Anti-tri-chiral structure-based flexoelectric metamaterial

Abstract

The invention discloses a flexoelectric metamaterial based on an anti-tri-chiral structure, and the method comprises the steps: building an anti-tri-chiral structure flexoelectric metamaterial theoretical model, describing the deformation and flexoelectric response of an internal ligament of the anti-tri-chiral structure flexoelectric metamaterial, and predicting the mechanical properties and flexoelectric properties of the anti-tri-chiral structure theoretically; finite element numerical simulation is carried out on the inverted tri-chiral structure of the U * V array, and the mechanical property of the flexoelectric metamaterial model of the inverted tri-chiral structure is verified; preparing an anti-tri-chiral structure of a U * V array, measuring an equivalent piezoelectric coefficient of the flexoelectric metamaterial of the anti-tri-chiral structure of the U * V array through a flexoelectric metamaterial experimental device, and comparing the equivalent piezoelectric coefficient with an equivalent piezoelectric coefficient obtained by a theoretical model of the flexoelectric metamaterial of the anti-tri-chiral structure; and the flexoelectric performance of the theoretical model of the flexoelectric metamaterial with the anti-tri-chiral structure is verified. The invention provides a new thought for design and experimental characterization of the flexoelectric metamaterial.

Description

Technical Field

[0001] The present invention relates to the technical field of metamaterial structure design, and more specifically, to a flexoelectric metamaterial based on an anti-trigonal chiral structure. Background Art

[0002] The flexoelectric effect is a force-electric coupling effect that describes the interaction between the strain gradient and the electrode polarization intensity in dielectric materials, and can be expressed by the following formula (1):

[0003]

[0004] where P i is the induced electrode polarization, μ ijkl is the flexoelectric coefficient, ε kl is the applied strain, x j is the position coordinate. The main advantage of the flexoelectric effect is that it widely exists in any dielectric and semiconductor materials without being restricted by crystal symmetry. At the same time, the flexoelectric effect is not affected by ferroelectric phase transitions, and can better resist extreme environments such as high frequency, low temperature, and radiation, so it is widely used in fields such as semiconductors, memories, microelectromechanical systems (MEMS), and chemical catalysis, showing great potential in multiple interdisciplinary fields.

[0005] At present, the theoretical system of flexoelectric metamaterials is in the initial stage of development, and there is still relatively little related structural design work. Cross first designed a piezoelectric composite material composed of multiple pyramid-shaped blocks with variable cross-sections based on barium strontium titanate ceramics with ultra-high dielectric constants, achieving piezoelectric properties comparable to those of commonly used lead-containing piezoelectric ceramics (PZT); subsequently, Cross continued to design a periodic curved thin-film multilayer composite structure based on beam bending deformation, and obtained an equivalent piezoelectric coefficient of 4300 pC / N in the resonance mode through the large strain gradient generated transversely, exceeding that of common piezoelectric single crystals. However, its design is still relatively simple, mainly manifested as models such as variable cross-section beams and variable cross-section columns, lacking mechanical design and being difficult to be called a metamaterial structure. Arias et al. proposed a type of flexoelectric metamaterial with a low area fraction and dominated by bending deformation through precise simulation and geometric topology optimization of flexoelectricity. As the area fraction of the structure decreases, its apparent piezoelectricity increases, and the equivalent piezoelectric performance of the optimized structure is comparable to that of the currently best-performing piezoelectric ceramics, but there is still no relevant experimental verification. Recently, Xu Minglong et al. from Xi'an Jiaotong University proposed a flexoelectric displacement sensor based on a quasi-zero stiffness beam. The main advantage of this flexoelectric device based on a metamaterial structure is that within the quasi-zero stiffness range, the charge output has a significant linear relationship with the structural deformation. However, unstable mechanical properties and easy instability are its main hidden dangers.

[0006] The prior art 1 (application number 2021116029245, application date December 24, 2021) discloses a thermally expansible controllable electromagnetic metamaterial based on continuous fiber 3D printing and its preparation process, and specifically discloses an arrayed electromagnetic metamaterial unit. The structural cell of the electromagnetic metamaterial unit includes a node circle and bimaterial rods connected to the outside thereof. The bimaterial rods are rotationally symmetric about the center of the node circle, the bimaterial rods are tangent to the node circle, and the side close to the node circle is fused with the node circle, and the materials are the same; the number of bimaterial rods is 3, 4 or 6; for the anti-chiral structure, the number of bimaterial rods is 3 or 4, and the electromagnetic metamaterial units formed are the anti-chiral three-tangent rod configuration and the anti-chiral four-tangent rod configuration respectively. However, the flexoelectric effect of this electromagnetic metamaterial is not described in this patent. It focuses on obtaining stable electromagnetic properties at extreme temperatures and achieving controllable thermal expansion, which has nothing to do with the flexoelectric effect to be studied in the present invention. In addition, most of the prior art research on the anti-chiral structure stays at the mechanical properties, and no relevant research on the anti-chiral structure as a flexoelectric metamaterial has been proposed.

