A lattice piezoelectric metamaterial

Abstract

This invention discloses a lattice piezoelectric metamaterial comprising multiple interconnected unit cell structures in three-dimensional space. Each unit cell includes a first planar unit, a second planar unit, and connecting pillars. The first planar unit includes: first pillar A, second pillar A, third pillar A, fourth pillar A, fifth pillar A, and sixth pillar A. The second planar unit includes first pillar B, second pillar B, third pillar B, fourth pillar B, fifth pillar B, and sixth pillar B. Adjacent unit cell structures share the first pillar A, third pillar A, fourth pillar A, sixth pillar A, first pillar B, third pillar B, fourth pillar B, and sixth pillar B. By manipulating the geometric parameters of the three-dimensional lattice structure, the piezoelectric coefficient can be continuously manipulated over a wide range from positive to negative values. The constructed metamaterial exhibits theoretically all electromechanical coupling modes, meaning that normal and shear stresses in any direction can generate electrical responses in all directions, and vice versa.

Description

Technical Field

[0001] This invention relates to the field of mechanical metamaterial structure design, and more specifically, to a lattice piezoelectric metamaterial. Background Technology

[0002] Piezoelectric materials are crystalline materials that exhibit a voltage between their two ends when subjected to pressure. The mechanism of the piezoelectric effect is as follows: piezoelectric crystals have low symmetry. When deformed under external force, the relative displacement of positive and negative ions in the unit cell causes the centers of positive and negative charges to no longer coincide, resulting in macroscopic polarization of the crystal. Since the surface charge density of the crystal is equal to the projection of the polarization intensity onto the surface normal, opposite charges will appear on the two ends of the piezoelectric material when deformed under pressure. Conversely, when a piezoelectric material is polarized in an electric field, the displacement of the charge centers will cause the material to deform.

[0003] Obtaining counterintuitive physical properties is a crucial topic in the field of metamaterials, including negative refraction, negative Poisson's ratio, shape reconfigurability, and piezoelectric resonant bandgap. These unique properties originate from artificial structures rather than inherent material properties. Designing topological artificial structures with non-natural parameters and properties is a major challenge in metamaterials, especially for the relatively unexplored piezoelectric materials with mechanoelectric coupling effects. Piezoelectric materials mainly include ceramics, single crystals, and polymers, among which piezoelectric ceramics have excellent mechanoelectric coupling properties and are easy to fabricate, making them the most widely used materials. Piezoelectric ceramics and polymers play important roles in aerospace, industrial equipment, and medical instruments.

[0004] Piezoelectric metamaterials have attracted widespread attention in fields such as robotics, nondestructive testing, and energy harvesting. The piezoelectric coefficient, describing the electromechanical coupling properties, is the most important parameter for evaluating the performance of piezoelectric materials. Due to the ∞mm crystal symmetry, natural piezoelectric ceramics or piezoelectric polymers have only five non-zero piezoelectric coefficients, among which d0... 31 d 32 If negative, d 33 d 15 d 24 It is positive. In fact, different piezoelectric coefficients have their own advantages and applications. For example, the piezoelectric coefficient d... 36 It can be used to excite horizontal shear waves to detect structural damage. Furthermore, depolarization caused by an external electric field can be avoided by applying an electric field parallel to the polarization direction (third direction Z). Therefore, the variety of piezoelectric coefficients in natural piezoelectric ceramics is insufficient to meet practical needs, hindering the development and application of related piezoelectric devices. Currently, various methods have been developed to obtain non-zero piezoelectric coefficients. To obtain horizontal shear waves, a non-zero piezoelectric coefficient d... 36Various methods have been employed, including introducing ferroelastic or electric domains into piezoelectric ceramics or using two-dimensional antiparallel polarization. However, the mode combinations of each ceramic unit can only achieve inverse piezoelectric effects with localized deformation, and are not applicable to direct piezoelectric effects. These methods only achieve partially non-zero piezoelectric coefficients or locally deformable modes, and cannot manipulate the piezoelectric coefficient over a large range.

[0005] Existing literature (publication number: CN112530395 A) discloses a layout structure and method for a low-frequency broadband piezoelectric acoustic metamaterial, comprising several cells. Each cell includes a piezoelectric sheet and a substrate plate. The substrate plates of all cells together constitute an outer substrate plate. The piezoelectric sheet is a four-pointed star shape, with its four corners truncated by rectangles. Two piezoelectric sheets are respectively provided on the front and back sides of the substrate plate. The two piezoelectric sheets are connected in parallel and electrically connected to a shunt inductor circuit. The piezoelectric sheets between adjacent cells do not contact each other. However, this structure cannot achieve a non-zero piezoelectric coefficient or a locally deformable mode, and cannot manipulate the piezoelectric coefficient over a large range. Summary of the Invention

[0006] In view of this, the present invention provides a lattice piezoelectric metamaterial that solves the problem of not being able to achieve all non-zero piezoelectric coefficients and not being able to manipulate the piezoelectric coefficient over a wide range.

