Flexible piezoelectric composite material parameter optimization analysis method and system, medium, and terminal

Abstract

The present application relates to the technical field of flexible piezoelectric composite material, and particularly relates to a flexible piezoelectric composite material parameter optimization analysis method and system, medium and terminal.The method comprises the following steps: mesoscopic model establishment, piezoelectric ceramic fiber parameter analysis, interdigital electrode parameter analysis, macroscopic model establishment and parameter optimization.Through joint modeling analysis on mesoscopic scale and macroscopic scale and based on the analysis of the influence of the parameters of the flexible piezoelectric composite material on its performance from the aspect of the action mechanism, the parameters of the flexible piezoelectric composite material are optimized and adjusted from multiple scales, so as to effectively improve the performance of the flexible piezoelectric composite material and provide a reliable reference for the preparation of the flexible piezoelectric composite material.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric composite materials, and in particular to a parameter optimization analysis method, system, medium, and terminal for a flexible piezoelectric composite material. Background Art

[0002] Flexible piezoelectric composites (FPCs) are a new type of piezoelectric composite material that combines piezoelectric materials with flexible substrate materials in a specific proportion and structure. They possess both the electrical properties of piezoelectric materials and the mechanical properties of flexible substrate materials. FPCs primarily consist of piezoelectric ceramics, interdigitated electrodes, and a flexible polymer matrix. Due to their piezoelectric ceramics' electromechanical coupling conversion properties and high flexibility, FPCs are suitable for structural surfaces of varying curvatures. Furthermore, they offer advantages such as high strain energy density, directional actuation, flexibility, and durability, making them suitable for deployment in vibration monitoring and control of curved spacecraft structures, as well as other applications such as wearable devices and biomedical devices, and hold great promise for development.

[0003] Currently, many existing technologies only describe the FPC preparation process, without providing detailed descriptions of the specific dimensional parameters, component parameters, and other design details of each structure. However, the inventors have discovered that different designs of the FPC parameters can affect the FPC's flexibility, bendability, driving effect, polarization effect, electric field distribution, and other performance properties, thereby affecting the FPC's vibration sensing and actuation performance. This is crucial for the reliability and safety of vibration monitoring and vibration control applied to curved structures in spacecraft. In particular, when the application environment and the curvature of the controlled structural components differ, the requirements for the FPC's vibration sensing and actuation performance and flexibility also vary. Therefore, optimizing the design of FPC parameters based on application requirements is of great significance. Summary of the Invention

[0004] In order to solve the above-mentioned shortcomings in the prior art of FPC performance, the present invention provides a parameter optimization analysis method for a flexible piezoelectric composite material, comprising the following steps:

[0005] A mesoscopic model establishment step: at the mesoscopic scale, establishing a representative volume unit RVE model of the FPC based on the initial geometric parameters of the FPC, and constructing a structural model of the FPC, wherein the structural model includes at least piezoelectric ceramic fibers, a polymer matrix, and interdigital electrodes;

[0006] a piezoelectric ceramic fiber parameter analysis step; based on the representative volume unit RVE model, adjusting the volume fraction of the piezoelectric ceramic fiber to calculate the deformation of the RVE model under a preset voltage under different parameters, thereby obtaining the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant;

[0007] An interdigital electrode parameter analysis step: Based on the representative volume unit RVE model, adjusting the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, thereby obtaining the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect;

[0008] Macro model establishment step: On a macro scale, a homogenized model of the FPC is established, and the flexibility and piezoelectric constant of the FPC are calculated according to a mixing rule to obtain a relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC;

[0009] Parameter optimization step: According to the preset flexibility range requirements and piezoelectric constant requirements of the FPC, combined with the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC, the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes are derived.

[0010] In some embodiments, in the mesoscopic model establishment step, the structural model includes at least piezoelectric ceramic fibers, a polymer matrix, and interdigitated electrodes; the polymer matrix is ​​respectively located on opposite sides of the piezoelectric ceramic along the X direction to form a piezoelectric active layer with the piezoelectric ceramic, and the interdigitated electrodes are respectively located on opposite sides of the piezoelectric active layer along the Z direction, wherein the X direction is perpendicular to the Z direction; the structural model includes a d31-type structural model and a d33-type structural model with different polarization types; wherein the polarization type of the d31-type structural model is transverse polarization with a polarization direction perpendicular to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d31-type structural model are respectively located on the opposite surfaces of the flexible piezoelectric composite material sheet; the polarization type of the d33-type structural model is longitudinal polarization with a polarization direction parallel to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d33-type structural model are both located on the opposite surfaces of the flexible piezoelectric composite material sheet.

[0011] In some embodiments, the volume fraction of the piezoelectric ceramic fiber is satisfy: Where, is the width of the piezoelectric ceramic fiber, is the width of the polymer matrix.

[0012] In some embodiments, the spacing between adjacent interdigital electrodes is between 0.5 and 1 mm, and the width of the interdigital electrodes is between 0.8 and 1.5 mm.

[0013] In some embodiments, the interdigital electrode parameter analysis step further includes adjusting the width of the interdigital electrodes and performing a mechanical simulation under a preset stress applied to the RVE model to obtain a relationship between the width of the interdigital electrodes and the maximum stress in the RVE model;

[0014] The parameter optimization step also includes determining the width of the interdigital electrode according to the flexibility range requirement, the piezoelectric constant requirement, the maximum stress in the RVE model, and the proportion of the uniform polarization region.

[0015] In some embodiments, in the macro model building step, the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility of the FPC and the piezoelectric constant of the FPC is represented by a piezoelectric constitutive equation characterizing a flexible piezoelectric composite material;

[0016] The piezoelectric constitutive equation is expressed as:

[0017]

[0018]

[0019] Where, Expressed as the stiffness matrix of FPC under orthotropic conditions; Expressed as a piezoelectric coupling matrix; 、 、 It is expressed as the normal stress of the piezoelectric active layer in the x-axis, y-axis, and z-axis; 、 、 They are respectively represented as the shear stress of the piezoelectric active layer in the x-axis, y-axis and z-axis; 、 、 are the normal strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 are the shear strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric field strength of the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric displacements of the x-axis, y-axis, and z-axis respectively.

[0020] In some embodiments, the volume fraction of the piezoelectric ceramic fibers is between 70% and 85%.