[0007] In summary, the systematic research work on flexoelectric metamaterials is currently lacking. Most of it stays at the theoretical assumption level, and there are problems such as unstable mechanical properties. Therefore, it is urgent to design and characterize a flexoelectric metamaterial with stable mechanical properties. Summary of the Invention

[0008] In view of this, the present invention provides a flexoelectric metamaterial based on an anti-trigonal chiral structure. The invention name of the present invention can also be a flexoelectric metamaterial based on an anti-trigonal chiral structure and its manufacturing method, so as to provide a flexoelectric metamaterial with stable mechanical properties.

[0009] On the one hand, the present invention provides a manufacturing method of a flexoelectric metamaterial based on an anti-trigonal chiral structure, including:

[0010] Establish a theoretical model of the flexoelectric metamaterial with an anti-trigonal chiral structure, describe the deformation and flexoelectric response of the internal ligaments of the flexoelectric metamaterial with an anti-trigonal chiral structure, and theoretically predict the mechanical properties and flexoelectric properties of the anti-trigonal chiral structure, including:

[0011] The anti-chiral structure includes units arranged in an array along the x-axis direction and the y-axis direction, where the x-axis direction and the y-axis direction are perpendicular. Each unit consists of 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 the ligaments are made of the same material. The ligaments include one horizontal ligament and two inclined ligaments. When the anti-chiral structure is loaded in the y-axis direction or the x-axis direction, the solid cylinder rotates around its own axis, the ligaments bend to generate a strain gradient, and the flexoelectric effect is induced. Its mechanical properties are characterized by the equivalent Young's modulus, and its flexoelectric properties are characterized by the equivalent piezoelectric coefficient. Among them,

[0012] The mechanical properties are characterized by the following method:

[0013]

[0014] The flexoelectric properties are characterized by the following method:

[0015]

[0016] Among them, E s is the Young's modulus of the material used for the unit cell, r is the radius of the solid cylinder, the inclination angle η is the angle between the inclined ligament and the plane where the horizontal ligament is located, t is the thickness of the ligament, L 1 is the length of the horizontal ligament, L 2 is the length of the inclined ligament, L' 1 is the equivalent length of the horizontal ligament, representing the length of the part of the horizontal ligament that does not overlap with the solid cylinder, L' 2 is the equivalent length of the inclined ligament, representing the length of the part of the inclined ligament that does not overlap with the solid cylinder;

[0017] E y is the equivalent Young's modulus of the anti-chiral structure in the y-axis direction, E x is the equivalent Young's modulus of the anti-chiral structure in the x-axis direction;

[0018] is the equivalent piezoelectric coefficient of the anti-chiral structure when loaded in the y-axis direction, is the equivalent piezoelectric coefficient of the anti-chiral structure when loaded in the x-axis direction, n 3 is the number of unit cells in the y-axis direction, n 1 is the number of unit cells in the x-axis direction, and μ is the flexoelectric coefficient of the material used for the unit cell;

[0019] Verify the mechanical properties of the flexoelectric metamaterial model of the anti-trigonal chiral structure by performing finite element numerical simulation on the anti-trigonal chiral structure of the U×V array, where both U and V are positive integers greater than 2;

[0020] Fabricate the anti-trigonal chiral structure of the U×V array, measure the equivalent piezoelectric coefficient of the flexoelectric metamaterial of the anti-trigonal chiral structure of the U×V array through a flexoelectric metamaterial experimental device, and compare the equivalent piezoelectric coefficient with the equivalent piezoelectric coefficient obtained from the theoretical model of the flexoelectric metamaterial of the anti-trigonal chiral structure to verify the flexoelectric properties of the theoretical model of the flexoelectric metamaterial of the anti-trigonal chiral structure.

[0021] Optionally, the measuring the equivalent piezoelectric coefficient of the anti-trigonal chiral structure of the U×V array through a flexoelectric metamaterial experimental device includes:

[0022] A force sensor is installed on the fixed plate to measure the force applied to the anti-trigonal chiral structure of the U×V array;

[0023] Deposit electrodes on all surfaces of K ligaments of the anti-trigonal chiral structure of the U×V array that are not at the edges, where the surface specified to be subjected to ligament tensile strain is the positive electrode, and the opposite surface is marked as the negative electrode, and K is a positive integer;

[0024] All the positive electrodes are interconnected through the conductive material on the back of the solid cylinder; all the negative electrodes are interconnected through the conductive material on the front of the solid cylinder;

[0025] Select two connection points on the front and back of the anti-trigonal chiral structure of the U×V array, and place two wires at the two connection points as the positive wire and the negative wire respectively, and coat the surface of the wires with conductive material. After the conductive material dries, connect the positive wire to the positive electrode and the negative wire to the negative electrode;

[0026] Connect the wires to a lock-in amplifier for current measurement;

[0027] Apply a sinusoidal displacement signal to the anti-trigonal chiral structure of the U×V array through a piezoelectric actuator for periodic loading;

[0028] Calculate the equivalent piezoelectric coefficient of the anti-trigonal chiral structure of the U×V array.

