispersion of the data. Semi represents the theoretically calculated value of the equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the fan-shaped ligament; Arc represents the theoretically calculated value of the equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the semi-circular ligament.

[0151] Figure 10 The equivalent piezoelectric coefficient of the four-chiral flexure-electric supermaterial of the fan-shaped ligament is 8.32 pC / N, and the equivalent piezoelectric coefficient of the four-chiral flexure-electric supermaterial of the semicircular ligament is 16.87 pC / N, when the length L = 14 mm of the horizontal flexure 1111a and the vertical flexure 1111b is 14 mm.

[0152] Clearly, due to the reduction in effective modulus, the force experienced by the tetrachiral flexure-electric supermaterial of the flexure ligament is significantly lower than that of the tetrachiral flexure-electric supermaterial of the straight ligament under the same displacement. Under the same load, the flexure ligament 1111 corresponding to the tetrachiral flexure-electric supermaterial of the flexure ligament undergoes greater deformation, thereby generating a stronger strain gradient and flexural charge within the flexure ligament 1111, and thus significantly improving the overall piezoelectric properties. Figure 11The equivalent piezoelectric coefficients of all metamaterials under different lengths of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b were further demonstrated. The equivalent piezoelectric coefficients gradually increase with the increase of the length of the horizontally flexed ligament 1111a and the vertically flexed ligament 1111b, which is in high agreement with the theoretical predictions. The experiments verified the accuracy of the theoretical model of the four-chiral flexoelectric metamaterial and confirmed the effectiveness of the strategy of introducing the flexoelectric ligament 1111 to enhance the performance of the flexoelectric metamaterial.

[0153] This embodiment uses a four-chiral flexural electric supermaterial for a fan-shaped ligament as an example. The process of substituting specific data into formulas (1) to (11) for calculation is as follows:

[0154] Combination Figures 2 to 11 As shown, the basic structural parameters of the metamaterial proposed in this embodiment are first set: the length L of the horizontal bending ligament 1111a and the vertical bending ligament 1111b is 12 mm, the thickness t of the horizontal bending ligament 1111a and the vertical bending ligament 1111b is 1 mm, the radius r of the cylindrical node 1101 is 1.5 mm, and the width of the horizontal bending ligament 1111a and the vertical bending ligament 1111b is... =1 mm. The central angles of the corresponding circles of the arc-shaped horizontal curved ligament 1111a and the vertical curved ligament 1111b are π / 3. Therefore, the radius of the circle corresponding to the arc-shaped curved ligament 1111 is... =6.93 mm, the basic parameters of the substrate are elastic modulus E=70 GPa, flexural coefficient μ=0.21 μC / m. The number of unit cells in the four-chiral structure n=4. Assuming that the four-chiral structure 1 is subjected to a uniform compressive load in the uniaxial (vertical direction y) direction, the stress σ=25 kPa, according to formula (1) and formula (4), the external forces on the unit cells in the four-chiral structure can be calculated as F=0.3 N, M=0.924 mN•m, M1=0.565 mN•m.

[0155] According to formula (2), the strain energy of the unit cell is calculated to be U=0.952 μJ. Combining formulas (5) and (6), the equivalent elastic modulus of the four-chiral flexoelectric supermaterial of the fan-shaped ligament is calculated. =48.76 MPa.

[0156] Next, using formula (7), the strain gradient of the flexural ligament 1111 during bending can be calculated. and The values ​​are 0.161 and 0.098, respectively. The total polarization of the unit cell can then be calculated using formulas (8) and (9):

[0157] =0.599 pC, =9.592 pC. The total pressure on the structure is calculated according to formula (10). =1.2N. Then, using formula (11), the equivalent piezoelectric coefficient of the four-chiral flexure-electric supermaterial of the fan-shaped ligament is calculated to be =5.73pC / N.

[0158] Similarly, using formulas (12) to (18), the equivalent elastic modulus and equivalent piezoelectric coefficient of the four-chiral flexoelectric metamaterial of the semicircular ligament are calculated. =36.4 MPa =14.88 pC / N.