[0021] In a second aspect, the present invention further provides a parameter optimization system for a flexible piezoelectric composite material, comprising:

[0022] A mesoscopic model building module; used to establish a representative volume unit RVE model of the FPC based on the initial geometric parameters of the FPC at the mesoscopic scale, and to construct a structural model of the FPC, wherein the structural model includes at least piezoelectric ceramic fibers, a polymer matrix, and interdigital electrodes;

[0023] a piezoelectric ceramic fiber parameter analysis module configured to adjust the volume fraction of the piezoelectric ceramic fiber based on the representative volume element RVE model to calculate the deformation of the RVE model under a preset voltage under different parameters, thereby obtaining a relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant;

[0024] an interdigital electrode parameter analysis module configured to adjust the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes based on the representative volume element RVE model to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, thereby obtaining the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes, and the polarization effect;

[0025] A macro model building module; used to establish a homogenized model of the FPC on a macro scale, and calculate the flexibility and piezoelectric constant of the FPC according to a mixing rule to obtain the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility of the FPC and the piezoelectric constant of the FPC;

[0026] A parameter optimization module is used to derive the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrode, and the spacing between adjacent interdigital electrodes based on the preset flexibility range and piezoelectric constant requirements of the FPC, combined with the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC.

[0027] In a third aspect, the present invention also provides a storage medium, which is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored. When the computer program is run by a processor, the parameter optimization analysis method of the flexible piezoelectric composite material described in the above embodiment is executed.

[0028] In a fourth aspect, the present invention also provides a terminal comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor operates the computer program, it executes the parameter optimization analysis method of the flexible piezoelectric composite material as described in the above embodiment.

[0029] Based on the above, compared with the existing technology, the parameter optimization analysis method of the flexible piezoelectric composite material provided by the present invention jointly models and analyzes the influence of the parameters of the flexible piezoelectric composite material on the performance based on the mechanism of action, thereby optimizing and adjusting the parameters of the flexible piezoelectric composite material from multiple scales to effectively improve the performance of the flexible piezoelectric composite material and provide a reliable reference basis for the preparation of flexible piezoelectric composite materials.

[0030] Other features and beneficial effects of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The objectives and other beneficial effects of the present invention can be achieved and obtained by the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work. The positional relationships described in the drawings in the following description are based on the directions of the components drawn in the diagrams, unless otherwise specified.

[0032] Figure 1 A flowchart of the steps of a parameter optimization analysis method for a flexible piezoelectric composite material provided by one embodiment of the present invention;

[0033] Figure 2a 、 Figure 2b Schematic diagrams of the d31 type FPC structure model and the d33 type FPC structure model respectively;

[0034] Figure 3a 、 Figure 3b Composition diagrams of the representative volume unit RVE models of d31-type FPC and d33-type FPC, respectively;

[0035] Figure 4a 、 Figure 4b Schematic diagrams of the internal electric field distribution of d31 type FPC and d33 type FPC respectively;

[0036] Figure 5a 、 Figure 5b Schematic diagrams of the relationship between the spacing between adjacent interdigital electrodes and the proportion of the uniform polarization area in d31-type FPC and d33-type FPC respectively;

[0037] Figure 6a 、 Figure 6bSchematic diagrams of the relationship between the width of the interdigital electrode and the proportion of the uniform polarization area in d31 type FPC and d33 type FPC respectively;

[0038] Figure 7 Schematic diagram of the relationship between the width of the interdigitated electrode and the maximum stress generated when an electric potential is applied;

[0039] Figure 8a 、 Figure 8b Schematic diagram of the relationship between the volume fraction of piezoelectric ceramic fibers and strain under the same electromechanical working conditions for d31-type FPC and d33-type FPC, respectively;

[0040] Figure 9 Schematic diagram of the relationship between the volume fraction of piezoelectric ceramic fibers and the Poisson's ratio of the FPC piezoelectric active layer;

[0041] Figure 10 Schematic diagram of the relationship between the volume fraction of piezoelectric ceramic fibers and the flexibility of the FPC piezoelectric active layer. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments; the technical features designed in different implementation modes of the present invention described below can be combined with each other as long as they do not conflict with each other; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0043] In the description of the present invention, it should be noted that all terms used in the present invention (including technical terms and scientific terms) have the same meanings as those generally understood by ordinary technicians in the field to which the present invention belongs, and should not be understood as limiting the present invention; it should be further understood that the terms used in the present invention should be understood to have the same meanings as these terms in the context of this specification and the relevant field, and should not be understood in an idealized or overly formal sense, unless explicitly defined as such in the present invention.

[0044] Currently, the component proportion parameters and the structure parameters of each component of the flexible piezoelectric composite material are not described in detail in the prior art, so in the preparation of the FPC, the component parameters of the FPC are generally designed only by relying on the existing experience and cannot be optimized and adjusted according to the application requirements. In addition, the existing model analysis method of the FPC generally adopts a simplified macro model. However, it is difficult to intuitively investigate the component and structure parameters of the FPC, and changing the component and structure parameters requires re-computing the constitutive equation of the simplified macro model, constructing the simplified model, which easily leads to problems such as complex calculation and large amount of calculation in the parameter design process.

[0045] Therefore, the present application provides a parameter optimization analysis method of a flexible piezoelectric composite material to effectively solve the above problems. The technical solutions of the present application are described and explained in detail through various specific embodiments in combination with the accompanying drawings.

[0046] Embodiment one

[0047] Please refer to Figure 1 The parameter optimization analysis method of the flexible piezoelectric composite material provided by the present embodiment comprises the following steps:

[0048] A mesoscopic model establishing step; on the mesoscopic scale, a representative volume element RVE model of the FPC is established based on the initial geometric parameters of the FPC, and a structure model of the FPC is constructed, the structure model at least comprising piezoelectric ceramic fibers, polymer matrix and interdigital electrodes.

[0049] In specific implementation, according to the structural characteristics that the piezoelectric ceramic fibers, the polymer matrix and the interdigital electrodes inside the FPC are periodically arranged, the present embodiment selects a micro unit containing piezoelectric ceramic fibers, polymer matrix and interdigital electrodes for unit periodicity research. The FPC can be regarded as a periodic RVE array, and the deformation and the electric field distribution of the FPC can be reflected by calculating the deformation and the electric field distribution of the RVE model under a certain voltage condition. Therefore, the present embodiment establishes the representative volume element RVE model of the FPC on the mesoscopic scale based on the initial geometric parameters of the FPC, and analyzes the influence of each parameter on the performance through the representative volume element RVE model of the FPC.

[0050] Preferably, the representative volume element RVE model comprises one piezoelectric ceramic fiber, two polymer matrices and three interdigital electrodes, and comprises a structure model and corresponding material properties. The material properties include the elastic modulus, Poisson's ratio, conductivity and other parameters of the materials used. For example, in the present embodiment, PZT-5H is preferably used for the piezoelectric ceramic fiber, epoxy resin is preferably used for the polymer matrix, and copper electrode is preferably used for the interdigital electrode, and the Young's modulus, shear modulus, Poisson's ratio, dielectric constant and piezoelectric constant of these materials can be obtained.