[0007] This invention provides a lattice piezoelectric metamaterial comprising multiple interconnected unit cell structures in three-dimensional space;

[0008] The unit cell structure includes a first planar unit, a second planar unit, and connecting struts; the first planar unit includes: a first A strut, a second A strut, a third A strut, a fourth A strut, a fifth A strut, and a sixth A strut; the first A strut has a first A node in its middle part, the first A node is connected to the first end point of the second A strut, the second end point of the second A strut is connected to the first end point of the third A strut; the first end point of the fourth A strut is connected to the first end point of the fifth A strut; the sixth A strut has a second A node in its middle part, the second A node is connected to the second end point of the fifth A strut; the second A strut has a third A node in its middle part, the fifth A strut has a fourth A node in its middle part, the first end point of the connecting strut is connected to the third A node, and the second end point of the connecting strut is connected to the fourth A node;

[0009] The second planar unit includes a first B-pillar, a second B-pillar, a third B-pillar, a fourth B-pillar, a fifth B-pillar, and a sixth B-pillar; the first B-pillar has a first B-node in its middle section, the first B-node is connected to the first end point of the second B-pillar, the second end point of the second B-pillar is connected to the first end point of the third B-pillar; the first end point of the fourth B-pillar is connected to the first end point of the fifth B-pillar, the sixth B-pillar has a second B-node in its middle section, the second B-node is connected to the second end point of the fifth B-pillar; the second B-pillar has a third B-node in its middle section, the fifth B-pillar has a fourth B-node in its middle section, the first end point of the connecting pillar is connected to the third B-node, and the second end point of the connecting pillar is connected to the fourth B-node;

[0010] The first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, the sixth B pillar, and the connecting pillar are parallel to each other; the first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, and the sixth B pillar have the same length; adjacent unit cell structures share the first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, and the sixth B pillar.

[0011] Compared with existing technologies, the lattice piezoelectric metamaterial provided by this invention achieves at least the following beneficial effects:

[0012] This invention provides a lattice piezoelectric metamaterial. By analyzing the relationship between macroscopic effective stress and structural support stress, symmetry breaking can be achieved using the lattice piezoelectric metamaterial, thereby obtaining all non-zero piezoelectric coefficients. By manipulating the geometric parameters of the three-dimensional lattice structure, the piezoelectric coefficients can be continuously manipulated over a wide range from positive to negative values. The constructed metamaterial exhibits theoretically all mechanoelectric coupling modes, meaning that normal and shear stresses in any direction can produce electrical responses in all directions, and vice versa.

[0013] Of course, any product implementing this invention does not necessarily need to achieve all of the technical effects described above at the same time.

[0014] 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

[0015] 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.

[0016] Figure 1 This is a schematic diagram of the structure of a lattice piezoelectric metamaterial provided in this embodiment;

[0017] Figure 2 yes Figure 1 Top view of a mid-lattice piezoelectric metamaterial;

[0018] Figure 3 yes Figure 1 Front view of a mid-lattice piezoelectric metamaterial;

[0019] Figure 4 yes Figure 1 Side view of a mid-lattice piezoelectric metamaterial;

[0020] Figure 5 This is a schematic diagram of a single-cell structure provided in this embodiment;

[0021] Figure 6 yes Figure 5 Top view of the middle unit cell structure;

[0022] Figure 7 yes Figure 5 Front view of the middle unit cell structure;

[0023] Figure 8 yes Figure 5 Side view of the middle unit cell structure;

[0024] Figure 9 This is a schematic diagram of another unit cell structure provided in this embodiment;

[0025] Figure 10 This is a schematic diagram of another unit cell structure provided in this embodiment;

[0026] Figure 11 This is a schematic diagram of another unit cell structure provided in this embodiment;

[0027] Figure 12 This is a schematic diagram of another unit cell structure provided in this embodiment;

[0028] Figure 13 This is a schematic diagram of another unit cell structure provided in this embodiment;

[0029] Figure 14 This is a schematic diagram of the piezoelectric coefficient matrix and the electromechanical coupling mode;

[0030] Figure 15 This is a schematic diagram of a classic eight-pillar structure;

[0031] Figure 16 This is a schematic diagram of the force analysis and stress transformation of the support column;

[0032] Figure 17 This is a diagram showing the calculated electrical displacement of the support column in the second (first) direction caused by macroscopic stress σ2(σ1);

[0033] Figure 18 This is a diagram showing the calculated electrical displacement of the support column in the second (first) direction caused by macroscopic stress σ1(σ2);

[0034] Figure 19 This is a diagram showing the calculated electrical displacement of the support column in the second (first) direction caused by macroscopic stress σ3.

[0035] Figure 20 This is a diagram showing the calculated electrical displacement of the support column in the second (first) direction caused by macroscopic stress σ5 (σ4);

[0036] Figure 21 This is a diagram showing the calculated electrical displacement of the support column in the second (first) direction caused by macroscopic stress σ6.