[0029] Optionally, the equivalent piezoelectric coefficient of the anti-trigonal chiral structure of the U×V array is calculated according to the following method:

[0030]

[0031] where F pis the amplitude of the pressure applied by the flexoelectric metamaterial experimental device, f is the frequency of the load applied by the flexoelectric metamaterial experimental device, i is the amplitude of the current when the flexoelectric metamaterial experimental device is measuring, ε is the overall strain of the anti-trigonal chiral structure of the U×V array, and b is the width of the ligament.

[0032] Optionally, the overall strain ε of the anti-trigonal chiral structure of the U×V array is calculated according to the following method:

[0033]

[0034] where Δy is the amplitude of the displacement load applied when the flexoelectric metamaterial experimental device is measuring.

[0035] Optionally, the equivalent length L 2 ’ of the horizontal ligament and the length L 1 of the horizontal ligament have the following relationship:

[0036]

[0037] The equivalent length L 2 ’ of the diagonal ligament and the length L 2 of the diagonal ligament have the following relationship:

[0038]

[0039] Optionally, 10° ≤ η ≤ 80°.

[0040] Optionally, the materials of the solid cylinder and the ligament are both dielectrics.

[0041] On the other hand, the present invention also provides a flexoelectric metamaterial based on an anti-trigonal chiral structure, which is manufactured according to the above manufacturing method.

[0042] Compared with the prior art, the flexoelectric metamaterial based on the anti-trigonal chiral structure provided by the present invention has at least achieved the following beneficial effects:

[0043] Based on the bending-dominated deformation mode of the anti-trigonal chiral structure, the present invention designs a flexoelectric metamaterial with a stable mechanical property of the anti-trigonal chiral structure, and conducts systematic research in aspects such as theoretical models, numerical simulations, and experimental characterizations, providing new ideas for the design and experimental characterization of flexoelectric metamaterials.

[0044] Of course, it is not necessary for any product implementing the present invention to simultaneously achieve all the above-mentioned technical effects.

[0045] Through the following detailed description of the exemplary embodiments of the present invention with reference to the accompanying drawings, other features and advantages of the present invention will become clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

[0047] Figure 1 It is a flowchart of a manufacturing method of a flexoelectric metamaterial based on an anti - trihelical structure provided by the present invention;

[0048] Figure 2 It is a schematic diagram of the structure of a flexoelectric metamaterial with an anti - trihelical structure provided by the present invention;

[0049] Figure 3 It is a definition of a local Cartesian coordinate system and a schematic diagram of ligament bending;

[0050] Figure 4 It is a force analysis diagram of a unit cell when the anti - trihelical structure is subjected to uniaxial compression in the y - axis direction;

[0051] Figure 5 It is the finite - element numerical simulation analysis result of the anti - trihelical structure;

[0052] Figure 6 It is a schematic diagram of an experimental device for flexoelectric metamaterials;

[0053] Figure 7 It is the test result of the equivalent piezoelectric coefficient of an unpolarized PZT - based metamaterial;

[0054] Figure 8 It is the test result of the equivalent piezoelectric coefficient of resin - based metamaterials with different tilt angles. Detailed implementation manners

[0055] Now, various exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that: unless otherwise specifically stated, the relative arrangements, numerical expressions, and numerical values of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0056] The following description of at least one exemplary embodiment is merely illustrative in nature and in no way serves as a limitation on the present invention, its application, or its use.

[0057] Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such technologies, methods, and devices should be considered as part of the specification.

[0058] In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0059] It should be noted that like reference numerals and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.

[0060] The present invention proposes a flexoelectric metamaterial based on an anti-chiral structure. First, a theoretical model is established to characterize the mechanical and flexoelectric properties of the anti-chiral structure, and numerical analysis is performed on the key parameters of the anti-chiral structure. Then, finite element numerical simulation is carried out to further analyze the deformation principle and mechanism of the structure and verify the correctness of the theoretical model. Finally, an anti-chiral flexoelectric metamaterial is prepared using unpolarized piezoelectric ceramics (PZT) and its apparent piezoelectric properties are experimentally characterized.