[0051] The structural model is, for example, Figure 2a 、 Figure 2b As shown, the polymer matrix is ​​located on opposite sides of the piezoelectric ceramic along the X direction to form a piezoelectric active layer with the piezoelectric ceramic, and the interdigitated electrodes are located on opposite sides of the piezoelectric active layer along the Z direction, wherein the X direction is perpendicular to the Z direction.

[0052] Generally, at present, the structural models mainly include d31 type structural model and d33 type structural model with different polarization types; Figure 2a The d31-type structural model shown and Figure 2b The parameter design and optimization process of the two are described in detail by taking the d33 type structural model shown as an example. Among them, the polarization type of the d31 type structural model is transverse polarization with the polarization direction perpendicular to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d31 type structural model are respectively located on the two opposite surfaces of the flexible piezoelectric composite material sheet; the polarization type of the d33 type structural model is longitudinal polarization with the polarization direction parallel to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d33 type structural model are both located on the two opposite surfaces of the flexible piezoelectric composite material sheet.

[0053] Piezoelectric ceramic fiber parameter analysis step: Based on the representative volume unit RVE model, adjust the volume fraction of the piezoelectric ceramic fiber to calculate the deformation of the RVE model under a preset voltage under different parameters, and then obtain the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant.

[0054] In specific implementation, in the process of optimizing the volume fraction of piezoelectric ceramic fibers in FPC, the volume fraction of piezoelectric ceramic fibers in FPC can be adjusted by adjusting the ratio of the width of piezoelectric ceramic fibers to the width of polymer matrix while ensuring the same width of RVE model, that is, the sum of the width of piezoelectric ceramic fibers and polymer matrix is ​​the same. satisfy: Where, is the width of the piezoelectric ceramic fiber, is the width of the polymer matrix. Under the same voltage conditions, calculating the deformation of the RVE model at different piezoelectric ceramic fiber volume fractions under a preset voltage can reveal the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant, and thus the relationship between the FPC's actuation displacement and the piezoelectric ceramic fiber volume fraction.

[0055] According to the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant, when the volume fraction of the piezoelectric ceramic fiber is increased, the model strain under the same preset voltage conditions increases, thereby effectively improving the piezoelectric performance of the FPC. In addition, when the volume fraction of the piezoelectric ceramic fiber is less than the preset value, the growth trend of the volume fraction of the piezoelectric ceramic fiber is slow. When the volume fraction of the piezoelectric ceramic fiber is greater than the preset value, increasing the fiber volume fraction will make the piezoelectric performance more significantly improved, that is, the volume fraction of the piezoelectric ceramic fiber should be set to be greater than the preset value. Then, when optimizing the specific parameters of the volume fraction of the piezoelectric ceramic fiber, the appropriate volume fraction of the piezoelectric ceramic fiber can be obtained based on the actual piezoelectric performance requirements and the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant. As an example, in this embodiment, the volume fraction of the piezoelectric ceramic fiber is preferably between 70% and 85%. More preferably, the volume fraction of the piezoelectric ceramic fiber is 75%.

[0056] Furthermore, the present invention also found that increasing the volume fraction of piezoelectric ceramic fibers will affect the mechanical properties of the piezoelectric active layer, thereby changing the flexibility and bendability of the FPC. Therefore, in the piezoelectric ceramic fiber parameter analysis step, the relationship between the mechanical properties of the FPC and the volume fraction of the piezoelectric ceramic fibers is also considered. Specifically, under the same force load, by adjusting different piezoelectric ceramic fiber volume fractions to calculate the RVE model strain of the FPC, the relationship between the mechanical properties of the FPC and the volume fraction of the piezoelectric ceramic fibers can be obtained. According to the relationship between the mechanical properties of the FPC and the volume fraction of the piezoelectric ceramic fibers, it can be seen that increasing the volume fraction of the piezoelectric ceramic fibers increases the stiffness of the piezoelectric active layer, thereby increasing the stiffness of the FPC and reducing the strain under the same force load, that is, the flexibility and bendability of the FPC are reduced.

[0057] Therefore, in the process of optimizing the volume fraction parameters of piezoelectric ceramic fibers, the actual piezoelectric performance requirements and the flexibility and bendability requirements can be comprehensively considered, and the actual volume fraction of piezoelectric ceramic fibers can be comprehensively determined through the relationship between the mechanical properties of FPC and the volume fraction of piezoelectric ceramic fibers, and the relationship between the volume fraction of piezoelectric ceramic fibers and the piezoelectric constant.

[0058] The interdigital electrode parameter analysis step; based on the representative volume unit RVE model, the width of the interdigital electrode and the spacing between adjacent interdigital electrodes are adjusted respectively to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, and then the relationship between the width of the interdigital electrode, the spacing between adjacent interdigital electrodes and the polarization effect is obtained.

[0059] In specific implementation, due to the presence of interdigital electrodes inside the FPC, the electric field distribution is uneven. According to the electric field distribution, the area inside the FPC can be divided into a dead zone and a uniform polarization zone, such as Figure 4a 、 Figure 4bAs shown in the figure, the dead zone refers to the region of the piezoelectric active layer located below the interdigitated electrodes. Within this region, the longitudinal electric field distribution is uneven, and the direction of the electric field lines varies significantly. The uniformly polarized region refers to the region of the piezoelectric active layer located between the two electrodes. Within this region, the longitudinal electric field distribution is uniform. When the FPC is polarized, the uniformly polarized region is polarized. And when the FPC is operating, the electric field in the uniformly polarized region is the primary operating field. Therefore, the proportion of the uniformly polarized region's length between the two electrodes is a key indicator affecting the FPC's sensing / actuation performance.

[0060] Furthermore, for the D33 type FPC in the D33 effect driving mode, its working electric field is parallel to the fiber direction, that is, the electric field along the Y-axis direction. Therefore, the Y component of the electric field strength is an important indicator affecting the sensing / actuation performance of the D33 type FPC; for the D31 type FPC in the D31 effect driving mode, its working electric field is perpendicular to the fiber direction, that is, the electric field along the Z-axis direction. Therefore, the Z component of the electric field strength is an important indicator affecting the sensing / actuation performance of the D31 type FPC.