[0037] Figure 22 This is a diagram showing the calculated electric displacement of the third-direction support caused by macroscopic stress σ5 (σ4);

[0038] Figure 23 This is a diagram showing the calculated electric displacement of the third-direction support caused by macroscopic stress σ6;

[0039] Figure 24 It is in d 22 (d 11 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0040] Figure 25 It is in d 21 (d 12 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0041] Figure 26 It is in d 23 (d 13 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0042] Figure 27 It is in d 25 (d 14 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0043] Figure 28 It is in d 26 (d 16 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0044] Figure 29 It is in d 35 (d 34 Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the ) mode;

[0045] Figure 30 It is in d 36Electric displacement diagram and unit cell design diagram of the eight-pillar structure under the model;

[0046] Figure 31 It is d 22 Force analysis diagram of a single cell;

[0047] Figure 32 It is d 22 (d 11 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0048] Figure 33 It is d 21 (d 12 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0049] Figure 34 It is d 23 (d 13 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0050] Figure 35 It is d 25 (d 14 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0051] Figure 36 It is d 26 (d 16 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0052] Figure 37 It is d 35 (d 34 Figure 1 shows the theoretical and finite element calculation results of a unit cell.

[0053] Figure 38 It is d 36 Figures showing the theoretical and finite element calculation results of a unit cell;

[0054] Figure 39 It is d 22 (d 11 Figure showing the finite element calculation results for multi-cell structures;

[0055] Figure 40 It is d 21 (d 12 Figure showing the finite element calculation results for multi-cell structures;

[0056] Figure 41 It is d 23 (d 13 Figure showing the finite element calculation results for multi-cell structures;

[0057] Figure 42 It is d 25 (d 14 Figure showing the finite element calculation results for multi-cell structures;

[0058] Figure 43 It is d 26 (d 16 Figure showing the finite element calculation results for multi-cell structures;

[0059] Figure 44 It is d 35 (d 34 Figure showing the finite element calculation results for multi-cell structures;

[0060] Figure 45 It is d 36 Figure showing the finite element calculation results for a multicellular array;

[0061] Figure 46 It is d 22 Schematic diagram of metamaterial structure optimization;

[0062] Figure 47 It is d 22 Figure showing the finite element calculation results of the metamaterial optimized structure. Detailed Implementation

[0063] Various exemplary embodiments of the 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. 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. Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and apparatus should be considered part of the specification. In all 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. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0064] like Figures 1 to 4As shown, this embodiment provides a lattice piezoelectric metamaterial 200, which can be a lattice piezoelectric metamaterial with all mechanoelectric coupling modes; in three-dimensional space, it includes multiple periodically arranged and interconnected unit cell structures 100; it can be understood that in three-dimensional space, the first direction X, the second direction Y, and the third direction Z intersect each other pairwise, specifically, the first direction X, the second direction Y, and the third direction Z can be arranged perpendicularly to each other; in a piezoelectric metamaterial 200, the structure and spatial arrangement angle of each unit cell structure 100 do not change, and multiple unit cell structures 100 can be arranged along the first direction X, the second direction Y, and the third direction Z respectively, with adjacent unit cell structures 100 interconnected; adjacent unit cell structures 100... The connection point of the cell structure 100 can be that the endpoints of the first cell structure 100 and the endpoints of the second cell structure 100 are in contact and connected; the connection point of two adjacent cell structures 100 can also be that the two cell structures 100 share a part of the same structure, thereby achieving mutual connection; the number of cell structures 100 in the first direction X, the second direction Y, and the third direction Z can be five, six, seven, or eight, and is not limited here; the placement angle of the cell structure 100 in three-dimensional space can be set according to the piezoelectric coefficient required by actual needs. The piezoelectric metamaterial 200 composed of cell structures 100 with different spatial placement angles can produce different piezoelectric coefficients, and the spatial placement angle of the cell structure 100 is not specifically limited here.

[0065] like Figures 5 to 8 As shown, the unit cell structure 100 includes a first planar unit 1, a second planar unit 2, and a connecting pillar 3. It can be understood that in three-dimensional space, the first planar unit 1 lies in one plane, and the second planar unit 2 lies in another plane; that is, the first planar unit 1 and the second planar unit 2 are not in the same plane, and the two planes containing the first planar unit 1 and the second planar unit 2 intersect each other but are not parallel. The plane containing the first planar unit 1 intersects with the plane containing the second planar unit 2 to form a common straight line, and the connecting pillar 3 lies on this common straight line. The connecting pillar 3 is located within the first planar unit 1... Between the first planar unit 1 and the second planar unit 2, and connected by the connecting pillar 3 to form an integral structure; specifically, the first planar unit 1 can be composed of upper and lower parts, the structures of the upper and lower parts can be completely identical, and the upper and lower parts are connected by the connecting pillar 3; the second planar unit 2 can also be composed of upper and lower parts, the structures of the upper and lower parts can be completely identical, and the upper and lower parts are connected by the connecting pillar 3; that is, the connecting pillar 3 is connected to both the upper and lower parts of the first planar unit 1 and the upper and lower parts of the second planar unit 2.