[0061] Specifically, it includes the steps:

[0062] S1. Establish a theoretical model of the flexoelectric metamaterial with an anti-chiral structure, describe the deformation and flexoelectric response of the internal ligaments of the flexoelectric metamaterial with an anti-chiral structure, and theoretically predict the mechanical properties and flexoelectric properties of the anti-chiral structure;

[0063] S2. Through finite element numerical simulation of the anti-chiral structure of the U×V array, verify the mechanical properties of the theoretical model of the flexoelectric metamaterial with an anti-chiral structure, where both U and V are positive integers greater than 2;

[0064] S3. Prepare the anti-chiral structure of the U×V array, measure the equivalent piezoelectric coefficient of the anti-chiral structure of the U×V array through the flexoelectric metamaterial experimental device, and compare the equivalent piezoelectric coefficient with the equivalent piezoelectric coefficient obtained from the theoretical model of the flexoelectric metamaterial with an anti-chiral structure to verify the flexoelectric properties of the theoretical model of the flexoelectric metamaterial with an anti-chiral structure.

[0065] For step S1:

[0066] The embodiment of the present invention proposes a deformation mechanism and a theoretical model.

[0067] It should be noted that among all metamaterial structures, the anti-chiral lattice is a very typical bending-dominated lattice, which is conducive to generating an obvious flexoelectric effect in the internal ligaments. Therefore, the present invention designs a flexoelectric metamaterial based on the anti-chiral structure and realizes the apparent piezoelectric effect.

[0068] Combined with Figure 2 , Figure 2 Schematic diagram of the structure of the flexoelectric metamaterial with an anti-chiral structure. The anti-chiral structure includes units arranged in an array along the x-axis direction and the y-axis direction, the x-axis direction and the y-axis direction are perpendicular, the unit includes six unit cells forming a hexagon, each unit cell consists of a solid cylinder and three ligaments tangentially connected to the cylinder, and the materials of the solid cylinder and the ligaments are the same. Figure 2The number of middle units is only for illustrative purposes and is not specifically defined here. The ligaments here are divided into one horizontal ligament and two oblique ligaments, and the angles between the oblique ligaments and the x-axis direction and the y-axis direction are both greater than 0°. Let the lengths of the horizontal ligament and the oblique ligament be L 1 and L 2 , and the lengths of the two oblique ligaments are equal, both being L 2 . Let the thickness of the ligament and the radius of the solid cylinder be t and r respectively. The inclination angle of the oblique ligament is η.

[0069] When the anti-triply chiral structure is axially compressed, the solid cylinder will rotate around the cylinder axis, and the ligament will bend as a slender beam. Therefore, the internally bent ligament causes the generation of a strain gradient and induces the flexoelectric effect, which exists in all dielectric materials. For this bending-dominated deformation mode, the axial compressive or tensile strain is converted into a strain gradient of the internal ligament, thereby generating equivalent piezoelectric properties by collecting the flexoelectric charges on the surface of the bent ligament.

[0070] The loading in the embodiments of the present invention can be compression or tension.

[0071] It should be noted that in the traditional anti-triply chiral structure, the angle between adjacent ligaments is fixed at 60°, while in the present invention, the inclination angle of the oblique ligament is regarded as a variable, denoted as η, 10° ≤ η ≤ 80°, for example, η can be 10°, 20°, 30°, 40°, 45°, 50°, 60°, 70°, 75°, 80°, and can also be any value between 10° and 80°, for example, 45° ≤ η ≤ 75°. Figure 2 Only η = 60° is taken as an example for illustrative purposes. When η = 60°, the unit is a regular hexagon, and when η is not 60°, the unit is a non-regular hexagon.

[0072] Optionally, the materials of the solid cylinder and the ligament are both dielectrics. A dielectric is an insulating material that can be polarized under the action of an electric field and store electrostatic energy, and there are almost no freely movable charges inside it. For example, it can be mica, ceramics (such as alumina, silicon nitride, barium titanate ferroelectric materials), glass, plastics (such as polyethylene, polystyrene), rubbers (such as silicone rubber), quartz, thin film materials (such as polyester film, polyimide, polypropylene), and composite materials (such as epoxy resin - glass fiber), as long as it is a dielectric, and it is not specifically defined here.

[0073] In this embodiment, a theoretical model of the anti-trigonal chiral structure is established to describe the deformation and flexoelectric effect of the ligaments inside the anti-trigonal chiral flexoelectric metamaterial, so as to predict the equivalent mechanical properties and equivalent flexoelectric properties of the structure. First, for the solid cylinder in the anti-trigonal chiral structure, it is assumed to be a rigid body, that is, only rigid displacement occurs and no elastic deformation occurs. For the ligaments, the bending deformation of each ligament can be obtained through the Euler-Bernoulli beam model, and the strain gradient distribution law can be obtained; finally, according to the flexoelectric-mechanical coupling relationship, the total charge response of the anti-trigonal chiral structure can be obtained, and the force-electric coupling performance of the anti-trigonal chiral structure is measured by the equivalent piezoelectric coefficient.