[0061] To effectively illustrate the impact of the spacing between adjacent interdigital electrodes on the sensing / actuation performance of FPCs, the interdigital electrode parameter analysis step involves adjusting the spacing between adjacent interdigital electrodes in the RVE models of d31 and d33 FPCs and calculating the electric field distribution within the FPC under the same voltage. This reveals the relationship between the spacing between adjacent interdigital electrodes and the proportion of the uniformly polarized region between the two electrodes. This relationship indicates that increasing the spacing between adjacent interdigital electrodes increases the proportion of the uniformly polarized region between the two electrodes, thereby enhancing the FPC's polarization effect and improving the FPC's vibration sensing / actuation performance. Therefore, the spacing between adjacent interdigital electrodes can be determined based on the actual polarization effect requirements of the FPC. Furthermore, when the overall active area length of the FPC is constant, increasing the spacing between adjacent interdigital electrodes results in a reduction in the number of electrodes, lowering the overall voltage and, consequently, decreasing the sensing / actuation performance. The spacing between adjacent interdigital electrodes must match the active area length and interdigit width. Based on the above, in this embodiment, the spacing between adjacent interdigital electrodes is preferably between 0.5 and 1 mm, such as 0.5 mm, 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, 1 mm, etc. The specific spacing between adjacent interdigital electrodes can be inferred based on the requirements of actual application scenarios.

[0062] Furthermore, the interdigital electrode parameter analysis step also adjusts the width of the interdigital electrodes in the RVE model of the d31 type FPC and the d33 type FPC, and calculates the electric field distribution inside the FPC under the same voltage to obtain the relationship between the width of the interdigital electrodes and the proportion of the uniform polarization area. According to this relationship, it can be seen that increasing the width of the interdigital electrodes increases the proportion of the uniform polarization area, enhances the polarization effect of the FPC, and improves the sensing / actuation performance of the FPC. However, when the electrode width increases to a certain value, continuing to increase the width of the interdigital electrodes will cause the proportion of the uniform polarization area to decrease instead of increase. In other words, an excessively large electrode width will affect the polarization working area between the two electrodes. Therefore, according to the actual polarization effect requirements of the FPC, the proportion of the uniform polarization area can be determined. Then, according to the relationship between the width of the interdigital electrodes and the proportion of the uniform polarization area, and the relationship between the spacing between adjacent interdigital electrodes and the proportion of the uniform polarization area, the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes can be determined.

[0063] In addition, due to the significant difference in stiffness between the interdigital electrodes and the piezoelectric ceramic fibers and polymer matrix within the piezoelectric active layer, when the FPC is subjected to force during operation, stress concentration occurs in the contact area between the interdigital electrodes and the piezoelectric active layer, which can lead to electrode debonding or ceramic fiber fracture in severe cases. Therefore, the interdigital electrode parameter analysis step also includes adjusting the width of the interdigital electrodes and performing a mechanical simulation under a preset stress on the RVE model to obtain the relationship between the width of the interdigital electrodes and the maximum stress within the RVE model generated when an electric potential is applied. According to the relationship, increasing the width of the interdigital electrodes can effectively reduce the maximum stress within the FPC, thereby reducing the risk of electrode debonding or ceramic fracture within the FPC and improving the fatigue strength of the FPC. Therefore, when optimizing the width of the interdigital electrodes, the width of the interdigital electrodes can be determined based on a comprehensive consideration of the flexibility range requirements, the piezoelectric constant requirements, the maximum stress within the RVE model, and the proportion of the uniform polarization region. As an example, in this embodiment, the width of the interdigital electrodes is preferably between 0.8 and 1.5 mm. For example, 0.8mm, 0.9mm, 1mm, 1.1mm, 1.2mm, 1.3mm, 1.4mm, 1.5mm, etc.

[0064] Macro model establishment step: On a macro scale, a homogenized model of the FPC is established, and the flexibility and piezoelectric constant of the FPC are calculated according to the mixing rule to obtain the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility of the FPC and the piezoelectric constant of the FPC.

[0065] In specific implementation, by establishing a macroscopic homogenization model of FPC, the influence of the volume fraction of piezoelectric ceramic fibers in FPC on the characteristics of the piezoelectric active layer can be analyzed from a macroscopic perspective, providing a solid theoretical basis for the optimal design of component parameters.

[0066] Taking PZT-5H as an example, the piezoelectric constitutive equation of the piezoelectric ceramic fiber is constructed according to the material parameters of PZT-5H: ; Where, represents the stiffness matrix when the electric field is constant, Represents the dielectric constant matrix when the strain is constant (second-order tensor 3*3), Represents the stress constant coupling matrix (third-order tensor 3*6, unit C / m 2 ), is stress, For strain, is the electric field, is the electric displacement.

[0067] The piezoelectric constitutive equation of the flexible piezoelectric composite material is converted into the Voigt symbol matrix form:

[0068]

[0069] According to the mixing principle, assuming that the strain and electric field components parallel to the bonding surface of the two phases are uniform and equal in the two phases, the stress and electric displacement directions of the two phase materials are also uniform and equal if they are parallel to the normal direction of the bonding surface. 、 、 、 、 、 、 、 、 The same physical quantities are uniform in the two phases of the material, while the remaining physical quantities 、 、 、 、 、 、 、 、 The corresponding values ​​are contributed by the volume fraction of each component, where represents the volume fraction of ceramic fibers, represents the volume fraction of epoxy resin matrix.

[0070] The hybrid principle (also known as the uniform field assumption) is a simplified assumption made about the distribution of physical quantities such as strain, stress, electric field, and electric displacement in each phase of a flexible composite piezoelectric material when bridging the gap between macroscopic and mesoscopic mechanical properties. This hybrid principle assumption allows for a simplified approach to estimating the macroscopic response of flexible piezoelectric composites when analyzing them, without having to consider complex microstructural details. This is extremely useful for engineering applications and design, as it effectively reduces computational complexity and allows for the use of equivalent homogeneous material properties for structural analysis and design.

[0071] Therefore, based on the above assumptions, the following formula can be obtained: ; ; ; ; ; Where, is expressed as the normal stress of the piezoelectric active layer, is expressed as the shear stress of the piezoelectric active layer, is the normal strain of the piezoelectric active layer, is expressed as the shear strain of the piezoelectric active layer, Expressed as the electric field strength, Expressed as electric displacement.

[0072] Then, the values ​​of the parameters of the elastic stiffness matrix of the flexible piezoelectric composite material are also calculated according to the linear mixing principle, so the Young's modulus of the piezoelectric active layer is , shear modulus and Poisson's ratio It is the following formula: ; ; ; Where, Expressed as the elastic modulus of the piezoelectric active layer, Expressed as the shear modulus of the piezoelectric active layer, Expressed as the Poisson's ratio of the piezoelectric active layer.