[0066] The first planar unit 1 includes: a first A pillar 11, a second A pillar 12, a third A pillar 13, a fourth A pillar 14, a fifth A pillar 15, and a sixth A pillar 16; the first A pillar 11 has a first A node P11 in its middle part, the first A node P11 is connected to the first end point of the second A pillar 12, the second end point of the second A pillar 12 is connected to the first end point of the third A pillar 13; the first end point of the fourth A pillar 14 is connected to the first end point of the fifth A pillar 15; the sixth A pillar 16 has a second A node P12 in its middle part, the second A node P12 is connected to the second end point of the fifth A pillar 15; The second A pillar 12 has a third A node P13 in the middle, and the fifth A pillar 15 has a fourth A node P14 in the middle. The first end of the connecting pillar 3 is connected to the third A node P13, and the second end of the connecting pillar 3 is connected to the fourth A node P14. It can be understood that the first A pillar 11, the second A pillar 12, the third A pillar 13, the fourth A pillar 14, the fifth A pillar 15, the sixth A pillar 16, and the connecting pillar 3 are located in the same plane. Specifically, the third A node P13 is located at the center of symmetry of the second A pillar 12, and the fourth A node P14 is located at the center of symmetry of the fifth A pillar 15.

[0067] The second planar unit 2 includes a first B-pillar 21, a second B-pillar 22, a third B-pillar 23, a fourth B-pillar 24, a fifth B-pillar 25, and a sixth B-pillar 26. The first B-pillar 21 has a first B-node P21 in its middle section, which connects to the first endpoint of the second B-pillar 22. The second endpoint of the second B-pillar 22 connects to the first endpoint of the third B-pillar 23. The first endpoint of the fourth B-pillar 24 connects to the first endpoint of the fifth B-pillar 25. The sixth B-pillar 26 has a second B-node P22 in its middle section, which connects to the second endpoint of the fifth B-pillar 25. The second B-pillar 22 has a third B-node P23 in its middle section. The fifth B-pillar 25 has a fourth B-node P24 in its middle section, connecting the first end of the connecting pillar 3 to the third B-node P23, and the second end of the connecting pillar 3 to the fourth B-node P24. It can be understood that the first B-pillar 21, the second B-pillar 22, the third B-pillar 23, the fourth B-pillar 24, the fifth B-pillar 25, the sixth B-pillar 26, and the connecting pillar 3 are located in the same plane. Specifically, the third B-node P23 is located at the center of symmetry of the second B-pillar 22, and the fourth B-node P24 is located at the center of symmetry of the fifth B-pillar 25. The third A-node P13 coincides with the third B-node P23, and the fourth A-node P14 coincides with the fourth B-node P24.

[0068] The first A pillar 11, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, the sixth B pillar 26, and the connecting pillar 3 are parallel to each other; the first A pillar 11, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, and the sixth B pillar 26 have the same length; adjacent unit cell structures 100 share the first A pillar 11, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, and the sixth B pillar 26. It is understandable that when multiple unit cell structures 100 are periodically arranged and interconnected in three-dimensional space, a portion of the structure of adjacent unit cell structures 100 can be shared. Specifically, the shared portion can be the first A pillar 11, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, and the sixth B pillar 26. Another portion of the structure of adjacent unit cell structures 100 can be in contact with each other. Specifically, the in contact with each other can be the endpoints of the first A pillar 11, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, and the sixth B pillar 26 that are away from the connecting pillar 3. Optionally, the cross-sectional shape of the first A pillar, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, the sixth B pillar 26, the second A pillar 12, the fifth A pillar 15, the second B pillar 22, the fifth B pillar 25, and the connecting pillar 3 can be circular, rectangular, square, or triangular, and this embodiment does not impose specific limitations on this. This embodiment does not impose specific limitations on the cross-sectional shape of the first A pillar, the third A pillar 13, the fourth A pillar 14, the sixth A pillar 16, the first B pillar 21, the third B pillar 23, the fourth B pillar 24, the sixth B pillar 26, the second A pillar 12, the fifth A pillar 15, the second B pillar 22, the fifth B pillar 25, and the connecting pillar 3, as long as a lattice piezoelectric metamaterial 200 with a non-zero piezoelectric coefficient can be achieved.

[0069] The piezoelectric metamaterial can be prepared by a three-dimensional additive manufacturing method, and the material can be a piezoelectric material with crystal symmetry of ∞ mm, mm2, 4 mm or 6 mm, such as piezoelectric ceramic or piezoelectric polymer.

[0070] Compared with existing technologies, the lattice piezoelectric metamaterial provided in this embodiment achieves at least the following beneficial effects:

[0071] This embodiment provides a lattice piezoelectric metamaterial. By analyzing the relationship between macroscopic effective stress and structural support stress, symmetry breaking can be achieved using the lattice piezoelectric metamaterial, thereby obtaining all non-zero piezoelectric coefficients. That is, by manipulating the geometric parameters of the three-dimensional lattice structure, the piezoelectric coefficients can be continuously manipulated in a wide range from positive to negative values. The constructed metamaterial exhibits all theoretically possible electromechanical coupling modes, that is, normal and shear stresses in any direction can produce electrical responses in all directions, and vice versa.

[0072] In some alternative embodiments, such as Figures 5 to 8 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other, and the connecting pillar 3 extends along the third direction Z. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the second direction Y and the third direction Z is a side view without symmetry.