[0074] Figure 4 Figure for the force analysis of the metamaterial unit cell, where the concentrated forces and moments at the ligament endpoints are unknowns to be determined. Since Figure 2 the geometric symmetry shown, the forces and moments at the endpoints of each unit cell can be analyzed as follows:

[0075] (1) According to the mirror symmetry line, it can be known that the structures on both sides of the symmetry line have symmetric force states and deformed shapes. Therefore, the external forces F xCD and F yCD applied at the endpoints of ligament CD satisfy the following equation:

[0076]

[0077] F xCD is the external force in the x-axis direction applied at the endpoints of ligament CD, and F yCD is the external force in the y-axis direction applied at the endpoints of ligament CD.

[0078] (2) According to the vertical secant line, it can be known that the sum of the external forces in the horizontal direction on the nodes tangent to the secant line is 0. Also, due to the translational symmetry of the structure, the external forces F xAB and F yEF in the x-axis direction applied at the endpoints of the inclined ligaments AB and EF are equal and both are 0, that is:

[0079]

[0080] (3) According to the zipper-shaped symmetry line, it can be obtained that the external forces in the y-axis direction applied at the endpoints of the inclined ligaments AB and EF are of the same magnitude and opposite in direction, that is: F yAB =F yEF . At the same time, the bending moments applied at the endpoints of the inclined ligaments AB and EF are the same, that is: N AB =N EF . According to the moment balance, the bending moment at the endpoints of ligament CD can be obtained as:

[0081] N CD =2F yABrsinη - 2N AB (3)

[0082] Next, the energy method is used to solve for the unknown bending moment N AB . First, write the distribution of the bending moment on ligaments AB, CD, and EF with respect to the coordinate x 1 (Combined with Figure 3 ):

[0083]

[0084] Ignoring the uniaxial compression and shear effects, the strain energy of the unit cell can be expressed as:

[0085]

[0086] where E s is the Young's modulus of the substrate, I = bt 3 / 12, I is the moment of inertia of the ligament, b is the width of the ligament, and t is the thickness of the ligament. L' 1 and L' 2 are the equivalent lengths of the ligaments, which are slightly smaller than the full lengths L 1 and L 2 because there is an intersection between the ligaments and the cylindrical region. L' 1 and L' 2 can be expressed as:

[0087]

[0088] The angles of rotation at endpoints A and E are named Δθ 1 and Δθ 2 . Since the anti-trigonal chiral structure maintains periodic symmetry before and after deformation, this means that all horizontal ligaments remain horizontal after deformation. Therefore, the nodal angles of rotation of the two inclined ligaments satisfy the following relationship: Δθ 2 = -Δθ 1 , which is equivalent according to Castigliano's theorem as:

[0089]

[0090] Substitute Equation 8 into Equation 6 to obtain the analytical expression for N AB :

[0091]

[0092] Analyze the flexoelectric response of each ligament. For ligament AB, its deflection after bending is w(x 1 ), and the axial strain distribution is According to the Euler-Bernoulli beam model, the relationship between them is:

[0093]

[0094] The balance equation is:

[0095]

[0096] According to Equation 5, Equation 9, Equation 10, and Equation 11, the distribution of the transverse strain gradient of ligament AB along the x 1 axis direction is:

[0097]

[0098] And so on, the strain gradient distributions on ligaments CD and EF can be expressed as:

[0099]

[0100] The total flexoelectric charge Q of the unit cell is the superposition of the flexoelectric charges of the three ligaments, and the flexoelectric charge of the ligament can be obtained by integrating the flexoelectric polarization distribution on the ligament over the ligament surface area, that is:

[0101]

[0102] Among them, μ is the transverse flexoelectric coefficient of the substrate, and the substrate here is the material used for the unit cell. In this embodiment, a metamaterial structure of 2n 1 ×2n 3 array is considered, where 2n 1 and 2n 3 represent the number of unit cells in the x-axis direction and y-axis direction of the structure respectively, and the number of unit cells here is an even number. For this anti-triple-chiral structure, the total flexoelectric charge is:

[0103] Q tot = 4n 1 n 3 Q(14)

[0104] As Figure 2 shown, the total pressure received by the anti-triple-chiral structure is F tot , and it can be expressed as:

[0105] F tot = 2n 1 F yAB (15)

[0106] It should be noted that the force-electric coupling performance of the flexoelectric structure is often characterized by the equivalent piezoelectric coefficient. For the flexoelectric metamaterial designed in the embodiment of the present invention, the equivalent piezoelectric coefficient is defined as the flexoelectric charge generated by a unit force. When loaded in the y-axis direction, the equivalent piezoelectric coefficient of the anti-triple-chiral structure is:

[0107]

[0108] Subsequently, the equivalent Young's modulus of the anti-trigonal chiral structure in the y-axis direction is derived. According to Castigliano's second theorem, the relative displacement between endpoint A and endpoint E along the external force loading direction, which is the height change of the unit cell as a whole in the y-axis direction, can be obtained by the following formula:

[0109]

[0110] According to the geometric relationship, the strain of the unit cell in the y-axis direction can be obtained:

[0111]

[0112] The stress σ applied to the unit cell y is:

[0113]

[0114] According to Eqs. (18), (19), and (20), the equivalent Young's modulus of the anti-trigonal chiral structure in the y-axis direction is:

[0115]

[0116] Using a similar method, the equivalent piezoelectric coefficient and equivalent Young's modulus of the anti-trigonal chiral structure in the x-axis direction can also be obtained. The results are directly listed here:

[0117]

[0118] For the finite element numerical simulation of step S2, specifically:

[0119] In this embodiment, only the anti-trigonal chiral structure with a 4×8 array is used for the finite element numerical simulation, that is, U = 4, V = 8, and U and V are not specifically limited here.

[0120] The finite element method is used to numerically simulate the behavior of the 4×8 array of anti-trigonal chiral structures under compressive deformation. The mesh division model uses tetrahedral elements, and mesh sensitivity analysis is carried out to ensure sufficient mesh density. Mesh refinement is performed at the junction of the ligament and the cylinder to improve the calculation accuracy.

[0121] Figure 5 The finite element numerical simulation analysis results of the anti-trigonal chiral structure are shown. Among them, (a) is a schematic diagram of the deformation mode of the anti-trigonal chiral structure under compression in the x-axis direction; (b) is the strain gradient distribution of the horizontal ligament and the inclined ligament; (c) and (d) are the schematic diagram of the deformation mode of the anti-trigonal chiral structure under compression in the y-axis direction and the strain gradient distribution of the ligament. In order to have a more intuitive display effect, the deformation of the anti-trigonal chiral structure is magnified by 350 times. Figure 5 In order to clearly show the displacement change and strain gradient distribution, it is shown in color diagrams.

[0122] From Figure 5 Figure 5

[0123] For step S3:

[0124] In Example 1 of the present invention, a counter-triple chiral structure prepared from non-polarized PZT-5H piezoelectric ceramics is taken as an example to verify the effectiveness of the designed flexoelectric metamaterial. PZT is the industrial specific name of piezoelectric ceramics based on barium titanate (BaTiO3), which is divided into different types according to different physical and chemical properties. Among them, PZT-2, PZT-4 (divided into PZT-4A, PZT-4D, PZT-4E) and PZT-8 belong to the hard material category, and PZT-5 (divided into PZT-5A, PZT-5D, PZT-5J, PZT-5H, PZT-5X) belongs to the soft material category, and the lead-free type is BT-1. PZT-5H piezoelectric ceramics belong to the soft material category. The present invention selects PZT-5H to more easily verify the flexoelectric effect.

[0125] The counter-triple chiral structure prepared in this example contains a flexoelectric metamaterial sample of 4×8 unit cells, which is prepared by laser cutting a 1-mm-thick PZT-5H ceramic plate. The ligament thickness t of all samples is kept at 1 mm, and the key geometric parameters are set as r = 1.5 mm L 1 = L 2 = 11 mm, η = 60°.

[0126] Figure 6 Fig. shows a schematic diagram of the flexoelectric metamaterial experimental device. In order to distinguish the positive and negative electrodes, Figure 6 it is shown in color illustration. Silver paste electrodes are used on the front and back of the sample to output flexoelectric charges. In order to fully capture the strain gradient of the entire counter-triple chiral structure, the electrodes are deposited on all surfaces of 15 ligaments at the center of the structure. The 15 ligaments here do not include the ligaments of the unit cells at the outer edge of the counter-triple chiral structure. The surface subjected to ligament tensile strain is designated as the positive electrode (marked with a red line), while the opposite surface is marked as the negative electrode (marked with a blue line). The positive and negative electrodes on the 15 ligaments are connected to each other through silver paste on a solid cylinder (marked as connection points) to prevent any charge neutralization. Two connection points are selected on the front and back of the counter-triple chiral structure, and platinum wires (Pt) are placed at each point. The connection points here refer to Figure 7, which is the connection point for connecting the negative or positive electrode on the fixed cylinder. The front is the connection point for the negative electrode, and the back is the connection point for the positive electrode. Apply a small amount of silver paste to cover the wire. After the silver paste is completely dry, connect two platinum wires to the positive and negative electrodes. The resistance of the conduction path is less than 5 Ω, proving that the connection between the platinum wire and the electrode is reliable. Then connect the platinum wire to a lock-in amplifier for current measurement. Apply a sinusoidal displacement signal to the overall anti-trigonal chiral structure by a piezoelectric actuator for periodic loading. In this embodiment, the loading frequency f = 40 Hz.