[0159] It should be emphasized that, based on existing technology 1 and combined with existing technology 2, those skilled in the art cannot obtain a four-chiral flexural electric supermaterial for flexural ligaments, as detailed below:

[0160] Prior art 1 discloses a metallic glass metamaterial with a chiral microstructure, but the chiral microstructure is applied to metallic glass materials and cannot be applied to the field of flexoelectricity, and each ligament is a straight ligament; prior art 2 discloses a method for fabricating a flexoelectric metamaterial based on an inverse trichiral structure, in which one horizontal ligament and two oblique ligaments are straight ligaments. Even if prior art 1 is combined with prior art 2, those skilled in the art cannot obtain the four-chiral structure flexoelectric metamaterial of the bending ligaments proposed in this embodiment, nor can they solve the above-mentioned technical problems: because the structural design of traditional flexoelectric metamaterials has problems such as high stiffness and difficulty in deformation, the structural deformation is small under external load, making it difficult to generate the strain gradient required for the flexoelectric effect, resulting in weak equivalent piezoelectric properties under macroscopic conditions.

[0161] Compared with the prior art, the fabrication method of flexoelectric metamaterial based on a four-chiral structure provided in this embodiment achieves at least the following beneficial effects:

[0162] First, the equivalent elastic modulus of the tetrachiral flexoelectric supermaterial of the flexural ligament is significantly lower than that of the inverse trichiral flexoelectric supermaterial in prior art 2. Due to the lower equivalent elastic modulus of the tetrachiral flexoelectric supermaterial of the flexural ligament, its structural deformation is more complete under the same external load, resulting in greater bending deformation of the horizontal flexural ligament 1111a and the vertical flexural ligament 1111b of the rotating unit 11. This leads to a larger strain gradient, enhancing the induced flexural charge. Consequently, the equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial of the flexural ligament can be increased to 16.87 pC / N, far exceeding the equivalent piezoelectric coefficient of the inverse trichiral structure in prior art 2. This solves the problem that traditional flexoelectric supermaterials suffer from high stiffness and difficulty in deformation, resulting in small structural deformation under external loads and a strain gradient required to generate the flexural effect, thus leading to weak macroscopic equivalent piezoelectric properties. Second, it has high sensitivity to small strain gradients, making it suitable for high-precision micro-force / deformation sensing and biomechanical signal (such as pulse and acoustic vibration) detection. It can also be adapted to flexible / low-frequency scenarios and reduce driving energy consumption. It has good low-frequency response and can cover the range of low-frequency mechanical signals that are difficult for traditional piezoelectric materials to adapt to.

[0163] Example 2

[0164] This embodiment provides a flexural electric supermaterial based on a four-chiral structure, which is prepared using the fabrication method described in Embodiment 1. Its structure is completely consistent with that of the four-chiral flexural electric supermaterial of the flexural ligament. Correspondingly, the technical effects achieved are also the same as those in Embodiment 1. This embodiment will not elaborate on its structure and technical effects.

[0165] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of the invention. Those skilled in the art should understand that modifications can be made to the above embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.