[0073] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular, the connecting pillar 3 extends along the third direction Z, and the orthographic projection of the unit cell structure 100 on the plane jointly formed by the second direction Y and the third direction Z is a side view without symmetry; it can be understood that, as Figure 7 As shown, Figure 7 The orthographic projection of unit cell structure 100 onto the plane jointly formed by the second direction Y and the third direction Z has zero axes of symmetry for unit cell structure 100 in this orthographic projection. Figure 7 This is a side view without symmetry; that is, Figure 5 The orthographic projection of the unit cell structure 100 onto the plane jointly formed by the second direction Y and the third direction Z is a side view without symmetry; as shown... Figure 8 As shown, Figure 8 Let A be the orthographic projection of unit cell structure 100 onto the plane jointly formed by the first direction X and the third direction Z; where A-A' and B-B' are the axes of symmetry of the two unit cell structures 100 in this figure; that is to say... Figure 5 The orthographic projection of the unit cell structure 100 onto the plane formed by the first direction X and the third direction Z is a side view with a symmetry axis; the non-zero piezoelectric coefficient that can be obtained in this case can be d. 22 d 21 d 16 and d 34 .

[0074] In some alternative embodiments, such as Figure 9 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other, and the connecting pillar 3 extends along the third direction Z. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the first direction X and the third direction Z is a side view without symmetry.

[0075] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular, and the connecting pillar 3 extends along the third direction Z. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the first direction X and the third direction Z is a side view without symmetry; the orthographic projection of the unit cell structure 100 on the plane jointly formed by the second direction Y and the third direction Z is a side view with symmetry. The non-zero piezoelectric coefficient that can be obtained in this case can be d. 11 d 12 d 26 and d 35 .

[0076] In some alternative embodiments, such as Figure 10 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other. The connecting pillar 3 extends along the second direction Y. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the second direction Y and the third direction Z is a side view without symmetry.

[0077] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular. The connecting pillar 3 extends along the second direction Y. The orthographic projection of the unit cell structure 100 onto the plane jointly formed by the second direction Y and the third direction Z is a side view without symmetry; the orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the second direction Y is a side view with symmetry. The non-zero piezoelectric coefficient that can be obtained in this case can be d. 23 .

[0078] In some alternative embodiments, such as Figure 11 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other, and the connecting pillar 3 extends along the second direction Y. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the first direction X and the second direction Y is a side view without symmetry.

[0079] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular. The connecting pillar 3 extends along the second direction Y. The orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the second direction Y is a side view without symmetry; the orthographic projection of the unit cell structure 100 onto the plane jointly formed by the second direction Y and the third direction Z is a side view with symmetry. The non-zero piezoelectric coefficient that can be obtained in this case can be d. 25 and d 36 .

[0080] In some alternative embodiments, such as Figure 12 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other, and the connecting pillar 3 extends along the first direction X. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the first direction X and the third direction Z is a side view without symmetry.

[0081] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular. The connecting pillar 3 extends along the first direction X. The orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the third direction Z is a side view without symmetry; the orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the second direction Y is a side view with symmetry. The non-zero piezoelectric coefficient that can be obtained in this case can be d. 13 .

[0082] In some alternative embodiments, such as Figure 13 As shown, the first direction X, the second direction Y, and the third direction Z intersect each other. The connecting pillar 3 extends along the first direction X. The orthographic projection of the unit cell structure 100 on the plane jointly formed by the first direction X and the second direction Y is a side view without symmetry.

[0083] In the above embodiment, the first direction X, the second direction Y, and the third direction Z are mutually perpendicular. The connecting pillar 3 extends along the first direction X. The orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the second direction Y is a side view without symmetry; the orthographic projection of the unit cell structure 100 onto the plane jointly formed by the first direction X and the third direction Z is a side view with symmetry. The non-zero piezoelectric coefficient that can be obtained in this case can be d. 14 and d 36 .

[0084] In the design of lattice piezoelectric metamaterials, the electromechanical coupling effect of piezoelectric materials is related to the piezoelectric coefficient d. ij Related, such as Figure 14 As shown, the white background represents the inherent non-zero piezoelectric coefficient of the piezoelectric material, while the black background represents artificially created non-zero piezoelectric coefficients. The subscript i corresponds to the electric displacement direction, and the subscript j corresponds to the stress type (normal stress and shear stress). In piezoelectric ceramic theory, the polarization direction is set along the third direction Z. As shown in the white background, natural piezoelectric ceramics have only 5 non-zero piezoelectric coefficients, and due to symmetry, the number of independent coefficients is 3.