[0127] In this embodiment, the conductive material used is silver paste. Of course, it can also be other materials, such as conductive glue, etc., which are not limited here. The wire used in this embodiment is a platinum wire, and it can also be a wire of other materials, which is not specifically limited here.

[0128] A lock-in amplifier is a high-sensitivity signal detection instrument that can extract weak signals of a specific frequency from a strong noise background. The lock-in amplifier used in this embodiment is Stanford Research SR830.

[0129] A piezoelectric actuator is a precision micro-displacement device based on the piezoelectric effect, which can directly convert electrical energy into mechanical energy to achieve high-precision and fast-response motion control. The piezoelectric actuator used in this embodiment is Physik P-841.60.

[0130] The measured equivalent piezoelectric coefficient of the anti-trigonal chiral structure can be calculated by the following formula:

[0131]

[0132] where F p is the pressure amplitude, f is the frequency of the applied load, i is the measured current amplitude, and ε is the overall strain of the anti-trigonal chiral structure, which can be calculated by the following formula:

[0133]

[0134] Figure 7 Shows the test results of the equivalent piezoelectric coefficient of the PZT-5H ceramic-based metamaterial sample. Since the magnitudes of the equivalent piezoelectric coefficients in the x and y axis directions are relatively close, and the metamaterial sample is more stable under pressure in the y axis direction experimentally, only the equivalent piezoelectric coefficient in the y axis direction is measured in the embodiments of the present invention. During the test, a force sensor is installed on the fixed plate to measure the force applied to the anti-trigonal chiral structure.

[0135] By Figure 7It can be seen that as the excitation load increases, the ligament produces a greater bending deformation, and thus the flexoelectric current collected also increases linearly. The measured value of the PZT-5H-based sample calculated according to Equation (23) reaches 2.6 pC / N, which is in good agreement with the theoretical value of 1.8 pC / N, verifying the flexoelectric performance of the theoretical model of the flexoelectric metamaterial with an anti-triple chiral structure.

[0136] It should be noted that in this embodiment, comparing the equivalent piezoelectric coefficient with that obtained from the theoretical model of the flexoelectric metamaterial with an anti-triple chiral structure means comparing with or for comparison.

[0137] For step S3:

[0138] In Example 2 of the present invention, to explore the influence of geometric parameters on the flexoelectric performance of the metamaterial, resin-based flexoelectric metamaterials with different tilt angles were prepared using 3D printing technology. The elastic modulus of this resin material is 2.6 GPa, and it has excellent flexibility, making it suitable for constructing flexoelectric metamaterials. For the resin-based flexoelectric metamaterial, except that the ligament width b is set to 3 mm, the other parameter settings are the same as those of the PZT-based metamaterial. The tilt angles η are 45°, 60°, and 75°, respectively.

[0139] Subsequently, three resin-based flexoelectric metamaterial samples with different tilt angles were tested at the same frequency, and the experimental device and experimental method were the same as those in Example 1. As Figure 8 shown, the measured equivalent piezoelectric coefficients of the samples with tilt angles of 45°, 60°, and 75° are 0.081, 1.00, and 0.107 pC / N, respectively, and these measurement results are in good agreement with the theoretical values (0.075 pC / N, 0.091 pC / N, and 0.102 pC / N).

[0140] In addition, it should be noted that as the tilt angle increases, the measured current shows an upward trend, demonstrating that the flexoelectric performance of the anti-triple chiral structure can be enhanced by adjusting the tilt angle.

[0141] Although some specific embodiments of the present invention have been described in detail by way of examples, those skilled in the art should understand that the above examples are only for illustration and not for limiting the scope of the present invention. Those skilled in the art should understand that the above embodiments can be modified without departing from the scope and spirit of the present invention. The scope of the present invention is defined by the appended claims.