Claims

1. A method for fabricating a flexoelectric metamaterial based on a four-chiral structure, characterized in that, include: A four-chiral flexural electric supermaterial for constructing flexural ligaments is described. The four-chiral structure comprises rotating units arranged in a periodic array along the horizontal and vertical directions, perpendicular to each other. Each rotating unit consists of four unit cells, each including a cylindrical node and four flexural ligaments tangentially connected to the cylindrical node. The flexural ligaments include two horizontal flexural ligaments and two vertical flexural ligaments, all of which are coplanar and aligned with the same cross section of the cylindrical node. The ligaments are distributed with rotational symmetry along the circumference in the plane; the horizontal and vertical ligaments are both fan-shaped or semi-circular; when the horizontal and vertical ligaments are both fan-shaped, the four cylindrical nodes in the four unit cells form symmetrical double-ring quadrilaterals with a portion of the horizontal and vertical ligaments respectively; when the horizontal and vertical ligaments are both semi-circular, the four cylindrical nodes in the four unit cells form X-shaped structures with a portion of the horizontal and vertical ligaments respectively. Based on the aforementioned tetrachiral flexoelectric metamaterial of flexural ligaments, a theoretical model of the tetrachiral flexoelectric metamaterial of flexural ligaments is constructed to describe the deformation and flexoelectric effect of the flexural ligament inside the tetrachiral flexoelectric metamaterial of flexural ligaments, and to theoretically predict the mechanical properties and flexoelectric properties of the tetrachiral structure. It includes: Treating the cylindrical node as a rigid body, when the four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the cylindrical node rotates around its own axis. The horizontal bending ligament bends along its thickness direction, and the vertical bending ligament bends along its thickness direction, generating strain gradients and inducing flexural polarization. Its mechanical properties are characterized by the equivalent elastic modulus, and its flexural electrical properties are characterized by the equivalent piezoelectric coefficient. Specifically: When the horizontally curved ligament and the vertically curved ligament are fan-shaped, the equivalent elastic modulus and the equivalent piezoelectric coefficient are respectively expressed as: When the horizontally curved ligament and the vertically curved ligament are semi-circular in shape, the equivalent elastic modulus and the equivalent piezoelectric coefficient are expressed as follows: In the formula, E Arc σ represents the equivalent elastic modulus of the four-chiral flexural supermaterial of the fan-shaped ligament, σ represents the stress on the structure, ε represents the strain of the unit cell in the vertical direction, t represents the thickness of the horizontal and vertical flexural ligaments, L represents the length of the horizontal and vertical flexural ligaments, π represents the constant used in calculating the arc length, and r represents the radius of the cylindrical node. The equivalent elastic modulus of the tetrachiral flexural supermaterial of the semicircular ligament is represented by E, the elastic modulus of the substrate is represented by α, and the angle between the diameter of the semicircular arc and the line connecting the centers of two adjacent nodes is represented by α. denoted by , μ represents the equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the fan-shaped ligament, E represents the elastic modulus of the substrate, and n represents the number of unit cells contained in each row or column of the periodic array in the four-chiral flexoelectric supermaterial of the flexural ligament. The equivalent piezoelectric coefficient of the tetrachiral flexoelectric supermaterial representing the semicircular ligament; A finite element model of a four-chiral flexoelectric metamaterial of a bending ligament in an A×B periodic array was constructed using simulation software. Finite element numerical simulations were performed on this model to analyze the deformation behavior and strain gradient distribution of the bending ligament. A and B are both positive integers greater than 2, where A represents the number of four-chiral flexoelectric metamaterials in the row direction and B represents the number of four-chiral flexoelectric metamaterials in the column direction. A four-chiral flexoelectric supermaterial of a bending ligament with an A×B periodic array was prepared. The equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the bending ligament with an A×B periodic array was measured using a flexoelectric supermaterial experimental device. The equivalent piezoelectric coefficient of the four-chiral flexoelectric supermaterial of the bending ligament with an A×B periodic array was compared with the equivalent piezoelectric coefficient obtained from the theoretical model of the four-chiral flexoelectric supermaterial to verify the flexoelectric properties of the theoretical model of the four-chiral flexoelectric supermaterial.