[0085] Here, we study all non-zero piezoelectric coefficients by designing a lattice piezoelectric metamaterial composed of multiple pillars. The design strategy is to control the relationship between the macroscopic electric displacement of the metamaterial and the electric displacement of the pillars by manipulating the orientation of each pillar. Under macroscopic stress, the internal pillars generate normal and shear stresses. By designing the orientation of each pillar, a rich variety of pillar stresses can be utilized to generate electric displacements in a specified direction. The macroscopic electric displacement of the metamaterial can be obtained by superimposing the electric displacements generated by the stresses of each pillar within the metamaterial. Therefore, the macroscopic electric displacement of a specified electromechanical coupling mode can be controlled by designing the spatial orientation of each pillar. Here, an eight-pillar structure is designed to manipulate the macroscopic piezoelectric coefficient, such as... Figure 15As shown, the design of structures with non-zero piezoelectric coefficients is inspired by mapping the electric displacement of eight pillars under different macroscopic stresses.

[0086] The piezoelectric matrix contains the piezoelectric constants, with coefficients related to normal stress and shear stress each occupying half of the matrix. Natural piezoelectric ceramics have five non-zero piezoelectric coefficients, such as... Figure 14 As shown against a white background. The spatial orientation of the pillars in an eight-pillar structure is determined by θ and... The determination aims to map the electrical displacement of the eight pillars under different global stresses.

[0087] For each column, the electric displacement of the column was studied under the macroscopic stress of the eight-column structure. The stress of the column inside the structure in the local coordinate system is σ. l The stress in global coordinates can be expressed as σ. m The transpose of a matrix can be represented by the superscript T.

[0088] σ m =Nσ l N T (1)

[0089] The coordinate transformation matrix is ​​N;

[0090]

[0091] like Figure 16 As shown, the stress state of each column of the eight-column structure differs under external normal or shear stress along different directions in the local and global coordinate systems. Figures 17 to 23 As shown, under different normal or shear stresses, the electric displacement of the support varies with the spatial direction. These changes correspond to different electromechanical coupling modes. The numbers (1-8) on the diagram correspond to the supports in different quadrants of the spatial coordinate system.

[0092] According to the piezoelectric equation, the electric displacement D of each support can be obtained. n as follows;

[0093] D n =d nm σ m (3)

[0094] Where, d nm It is the inherent piezoelectric coefficient of the piezoelectric ceramic; the piezoelectric coefficient of the substrate is obtained from PZT-5H (piezoelectric ceramic) in the material library, d 31 =d 32 = -276pC / N, d 33 =549pC / N, d 15 =d 24 =741pC / N.

[0095] The entire structure is subjected to macroscopic normal or shear stress σ in different directions. First, the local stress state of the first column under the applied macroscopic stress is represented using a unit cell in a local coordinate system. The overall force on the eight-column structure is set as F, with an equivalent cross-sectional area A. Then the force on each column is F / 4. The local stress σ of the column is... l The transformation matrix N can be written as:

[0096]

[0097] Where S represents the cross-sectional area of ​​the rod; substituting equations (2) and (4) into (1) and (3), we can obtain the electric displacement D of the support column under the load along the second direction Y. n ,

[0098]

[0099] Similarly, the electric displacement of the supports under external loads in different directions can be obtained from the above derivation process, including normal stress and shear stress (σ1 to σ6). The supports inside the structure experience various types of stress, thus obtaining the complete intrinsic force-electric coupling mode of the piezoelectric ceramic. Here, the overall force of the eight-support structure is set to F = 1 N. The geometric dimensions and physical parameters of the supports are as follows: r = 0.25 mm is the support radius, and L = 5 mm is the support length. It is worth noting that the orientation of the supports in different quadrants... The electric displacement ranges from positive to negative.

[0100] In addition, by adjusting the direction This allows for the control of the positive and negative electric displacement of each support. Under different normal and shear forces, the macroscopic electric displacement of the metamaterial is manipulated in different directions by designing the orientation of each support. The macroscopic non-zero electric displacement is obtained through symmetry breaking in the lattice piezoelectric metamaterial. The electric displacement of the support is related not only to the macroscopic stress but also to the spatial orientation of the support. This is relevant. To design the structure, the electrical displacement of the supports in all spatial directions is calculated.

[0101] The piezoelectric coefficient depends on stress and electric displacement. By applying different global normal and shear stresses, different values ​​of θ and θ were obtained. The electric displacements of the supports are calculated. These results, derived from previously derived formulas, show that the sign of the electric displacement of the support is determined by its coordinate quadrant. The electric displacement diagram of an eight-support structure can be plotted accordingly, as shown in the figure below. Figures 24 to 30 As shown, the electric displacement of the black bars in the box is positive, the electric displacement of the white bars is negative, and the black arrows represent macroscopic stress. First, for symmetrical structures, all global electric displacements are zero, as shown... Figure 24As shown on the left. It can be observed that in the symmetrical 8-pillar structure, the number of pillars with positive electric displacement is always the same as the number of pillars with negative electric displacement. To design lattice piezoelectric metamaterials with non-zero piezoelectric coefficients, it is necessary to forcibly break the symmetry of the structure.

[0102] Guided by the electric displacement diagram, piezoelectric metamaterials were designed by selecting pillars from an eight-pillar structure. Due to the symmetry of the piezoelectric coefficients, only seven structures with non-zero piezoelectric coefficients need to be shown. The remaining piezoelectric coefficients can be obtained by rotating the structure 90° around its axis. Figures 24 to 30 In this method, four supports with the same electric displacement are first selected from the eight supports in the structure, and then these four supports are replicated. Vertical or horizontal supports are used for connection and load-bearing in the middle and at the edges. This intentionally disrupts the symmetry of the structure in the corresponding directions, thereby obtaining a non-zero piezoelectric coefficient.