Claims

1. A method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure, characterized in that: include: A theoretical model of anti-trichirality flexoelectric metamaterials is established to describe the deformation and flexoelectric response of the internal ligaments of anti-trichirality flexoelectric metamaterials, and theoretically predict the mechanical and flexoelectric properties of anti-trichirality structures, including: The anti-trichirality structure includes units arranged in an array along the x-axis and the y-axis, the x-axis and the y-axis are perpendicular, the unit includes six unit cells forming a hexagon, each of the unit cells includes a solid cylinder and three ligaments tangentially connected to the solid cylinder, the solid cylinder and the ligaments are made of the same material, and the ligaments include a horizontal ligament and two oblique ligaments; when the anti-trichirality structure is loaded in the y-axis direction or the x-axis direction, the solid cylinder rotates around its own axis, the ligaments bend to generate a strain gradient, and induce a flexoelectric effect, the mechanical properties are characterized by an equivalent Young's modulus, and the flexoelectric properties are characterized by an equivalent piezoelectric coefficient, wherein, The mechanical properties are characterized by the following method: The flexoelectric properties are characterized by the following method: Among them, E s is the Young's modulus of the material used in the unit cell, r is the radius of the solid cylinder, the inclination angle η is the angle between the plane where the oblique ligament and the horizontal ligament are located, t is the thickness of the ligament, L1 is the length of the horizontal ligament, L2 is the length of the oblique ligament, L'1 is the equivalent length of the horizontal ligament, indicating the length of the non-overlapping portion of the horizontal ligament and the solid cylinder, and L'2 is the equivalent length of the oblique ligament, indicating the length of the non-overlapping portion of the oblique ligament and the solid cylinder; E y is the equivalent Young's modulus of the anti-trichiral structure in the y-axis direction, E x is the equivalent Young's modulus of the anti-trichiral structure in the x-axis direction; is the equivalent piezoelectric coefficient of the anti-trichiral structure when loaded in the y-axis direction, is the equivalent piezoelectric coefficient of the anti-trichiral structure when loaded in the x-axis direction, n3 is the number of the unit cells in the y-axis direction, n1 is the number of the unit cells in the x-axis direction, and μ is the flexoelectric coefficient of the material used for the unit cells; The mechanical properties of the flexoelectric metamaterial model of the anti-trichirality structure are verified by performing finite element numerical simulation on the anti-trichirality structure of the U×V array, wherein U and V are both positive integers greater than 2; An anti-trichirality structure of a U×V array is prepared, and the equivalent piezoelectric coefficient of the flexoelectric metamaterial of the anti-trichirality structure of the U×V array is measured using a flexoelectric metamaterial experimental device. The equivalent piezoelectric coefficient is compared with the equivalent piezoelectric coefficient obtained from the theoretical model of the flexoelectric metamaterial of the anti-trichirality structure, so as to verify the flexoelectric performance of the theoretical model of the flexoelectric metamaterial of the anti-trichirality structure.

2. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 1, characterized in that: The method of measuring the equivalent piezoelectric coefficient of the anti-trichirality structure of the U×V array by using a flexoelectric metamaterial experimental device comprises: The force sensor is mounted on a fixed plate to measure the force applied to the anti-trichiral structure of the U×V array; Depositing electrodes on all surfaces of K ligaments that are not edges of the anti-trichiral structure of the U×V array, where the surface subjected to the tensile strain of the ligament is designated as the positive electrode, the opposite surface is designated as the negative electrode, and K is a positive integer; All the positive electrodes are connected to each other through the conductive material on the back of the solid cylinder; all the negative electrodes are connected to each other through the conductive material on the front of the solid cylinder; Select two connection points on the front and back sides of the anti-trichiral structure of the U×V array, and place two wires as a positive electrode wire and a negative electrode wire on the two connection points respectively, and coat the surface of the wires with a conductive material, and after the conductive material is dried, connect the positive electrode wire to the positive electrode, and connect the negative electrode wire to the negative electrode; connecting the wire to a lock-in amplifier for current measurement; Applying a sinusoidal displacement signal to the anti-trichiral structure of the U×V array by a piezoelectric actuator for periodic loading; The equivalent piezoelectric coefficient of the anti-trichiral structure of the U×V array is calculated.

3. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 2, characterized in that: The equivalent piezoelectric coefficient of the anti-trichiral structure of the U×V array Calculate as follows: Among them, F p is the pressure amplitude applied by the flexoelectric metamaterial experimental device, f is the frequency of the load applied by the flexoelectric metamaterial experimental device, i is the current amplitude of the flexoelectric metamaterial experimental device during measurement, ε is the overall strain of the anti-trichirality structure of the U×V array, and b is the width of the ligament.

4. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 3, characterized in that: The overall strain ε of the anti-trichiral structure of the U×V array is calculated as follows: Wherein, Δy is the amplitude of the displacement load applied by the flexoelectric metamaterial experimental device during measurement.

5. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 1, characterized in that: The relationship between the equivalent length L2' of the horizontal ligament and the length L1 of the horizontal ligament is: The relationship between the equivalent length L2' of the oblique ligament and the length L2 of the oblique ligament is:

6. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 1, characterized in that: 10°≤η≤80°.

7. The method for manufacturing a flexoelectric metamaterial based on an anti-trichirality structure according to claim 1, characterized in that: The materials of the solid cylinder and the ligament are both dielectric.

8. A flexoelectric metamaterial based on an anti-trichirality structure, characterized in that: Made according to the making method of claims 1 to 7.

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