[0073] The above formula can be used to obtain the equivalent mechanical parameters of the flexible piezoelectric composite material after homogenization based on the mechanical parameters of each component material of the flexible piezoelectric composite material, and to establish the mechanical model of the macroscopic homogenized material of the FPC. According to material mechanics, the detailed form of the stiffness matrix of the FPC flexible piezoelectric composite material is:

[0074]

[0075] Among them, the preparation process of FPC makes it show obvious anisotropy in mechanical properties. From the component parameter composition of the flexible piezoelectric composite material, it can be found that the material has two orthogonal symmetry planes. Therefore, the anisotropic stiffness matrix can be further simplified, and the material stiffness matrix under orthogonal anisotropy conditions is obtained as follows:

[0076]

[0077] Then, according to the orthotropic anisotropy of material mechanics, the calculation formula of each parameter of the stiffness matrix can be obtained as follows:

[0078] , , , , , , .

[0079] Under the first type of mechanical boundary and electrical boundary conditions, when the FPC is under constant stress or no external load is applied, the material will be deformed by the electric field. Therefore, the electromechanical coupling coefficient of the FPC is:

[0080]

[0081] Among them, each coefficient represents the stress generated along the perpendicular fiber polarization direction by the external electric field along the fiber polarization direction, or the charge generated along the perpendicular fiber polarization direction by the material strain applied without applying an external electric field. The principles of the other electromechanical coupling coefficients are the same. The piezoelectric coupling matrix can be obtained as follows:

[0082]

[0083] Combining the above formulas, the piezoelectric constitutive equation that characterizes the flexible piezoelectric composite material can be obtained as follows:

[0084]

[0085]

[0086] Where, 、 、 It is expressed as the normal stress of the piezoelectric active layer in the x-axis, y-axis, and z-axis; 、 、 They are respectively represented as the shear stress of the piezoelectric active layer in the x-axis, y-axis and z-axis; 、 、 are the normal strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 are the shear strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric field strength of the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric displacements of the x-axis, y-axis, and z-axis respectively.

[0087] It should be noted that the material properties of the above-mentioned piezoelectric active layer, including the stiffness matrix, the flexibility matrix, and the piezoelectric constant matrix, can all be calculated from the size and component parameters of the piezoelectric ceramic fibers, the size and component parameters of the polymer matrix, and the volume fraction of the piezoelectric ceramic fibers.

[0088] According to the above formula, when the volume fraction of piezoelectric ceramic fibers in the piezoelectric active layer is different, the material parameters and piezoelectric effect parameters of the piezoelectric active layer change with the volume fraction. Therefore, the flexibility and load strain of the FPC are mainly affected by the material flexibility, and the flexibility matrix is ​​controlled by parameters such as the elastic modulus, shear modulus, and Poisson's ratio of the piezoelectric active layer. The piezoelectric effect is mainly affected by the piezoelectric constant of the piezoelectric active layer. By calculating the material elastic modulus, shear modulus, Poisson's ratio, flexibility, and piezoelectric constant of the piezoelectric active layer under different conditions of the piezoelectric ceramic fiber volume fraction, the relationship between the piezoelectric ceramic fiber volume fraction and flexibility and bendability can be obtained. That is, by comprehensively considering the performance of the piezoelectric and mechanical properties of the FPC at different piezoelectric ceramic fiber volume fractions, the specific parameters of the piezoelectric ceramic fiber volume fraction can be obtained. In this embodiment, the piezoelectric ceramic fiber volume fraction is preferably between 70% and 85%, and the piezoelectric ceramic fiber volume fraction is more preferably 80%.

[0089] Parameter optimization step: According to the preset flexibility range requirements and piezoelectric constant requirements of the FPC, combined with the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC, the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes are derived.

[0090] During specific implementation, the application environment and the controlled structural components are first evaluated to select the appropriate flexibility range requirements and piezoelectric constant requirements, and then the parameters of the flexible piezoelectric composite material are designed in combination with the above steps.

[0091] To effectively illustrate the scheme of the above embodiments, the piezoelectric ceramic fiber adopts PZT-5H, the polymer matrix adopts epoxy resin, and the interdigital electrode adopts copper electrode as an example to analyze the parameter optimization of d31 type FPC and d33 type FPC respectively. Among them, the representative volume element RVE model of FPC includes one piezoelectric ceramic fiber, two epoxy resin matrices and three copper electrodes. The structure model of d31 type FPC is shown in Figure 3a , and the structure model of d33 type FPC is shown in Figure 3b .

[0092] The initial geometric parameters of FPC are set as shown in the following table:

[0093]

[0094] The material parameters of each component of the RVE model are shown in the following table:

[0095]

[0096] Then, based on the above established mesoscopic RVE model of FPC, the parameters of the interdigital electrode are adjusted, including the distance between adjacent interdigital electrodes and the width of the interdigital electrode. In adjusting the distance between adjacent interdigital electrodes of d31 type FPC and d33 type FPC to calculate the electric field distribution in the FPC under the action of the same voltage, the proportion of the uniform polarization region between the two electrodes increases, the polarization effect of the FPC is enhanced, and the performance of the FPC vibration sensing / actuation is improved. Therefore, by obtaining the relationship between the distance between adjacent interdigital electrodes and the proportion of the uniform polarization region, the relationship between the distance between adjacent interdigital electrodes and the polarization effect of the FPC can be obtained.

[0097] Specifically, for d31 type FPC, increasing the distance between adjacent interdigital electrodes increases the proportion of the uniform polarization region, enhances the polarization effect of the FPC, and improves the performance of the FPC vibration sensing / actuation, wherein the relationship between the distance between adjacent interdigital electrodes and the proportion of the uniform polarization region is shown in Figure 5a . For d33 type FPC, increasing the distance between adjacent interdigital electrodes increases the proportion of the uniform polarization region between the two electrodes, enhances the polarization effect of the FPC, and improves the performance of the FPC vibration sensing / actuation, wherein the relationship between the distance between interdigital electrodes and the proportion of the uniform polarization region is shown in Figure 5b ; that is, by increasing the distance between adjacent interdigital electrodes, the proportion of the uniform polarization region between the two interdigital electrodes can be effectively increased, thereby enhancing the sensing / actuation performance of the FPC.

[0098] Therefore, when designing the spacing between adjacent interdigital electrodes of d31-type FPC and d33-type FPC, the proportion of the uniform polarization area can be adjusted accordingly according to the actual sensing / actuation performance requirements of the FPC, thereby obtaining the appropriate parameters for the spacing between adjacent interdigital electrodes. In addition, since the overall active area length of the FPC is constant, increasing the spacing between adjacent interdigital electrodes will lead to a reduction in the number of electrodes, reducing the overall voltage and thus causing a decrease in sensing / actuation performance. The spacing between adjacent interdigital electrodes needs to match the active area length and the interdigital width. Therefore, the relationship between the number of electrodes and the spacing between adjacent interdigital electrodes can be further comprehensively considered to further optimize the parameters.