[0103] In manipulating the piezoelectric coefficient, under the same macroscopic stress conditions, the positive or negative electric displacement can be designed by adjusting the angle α or β; where α is the angle between connecting support 3 and the fifth support 25, 0° < α < 90° and 90° < α < 180°, and β is half the angle between the second support 12 and the second support 24, that is, the angle between the bisector of the angle between the second support 12 and the second support 24 and the second support 12, 0° < β < 90°. The following theoretical and numerical calculation results further verify this conclusion. To calculate the piezoelectric coefficient of the metamaterial, a macroscopic normal stress or shear stress needs to be applied to the piezoelectric metamaterial, such as... Figure 31 As shown. The electric displacement generated by the support under macroscopic stress can be calculated by equations (1) to (5). In order to calculate the equivalent piezoelectric coefficient of the piezoelectric metamaterial, a volume-averaged model is established;

[0104]

[0105] Where eff represents the macroscopically effective (electric displacement or stress); D n Represents electric displacement; N represents the maximum rod number; d is the differential symbol; σ M Indicates stress; i represents the support column L. i The number (i = 1-17), d nm The piezoelectric coefficient matrix of the substrate (n = 1, 2, or 3; m = 1, 2, 3, 4, 5, or 6; M = 1, 2, 3, 4, 5, or 6), Let represent the stress transformation matrix from the local coordinate system (xyz) to the global coordinate system (1-2-3). It is the stress of the support column in the local coordinate system (r = xx, yy, zz, xy, xz, yz), V i V is the volume of the support, V is the volume of the metamaterial, and δ is the volume of the support. MmIt is the symbol for Kronecker delta;

[0106] The geometric dimensions and physical parameters of the support are as follows: r = 0.25 mm is the radius of the support, L... p =5mm (p=1-8), L 17 =13mm, L q =2L p cosα(q=9-16). Figure 31 With d 22 Taking a unit cell structure as an example, we analyze the stress on each support. Since the stress distribution in the pure bending of a beam is antisymmetric with the neutral layer as the boundary, the contribution of bending moment to the piezoelectric response can be neglected in the theoretical model. The supports that contribute to the macroscopic piezoelectric response of the metamaterial are the inclined supports L1-L8, and the vertical supports L9 and L... 10 L 15 and L 16 Based on geometric symmetry, diagonal member L1 can represent all diagonal members, and L9 can represent all vertical supports.

[0107] By using the angle θ in equation (5) and Replacing these values ​​with angles α and β respectively yields the electric displacement of the inclined rod. The stress matrix of the vertical support in the global coordinate system can be directly written as:

[0108]

[0109] in, This indicates the stress in a vertical support column; In this context, 'i' represents the rod number, and 'm' is a tensor index representing the type of stress, for example... The stress component σ4 represents the rod numbered 1.

[0110] According to equation (6), the macroscopic electric displacement and macroscopic stress of the metamaterial can be written as follows:

[0111]

[0112]

[0113] Therefore, the piezoelectric coefficient of metamaterials can be obtained;

[0114]

[0115] Similarly, expressions for other equivalent piezoelectric coefficients of metamaterials can be obtained, and the calculation results are as follows: Figures 32 to 38 As shown.

[0116] Figures 31 to 39 This is the calculated result of the unit cell piezoelectric coefficient. Figure 31 For d 22Force analysis of the element, the arrow indicates the external force F / 4 in the second direction. Figure 32 This is a comparison between theoretical and numerical results. As the angle α changes, the piezoelectric coefficient changes from negative to positive, and the theoretical and numerical calculation results agree very well.

[0117] Figure 46 For an infinite periodic piezoelectric metamaterial model, it can be simulated using an equivalent 5×5×5 unit structure. Figure 47 To design geometric parameters α and To control the spatial orientation of the tilted support. The piezoelectric coefficient can be manipulated by controlling the orientation α of the three-dimensional lattice structure. Designed within a wide range from positive to negative.

[0118] The calculation results for different piezoelectric coefficients are as follows: Figures 32 to 38 As shown, β is fixed at 45°, and α varies continuously from 0° to 180°, as follows: Figure 47 As shown, the theoretical results and finite element results are in excellent agreement. Each designed piezoelectric metamaterial has a non-zero target piezoelectric coefficient value. Furthermore, by designing the angle α, all piezoelectric coefficients can be tuned within a wide range from positive to negative.