2. The method for fabricating a flexoelectric metamaterial based on a four-chiral structure according to claim 1, characterized in that, The cylindrical node is considered a rigid body. When the four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the cylindrical node rotates about its own axis. Both the horizontal bending ligament and the vertical bending ligament bend along their thickness directions, generating strain gradients and inducing flexural polarization. Its mechanical properties are characterized by the equivalent elastic modulus, and its flexural electrical properties are characterized by the equivalent piezoelectric coefficient, including: When the four-chiral structure is subjected to a uniform compressive load in a uniaxial direction, the unknown forces and moments experienced by the horizontal and vertical bending ligaments under the load are analyzed. Based on the unknown forces and moments experienced by the horizontal and vertical bending ligaments under the load, the loads experienced by the horizontal and vertical bending ligaments in the unit cell are obtained. Based on the loads experienced by the horizontal and vertical bending ligaments in the unit cell, the strain energy of the unit cell is obtained. When the horizontal and vertical bending ligaments are fan-shaped, the loads on the horizontal and vertical bending ligaments in the unit cell are expressed as follows: The strain energy of the unit cell is expressed as: When the horizontal and vertical flexural ligaments are semi-circular in shape, the loads on the horizontal and vertical flexural ligaments in the unit cell are expressed as follows: F = σLh; The strain energy of the unit cell is expressed as: In the formula, F represents the vertical force on unit cell points A and B under uniaxial compression, h represents the width of the horizontal and vertical bending ligaments, M represents the bending moment on unit cell points A and B corresponding to the vertical bending ligament under uniaxial compression, M1 represents the bending moment on unit cell points C and D corresponding to the horizontal bending ligament under uniaxial compression, R represents the radius of the horizontal and vertical bending ligaments, θ represents the angle between the line connecting a point on the horizontal bending ligament and O and the x' axis, A represents the area of ​​the cross-section of the horizontal and vertical bending ligaments, I represents the moment of inertia of the cross-section of the horizontal and vertical bending ligaments, and α represents the angle between the semicircular diameter of the semicircular vertical bending ligament and the line connecting the centers of two adjacent cylindrical nodes.

3. The method for fabricating a flexoelectric metamaterial based on a four-chiral structure according to claim 2, characterized in that, The expression for the strain of the unit cell along the vertical direction is: In the formula, Δu represents the total displacement of the unit cell along the vertical direction.

4. The method for fabricating a flexoelectric metamaterial based on a four-chiral structure according to claim 1, characterized in that, When the horizontal and vertical bending ligaments are fan-shaped, the strain gradient and flexural polarization of the bending ligaments under uniaxial load are analyzed based on the equivalent elastic modulus of the four-chiral flexure-electric supermaterial of the fan-shaped ligaments. The strain gradient of the bending ligaments under uniaxial load is expressed as follows: The sum of the integrals of the flexural polarization on the horizontally curved ligament and the vertically curved ligament yields the total flexural charge of the unit cell, which is expressed as: For a four-chiral flexoelectric supermaterial for a fan-shaped ligament composed of an n×n unit cell periodic array, the total flexural charge of the structure is expressed as: When both the horizontal and vertical bending ligaments are semi-circular in shape, the strain gradient and flexural polarization of the bending ligament under uniaxial load are analyzed based on the equivalent elastic modulus of the four-chiral flexure-electric supermaterial of the semi-circular ligament. The strain gradient of the bending ligament under uniaxial load is expressed as follows: The sum of the integrals of the flexural polarization on the horizontally curved ligament and the vertically curved ligament yields the total flexural charge of the unit cell, which is expressed as: For a tetrachiral flexoelectric supermaterial for a semicircular ligament composed of an n×n unit cell periodic array, the total flexural charge of the structure is expressed as: In the formula, and These represent the transverse strain gradients of the vertical and horizontal bending ligaments, respectively; Q represents the total flexural charge of the unit cell, and dS represents the surface integral; Q s Q represents the total charge of the structure; s This represents the total charge of the structure.

5. The method for fabricating a flexoelectric metamaterial based on a four-chiral structure according to claim 1, characterized in that, The experimentally measured equivalent piezoelectric coefficient of the four-chiral flexoelectric metamaterial of the A×B periodic array of bending ligaments is expressed as: In the formula, Q represents the experimentally measured equivalent piezoelectric coefficient of a four-chiral flexoelectric metamaterial representing a periodic array of A×B ligaments. s F represents the amplitude of the total charge on the structure during measurement at the flexoelectric metamaterial experimental setup. s The amplitude of the compressive force applied to the flexoelectric metamaterial experimental device.

6. The method for fabricating a flexoelectric metamaterial based on a four-chiral structure according to claim 5, characterized in that, The amplitude of the total charge on the structure during measurement using the aforementioned flexoelectric metamaterial experimental device is expressed as follows: In the formula, I s denoted as , where is the amplitude of the total structural current, and f is the loading frequency of the load.

7. A flexoelectric supermaterial based on a four-chiral structure, characterized in that, It is manufactured using the method for fabricating flexoelectric supermaterials based on a four-chiral structure according to any one of claims 1 to 6.

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