[0099] Furthermore, when adjusting the width of the interdigital electrodes of the d31 type FPC and the d33 type FPC to calculate the electric field distribution when the same voltage acts on the inside of the FPC, increasing the width of the interdigital electrodes can increase the proportion of the uniform polarization area, enhance the polarization effect of the FPC, and improve the sensing / actuation performance of the FPC. Therefore, by obtaining the relationship between the width of the interdigital electrodes and the proportion of the uniform polarization area, the relationship between the width of the interdigital electrodes and the polarization effect of the FPC can be obtained. Specifically, for the d31 type FPC, the relationship between the spacing between adjacent interdigital electrodes and the proportion of the uniform polarization area is as follows: Figure 6a As shown. Figure 6a It can be seen that when the width of the interdigital electrode is 0.125mm, the proportion of the uniform polarization area is the largest. When it is lower or higher than 0.125mm, the proportion of the uniform polarization area decreases. Therefore, the electrode width can be preferably set to 0.125mm. Similarly, for the d33 type FPC, the relationship between the spacing between adjacent interdigital electrodes and the proportion of the uniform polarization area is as follows: Figure 6b As shown. Figure 6b It can be seen that when the interdigital electrode width increases to above 0.125 mm, further increasing the interdigital electrode width causes the proportion of the uniform polarization area to decrease instead of increase. This shows that an excessively large electrode width affects the polarization working area between the two electrodes. Therefore, the preferred electrode width here is 0.125 mm.

[0100] In addition, due to the large gap between the stiffness of the copper electrode and the stiffness of the piezoelectric ceramic fibers and epoxy resin matrix in the piezoelectric active layer, when the FPC is subjected to force during operation, stress concentration will occur in the contact area between the interdigitated electrodes and the piezoelectric active layer. In severe cases, this may lead to electrode debonding or ceramic fiber breakage. Therefore, stress is applied to the RVE model of the FPC and mechanical simulation is performed. This simulation calculation is independent of the electrode distribution. The results of the FPC with the two polarization modes are the same. The relationship between the width of the interdigitated electrodes and the maximum stress in the RVE model can be obtained as follows: Figure 7 As shown, according to Figure 7It can be seen that increasing the width of the interdigital electrode can effectively reduce the maximum stress in the FPC, reduce the risk of electrode debonding or ceramic fracture in the FPC, and improve the fatigue resistance of the FPC. In particular, when the width of the interdigital electrode is greater than 0.1 mm, the maximum stress in the FPC is significantly reduced. Therefore, in consideration of the above, the width of the interdigital electrode is preferably 0.125 mm.

[0101] Next, the optimization design of the volume fraction of the piezoelectric ceramic fiber in the FPC is considered. Under the condition of ensuring the same width of the model, i.e., the same sum of the widths of the piezoelectric ceramic fiber and the epoxy resin, adjusting the ratio of the widths of the piezoelectric ceramic fiber and the epoxy resin can adjust the volume fraction of the piezoelectric ceramic fiber in the FPC. Therefore, by adjusting different parameters of the volume fraction of the piezoelectric ceramic fiber and calculating the strain of the RVE model of the FPC under the same voltage condition, the relationship between the actuation displacement of the FPC and the volume fraction of the piezoelectric ceramic fiber can be obtained. The relationship between the volume fraction of the piezoelectric ceramic fiber and the strain of the model under the same voltage condition in the d31 type FPC and the d33 type FPC is shown in Figure 8a , Figure 8b respectively. It can be seen from Figure 8a , Figure 8b that when the volume fraction of the piezoelectric ceramic fiber is less than 75%, the piezoelectric performance grows slowly with the increase of the volume fraction of the piezoelectric ceramic fiber, and when the volume fraction of the piezoelectric ceramic fiber is greater than 75%, the piezoelectric performance is improved more obviously by increasing the volume fraction of the piezoelectric ceramic fiber. Therefore, the volume fraction of the piezoelectric ceramic fiber is preferably equal to 75% here.

[0102] In addition, increasing the volume fraction of the piezoelectric ceramic fiber will affect the mechanical properties of the piezoelectric active layer and change the flexibility and bendability of the FPC. Therefore, the relationship between the volume fraction of the piezoelectric ceramic fiber and its mechanical properties is also studied here. By adjusting the volume fraction of the piezoelectric ceramic fiber and calculating the strain of the RVE model of the FPC under the same force load, the relationship between the mechanical properties of the FPC and the volume fraction of the piezoelectric ceramic fiber can be obtained. The relationship between the volume fraction of the piezoelectric ceramic fiber and the strain under the same force load in the d31 type FPC and the d33 type FPC is shown in Figure 8a , Figure 8b respectively. It can be seen from Figure 8a , Figure 8b that by increasing the volume fraction of the piezoelectric ceramic fiber, the stiffness of the piezoelectric active layer can be increased, and in turn the stiffness of the FPC can be increased, and the strain under the same force load can be reduced, i.e., the bendability is reduced. Therefore, considering the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric performance and the mechanical properties, it can be obtained from Figure 8a , Figure 8b that when the volume fraction of the piezoelectric ceramic fiber of the FPC is about 75%, the piezoelectric performance and the mechanical properties of the FPC both reach a high level. Here, the volume fraction of the piezoelectric ceramic fiber of the FPC is preferably 75%.

[0103] Next, a macroscopic homogenization model of FPC is established to analyze the influence of the volume fraction of the piezoelectric ceramic fiber of FPC on the characteristics of the piezoelectric active layer from a macroscopic perspective. According to the aforementioned piezoelectric constitutive equation for characterizing flexible piezoelectric composite materials, it can be seen that when the volume fraction of the piezoelectric ceramic fiber material in the piezoelectric active layer is different, the material parameters and piezoelectric effect parameters of the piezoelectric active layer change with the volume fraction. Therefore, the elastic modulus, shear modulus, Poisson's ratio, flexibility and piezoelectric constant of the piezoelectric active layer are calculated by adjusting the volume fraction of the piezoelectric ceramic fiber. Figure 9 As shown in the figure, as the piezoelectric ceramic fiber volume fraction increases, the elastic modulus and shear modulus of the material increase with increasing piezoelectric ceramic fiber content. The Poisson's ratio in all five directions increases with increasing piezoelectric ceramic fiber content, while the Poisson's ratio in one direction decreases with increasing piezoelectric ceramic fiber content, but the change is relatively small. The flexibility matrix calculated from these material elastic parameters shows that as the piezoelectric ceramic fiber volume fraction increases, the flexibility of the piezoelectric active layer decreases significantly, indicating a decrease in the bendability of the FPC. As the piezoelectric ceramic fiber volume fraction increases, the overall piezoelectric constant of the piezoelectric active layer increases in both the d33-type FPC and the d31-type FPC. This indicates that the piezoelectric effect of both the d33-type FPC in the d33 drive mode and the d31-type FPC in the d31 drive mode is enhanced, improving the piezoelectric properties.