[0119] Furthermore, periodic piezoelectric metamaterials are used to simulate real-world cases with approximately infinite lattices. FEM (Finite Element Method) calculations were performed on a periodic piezoelectric metamaterial model, which can sufficiently simulate a 5×5×5 element structure, such as... Figure 46 As shown; the mechanical boundary conditions are set according to the type of piezoelectric coefficient, and the external load F is applied to the corresponding nodes, manifesting as macroscopic normal stress or shear stress of the metamaterial. The angle α changes continuously. The angles were set to 30° and 45° respectively. The piezoelectric coefficient can also be controlled; it is coupled with α, and the result resembles a trigonometric function curve. Each piezoelectric coefficient is symmetrical about the coordinate point (90°, 0°), and by manipulating the orientation of the three-dimensional lattice structure, piezoelectric coefficients can be designed over a wide range from positive to negative. Furthermore, when changing the sign of the piezoelectric coefficient, the designable metamaterials primarily depend on the angle α.

[0120] The previous results show that when β is 45°, the piezoelectric coefficient reaches its peak at approximately α = 60°. The piezoelectric coefficient can be further optimized by adjusting the metamaterial's topology. The structural design is based on a qualitative design of the piezoelectric response of the inclined support. In fact, the electric displacement of the vertical support also affects the equivalent piezoelectric coefficient of the metamaterial. The vertical support can be replaced with an inclined support for structural optimization to obtain a larger piezoelectric coefficient. The inclination angle γ controls the original vertical support, with the piezoelectric coefficient d... 22For example, finite element analysis was performed on piezoelectric metamaterial models (5×5×5 element structure) with different α and γ values. The piezoelectric coefficient d... 22 The absolute value has its maximum value at α = 30° and γ = 15°.

[0121] In summary, metamaterials with all non-zero piezoelectric coefficients were obtained through symmetry-breaking design of the lattice structure. The electric displacement mapping of the designable piezoelectric struts was investigated theoretically and numerically. Furthermore, the piezoelectric coefficients of the designed metamaterials can be controllably adjusted over a wide range from positive to negative using structural geometry parameters. The maximum piezoelectric coefficient range is 800 pC / N (PZT-5H).

[0122] 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 lattice piezoelectric metamaterial, characterized in that, In three-dimensional space, it includes multiple interconnected single-cell structures; The unit cell structure includes a first planar unit, a second planar unit, and connecting pillars; the first planar unit includes: a first A pillar, a second A pillar, a third A pillar, a fourth A pillar, a fifth A pillar, and a sixth A pillar; the first A pillar has a first A node in its middle portion, the first A node is connected to the first end point of the second A pillar, the second end point of the second A pillar is connected to the first end point of the third A pillar; the first end point of the fourth A pillar is connected to the first end point of the fifth A pillar; the sixth A pillar has a second A node in its middle portion, the second A node is connected to the second end point of the fifth A pillar; the second A pillar has a third A node in its middle portion, the fifth A pillar has a fourth A node in its middle portion, the first end point of the connecting pillar is connected to the third A node, and the second end point of the connecting pillar is connected to the fourth A node; The second planar unit includes a first B-pillar, a second B-pillar, a third B-pillar, a fourth B-pillar, a fifth B-pillar, and a sixth B-pillar; the first B-pillar has a first B-node in its middle portion, which is connected to the first end point of the second B-pillar, and the second end point of the second B-pillar is connected to the first end point of the third B-pillar; the first end point of the fourth B-pillar is connected to the first end point of the fifth B-pillar; the sixth B-pillar has a second B-node in its middle portion, which is connected to the second end point of the fifth B-pillar; the second B-pillar has a third B-node in its middle portion, and the fifth B-pillar has a fourth B-node in its middle portion; the first end point of the connecting pillar is connected to the third B-node, and the second end point of the connecting pillar is connected to the fourth B-node; The first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, the sixth B pillar, and the connecting pillar are parallel to each other; the first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, and the sixth B pillar have the same length; adjacent unit cell structures share the first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, and the sixth B pillar.

2. The lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the third direction, and the orthographic projection of the unit cell structure on the plane formed by the second direction and the third direction is a side view without symmetry.

3. The lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the third direction, and the orthographic projection of the unit cell structure on the plane formed by the first direction and the third direction is a side view without symmetry.

4. The lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the second direction, and the orthographic projection of the unit cell structure on the plane formed by the second direction and the third direction is a side view without symmetry.

5. A lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the second direction, and the orthographic projection of the unit cell structure on the plane jointly formed by the first direction and the second direction is a side view without symmetry.

6. The lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the first direction, and the orthographic projection of the unit cell structure on the plane formed by the first direction and the third direction is a side view without symmetry.

7. The lattice piezoelectric metamaterial according to claim 1, characterized in that, The first direction, the second direction, and the third direction intersect each other, the connecting pillar extends along the first direction, and the orthographic projection of the unit cell structure on the plane jointly formed by the first direction and the second direction is a side view without symmetry.

8. A lattice piezoelectric metamaterial according to claim 1, characterized in that, The cross-sectional shape of the first A pillar, the third A pillar, the fourth A pillar, the sixth A pillar, the first B pillar, the third B pillar, the fourth B pillar, the sixth B pillar, the second A pillar, the fifth A pillar, the second B pillar, the fifth B pillar, and the connecting pillar is circular, rectangular, square, or triangular.

9. A lattice piezoelectric metamaterial according to any one of claims 1-8, characterized in that, The multiple unit cell structures are arranged in a periodic manner.

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