[0104] Taking into account the piezoelectric and mechanical properties of d31 and d33 FPCs at different fiber volume fractions, when the piezoelectric ceramic fiber volume fraction is 80%, the piezoelectric and mechanical properties of the FPC are better. When the piezoelectric ceramic fiber volume fraction is higher than 80%, the piezoelectric properties are not significantly enhanced, and the FPC flexibility is significantly reduced, affecting its bendability. Therefore, the preferred piezoelectric ceramic fiber volume fraction is between 75% and 80%.

[0105] Finally, the application environment and controlled structural parts are evaluated, the appropriate flexibility range and piezoelectric characteristic requirements are selected, and the component parameters of the flexible piezoelectric composite material are designed to improve the actuation / sensing performance. While meeting the performance requirements, appropriate parameters are selected to reduce the production cost.

[0106] In summary, the flexible piezoelectric composite parameter optimization design method provided by the application uses multi-scale analysis modeling to study the influence of component parameters on the flexible piezoelectric composite FPC from the aspects of action mechanism and performance characterization, and can realize the design and selection of the component parameters of the flexible piezoelectric composite FPC according to application requirements. The method has the following advantages: 1. Through multi-scale modeling analysis, the action mechanism and performance characterization can be combined, and the influence of the fiber volume fraction on the sensing-actuating output and the flexibility of the sensing-actuator can be considered comprehensively. 2. The existing method cannot directly represent and modify the component and structure parameters of the flexible piezoelectric composite, while the parameter optimization design method of the application can not only modify the required design parameters in real time, but also can directly observe the relationship between the parameters and the required FPC performance through the simulation results of the multi-scale model.

[0107] Embodiment two

[0108] The embodiment two of the application further provides a flexible piezoelectric composite parameter optimization system, which at least comprises:

[0109] A mesoscale model establishing module; a representative volume element RVE model of the FPC is established based on the initial geometric parameters of the FPC at a mesoscale, and a structure model of the FPC is constructed, the structure model at least comprising piezoelectric ceramic fibers, a polymer matrix and interdigital electrodes;

[0110] A piezoelectric ceramic fiber parameter analysis module; based on the representative volume element RVE model, the volume fraction of the piezoelectric ceramic fibers is adjusted to calculate the deformation amount of the RVE model under the action of a preset voltage under different parameters, and then the relationship between the volume fraction of the piezoelectric ceramic fibers and the piezoelectric constant is obtained;

[0111] An interdigital electrode parameter analysis module; based on the representative volume element RVE model, the width of the interdigital electrodes and the distance between adjacent interdigital electrodes are adjusted respectively to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, and then the relationship between the width of the interdigital electrodes, the distance between adjacent interdigital electrodes and the polarization effect is obtained;

[0112] A macroscopic model establishing module; a homogenization model of the FPC is established at a macroscopic scale, the compliance and the piezoelectric constant of the FPC are calculated according to the mixing rule, so as to obtain the relationship between the volume fraction of the piezoelectric ceramic fibers and the compliance of the FPC and the piezoelectric constant of the FPC;

[0113] Parameter optimization module: based on the preset flexibility range requirements and piezoelectric constant requirements of the FPC, combined with the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC, the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes are derived.

[0114] The system uses joint modeling and analysis at the mesoscale and macroscale, and analyzes the influence of the parameters of the flexible piezoelectric composite material on the performance based on the mechanism of action, thereby optimizing and adjusting the parameters of the flexible piezoelectric composite material from multiple scales, effectively improving the performance of the flexible piezoelectric composite material, and providing a reliable reference for the preparation of the flexible piezoelectric composite material. The specific manner in which the operations of each module in the above-mentioned embodiment 2 are performed has been described in detail in the embodiment 1 of the method, and will not be elaborated here.

[0115] Example 3

[0116] An embodiment of the present invention also provides a storage medium, which is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the parameter optimization analysis method of the flexible piezoelectric composite material described in any of the above embodiments.

[0117] In a specific implementation, the storage medium is a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory, a hard disk drive (HDD) or a solid-state drive (SSD), etc.; the storage medium may also include a combination of the above types of memory.

[0118] Example 4

[0119] An embodiment of the present invention also provides a terminal, which includes a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor runs the computer program, it executes the parameter optimization analysis method of the flexible piezoelectric composite material described in any of the above embodiments.

[0120] In a specific implementation, the number of processors may be one or more, and the processor may be a central processing unit (CPU). The processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or a combination of the above chips. The general-purpose processor may be a microprocessor or any conventional processor.

[0121] The memory and the processor can be communicatively connected via a bus or other means. The memory stores program instructions that can be executed by at least one processor. The program instructions are executed by at least one processor so that the processor executes the parameter optimization analysis method of the flexible piezoelectric composite material as described in any of the above embodiments.

[0122] In summary, the parameter optimization and analysis method and system of the flexible piezoelectric composite material provided by the present invention, the medium, and the terminal are designed through the mesoscopic model establishment step, the piezoelectric ceramic fiber parameter analysis step, the interdigitated electrode parameter analysis step, the macroscopic model establishment step, and the parameter optimization step. It can jointly model and analyze at the mesoscopic scale and the macroscopic scale and analyze the influence of the parameters of the flexible piezoelectric composite material on its material properties, electric field distribution, polarization effect and other performance aspects based on the action mechanism and performance characterization level, thereby realizing the design and optimization adjustment of the parameters of the flexible piezoelectric composite material at multiple scales, so as to effectively improve the performance of the flexible piezoelectric composite material and provide a reliable reference basis for the preparation of flexible piezoelectric composite materials.

[0123] In addition, those skilled in the art should understand that, although there are many problems in the prior art, each embodiment or technical solution of the present invention may be improved in only one or several aspects, without having to simultaneously solve all the technical problems listed in the prior art or background art. Those skilled in the art should understand that any content not mentioned in a claim should not be construed as limiting the claim.

[0124] Although the terms such as mesoscopic model establishing step, piezoelectric ceramic fiber parameter analyzing step, interdigital electrode parameter analyzing step, macroscopic model establishing step, parameter optimizing step, representative volume element RVE model, piezoelectric ceramic fiber, polymer matrix, interdigital electrode, etc. are used more in this article, the possibility of using other terms is not excluded. The use of these terms is only for more convenient description and explanation of the essence of the present application; any kind of additional limitation by interpreting them is contrary to the spirit of the present application; the terms "first", "second", etc. (if any) in the specification and claims of the embodiments of the present application and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence.

[0125] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A parameter optimization analysis method for a flexible piezoelectric composite material, characterized in that: The following steps are involved: A mesoscopic model establishment step: at the mesoscopic scale, establishing a representative volume unit RVE model of the FPC based on the initial geometric parameters of the FPC, and constructing a structural model of the FPC, wherein the structural model includes at least piezoelectric ceramic fibers, a polymer matrix, and interdigital electrodes; a piezoelectric ceramic fiber parameter analysis step; based on the representative volume unit RVE model, adjusting the volume fraction of the piezoelectric ceramic fiber to calculate the deformation of the RVE model under a preset voltage under different parameters, thereby obtaining the relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant; An interdigital electrode parameter analysis step: Based on the representative volume unit RVE model, adjusting the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, thereby obtaining the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes and the polarization effect; Macro model establishment step: On a macro scale, a homogenized model of the FPC is established, and the flexibility and piezoelectric constant of the FPC are calculated according to a mixing rule to obtain a relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC; Parameter optimization steps; According to the preset flexibility range requirements and piezoelectric constant requirements of the FPC, the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrode and the spacing between adjacent interdigital electrodes are derived in combination with the relationship between the width of the interdigital electrode, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC.

2. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 1, characterized in that: In the mesoscopic model establishment step, the structural model includes at least piezoelectric ceramic fibers, a polymer matrix, and interdigital electrodes; the polymer matrix is ​​respectively located on opposite sides of the piezoelectric ceramic along the X direction to form a piezoelectric active layer with the piezoelectric ceramic, and the interdigital electrodes are respectively located on opposite sides of the piezoelectric active layer along the Z direction, wherein the X direction is perpendicular to the Z direction; The structural model includes a d31-type structural model and a d33-type structural model with different polarization types; wherein, the polarization type of the d31-type structural model is transverse polarization with the polarization direction perpendicular to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d31-type structural model are respectively located on the opposite surfaces of the flexible piezoelectric composite material sheet; the polarization type of the d33-type structural model is longitudinal polarization with the polarization direction parallel to the surface of the flexible piezoelectric composite material sheet, and the positive and negative poles of the interdigitated electrodes in the d33-type structural model are both located on the opposite surfaces of the flexible piezoelectric composite material sheet.

3. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 1, characterized in that: The volume fraction of the piezoelectric ceramic fiber satisfy: Where, is the width of the piezoelectric ceramic fiber, is the width of the polymer matrix.

4. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 1, characterized in that: The distance between adjacent interdigital electrodes is between 0.5 and 1 mm, and the width of the interdigital electrodes is between 0.8 and 1.5 mm.

5. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 1, characterized in that: The interdigital electrode parameter analysis step further includes adjusting the width of the interdigital electrodes and performing a mechanical simulation under a preset stress applied to the RVE model to obtain a relationship between the width of the interdigital electrodes and the maximum stress in the RVE model; The parameter optimization step also includes determining the width of the interdigital electrode according to the flexibility range requirement, the piezoelectric constant requirement, and the maximum stress and the proportion of the uniform polarization region in the RVE model.

6. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 4, characterized in that: In the macro model establishment step, the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility of the FPC and the piezoelectric constant of the FPC is represented by a piezoelectric constitutive equation characterizing a flexible piezoelectric composite material; The piezoelectric constitutive equation is expressed as: Where, Expressed as the stiffness matrix of FPC under orthotropic conditions; Expressed as a piezoelectric coupling matrix; 、 、 It is expressed as the normal stress of the piezoelectric active layer in the x-axis, y-axis, and z-axis; 、 、 They are respectively represented as the shear stress of the piezoelectric active layer in the x-axis, y-axis and z-axis; 、 、 are the normal strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 are the shear strains of the piezoelectric active layer in the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric field strength of the x-axis, y-axis, and z-axis, respectively. 、 、 They are represented as the electric displacements of the x-axis, y-axis, and z-axis respectively.

7. The parameter optimization analysis method for a flexible piezoelectric composite material according to claim 1, characterized in that: The volume fraction of the piezoelectric ceramic fibers is between 70% and 85%.

8. A parameter optimization system for a flexible piezoelectric composite material, characterized in that: include: Mesoscopic model building module; Used to establish a representative volume unit RVE model of the FPC based on the initial geometric parameters of the FPC at a mesoscopic scale, and construct a structural model of the FPC, wherein the structural model at least includes piezoelectric ceramic fibers, a polymer matrix, and interdigital electrodes; a piezoelectric ceramic fiber parameter analysis module configured to adjust the volume fraction of the piezoelectric ceramic fiber based on the representative volume element RVE model to calculate the deformation of the RVE model under a preset voltage under different parameters, thereby obtaining a relationship between the volume fraction of the piezoelectric ceramic fiber and the piezoelectric constant; an interdigital electrode parameter analysis module configured to adjust the width of the interdigital electrodes and the spacing between adjacent interdigital electrodes based on the representative volume element RVE model to calculate the electric field distribution between adjacent interdigital electrodes under the action of the preset voltage, thereby obtaining the relationship between the width of the interdigital electrodes, the spacing between adjacent interdigital electrodes, and the polarization effect; Macro model building module; Used to establish a homogenization model of the FPC on a macro scale, calculate the flexibility and piezoelectric constant of the FPC according to the mixing rule, so as to obtain the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility of the FPC and the piezoelectric constant of the FPC; Parameter optimization module; It is used to deduce the volume fraction of the piezoelectric ceramic fiber, the width of the interdigital electrode and the spacing between adjacent interdigital electrodes according to the preset flexibility range requirements and piezoelectric constant requirements of the FPC, combined with the relationship between the width of the interdigital electrode, the spacing between adjacent interdigital electrodes and the polarization effect, and the relationship between the volume fraction of the piezoelectric ceramic fiber and the flexibility and piezoelectric constant of the FPC.

9. A storage medium, characterized in that: The storage medium is a non-volatile storage medium or a non-transient storage medium, on which a computer program is stored. When the computer program is run by a processor, the parameter optimization analysis method of the flexible piezoelectric composite material according to any one of claims 1 to 7 is executed.

10. A terminal, characterized in that: It comprises a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and the processor executes the parameter optimization analysis method of the flexible piezoelectric composite material according to any one of claims 1 to 7 when running the computer program.

Images