Method for calculating magnetoelectric coefficient of multilayer nonlinear magnetostrictive piezoelectric composite material

Abstract

The application discloses a method for calculating magneto-electric coefficients of a multilayer nonlinear magnetostrictive and piezoelectric composite material, and is implemented according to the following steps: step (1): the magnetostrictive and piezoelectric composite material is composed of a magnetostrictive material with a magnetostrictive effect and a piezoelectric material with a piezoelectric effect; a constitutive equation of the magneto-electric coefficients of the magnetostrictive and piezoelectric composite material is given; step (2): according to the conclusion in step 1, a theoretical model for solving the magneto-electric coefficient components α 11 and α 33 is established; step (3): the theoretical model established in step (2) is discretized; step (4): according to the theoretical model for solving the magneto-electric coefficients α 11 and α 33 established in step (2), a finite program is written to complete the solution of the magneto-electric coefficient components in step (1). The composite material scale effect is considered by using the finite element method to simulate the real working condition of the magneto-electric composite material, and the obtained analytical expression is more reasonable and has strong universality.

Description

Technical Field

[0001] This invention belongs to the technical field of magnetoelectric coupling performance of magnetostrictive-piezoelectric composite materials, specifically involving a method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials. Background Technology

[0002] Existing research on solving the magnetoelectric coefficient of layered magnetostrictive-piezoelectric composites typically only focuses on two- or three-layer structures, failing to extend to multi-layer structures. Furthermore, the analysis of the scale effect on the magnetoelectric coefficient is not comprehensive enough, and the analytical models used are limited to a single stacking sequence, resulting in incomplete solutions for the magnetoelectric coefficient components. Therefore, these solutions are difficult to apply to subsequent studies, such as those on contact performance, cracking, and fatigue life. Summary of the Invention

[0003] This invention further addresses the above issues by extending the number of composite material layers to multiple layers. It comprehensively considers the influence of composite material structure and geometry on the magnetoelectric coefficient, presenting the results for magnetostrictive-piezoelectric composites in analytical form. Users no longer need to perform complex experiments or numerical calculations; they can directly calculate the magnetoelectric coefficient of the composite material based on its structure and operating mode. This significantly simplifies the design process for magnetoelectric composite electronic components and provides more reasonable and referable magnetoelectric coefficients for research on the contact performance and crack life prediction of magnetoelectric composite materials.

[0004] To achieve the above objectives, this invention provides the following technical solution: a method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials. This method employs a finite element program to calculate the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials. Specifically, it involves the deformation of a magnetostrictive material with a magnetostrictive effect under an applied magnetic field. This deformation, through strain transfer between contact surfaces, drives the piezoelectric material to generate an electric polarization reaction, achieving magnetoelectric coupling. The method then calculates the magnetoelectric coefficient, which describes the strength of this coupling. The specific steps are as follows:

[0005] Step (1): The magnetostrictive-piezoelectric composite material is composed of a magnetostrictive material with a magnetostrictive effect and a piezoelectric material with a piezoelectric effect; based on the properties of the magnetostrictive-piezoelectric composite material, the constitutive equation of the magnetoelectric coefficient of the magnetostrictive-piezoelectric composite material is given;

[0006] Step (2): Based on the conclusion in Step 1, establish a solution for the magnetoelectric coefficient component α. 11 With the magnetoelectric coefficient component α 33 Theoretical model;

[0007] Step (3): Discretize the theoretical model established in step (2);

[0008] Step (4): Based on the magnetoelectric coefficient α established in step (2), solve for the magnetoelectric coefficient α. 11 With α 33 Theoretical model, finite element program, complete the solution of magnetoelectric coefficient components in step (1). The specific steps of the finite element program solution are as follows:

[0009] Step ①: Establish a nonlinear magnetic-force coupling model for the magnetostrictive material and solve for its dynamic response. The dynamic response of the magnetostrictive material is driven by an external magnetic field. First, establish a nonlinear magnetic-force coupling model. To accurately describe the magnetization process of the magnetostrictive material, a nonlinear magnetization constitutive model is adopted. Then, solve for the dynamic response of the magnetostrictive material. During the solution process, the elastic field control equation, the magnetic field control equation, and the mechanical boundary conditions are introduced.

[0010] Step 2 establishes a linear force-electric coupling model to solve for the force and electric fields of the piezoelectric material. The dynamic response of the piezoelectric layer is driven by the strain transmitted through the connecting surface of the magnetostrictive material phase. It is assumed that the piezoelectric layer and the magnetostrictive layer are ideally connected. Considering that the strain of the piezoelectric layer is driven by the magnetostrictive layer and is within the linear elastic range, a linear piezoelectric constitutive model is adopted. To solve for the electric and elastic fields of the piezoelectric material, it is necessary to introduce the electric field control equation and the electric boundary conditions. The elastic field control equation and the mechanical boundary conditions of the piezoelectric material are consistent with those in step 1.

[0011] Step ③ stores the electric field obtained in step ②, and calculates the magnetoelectric coefficient using the magnetoelectric coefficient component calculation formula given in step (1);

[0012] Step 4: Perform a convergence check on the calculation results in Step 3. If converged, record the calculation results; if not converged, check the above steps until convergence is achieved.

[0013] Step (5): Change the structure and geometry of the magnetostrictive-piezoelectric composite material, repeat step (4), and perform a large number of finite element numerical simulations;

[0014] Step (6): Summarize the finite element simulation results from step (5) and perform formula fitting.

[0015] Preferably, step 1 specifically includes the following steps:

[0016] Step 1.1: The selected magnetostrictive material is a multilayer composite material, which is composed of alternating nonlinear magnetostrictive and piezoelectric materials; it belongs to transversely isotropic materials. Based on the properties of transversely isotropic materials, the parameter α used to describe the magnetoelectric coupling performance of the magnetostrictive phase and the piezoelectric phase of the magnetostrictive-piezoelectric composite material is used. ij Represented as:

[0017]

[0018] In the formula, H i (i = 1, 2, 3) represents the magnetic field components, E j (j=1,2,3) represents the electric field components; when the subscript i=j Establish a rectangular coordinate system (x, y, z). If we assume that xy is an isotropic plane, then α 11 =α 22 When the subscript i ≠ j, α ij =0;

[0019] Step 1.2: Based on the conclusion in Step 1.1, establish α. 11 With α 33 The theoretical model was used to solve the constitutive equation for the magnetoelectric coefficient of the magnetostrictive-piezoelectric composite material. The total length of the magnetostrictive-piezoelectric composite material is l, the width is w, and the total number of layers is n; the total number of magnetostrictive layers is i+1, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j, and the thickness of the j-th layer is k. p The total number of magnetostrictive layers is i, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j+1, and the thickness of the j-th layer is k. p The magnetization direction of the magnetic stretching layer is denoted by M, and the polarization direction of the piezoelectric layer is denoted by P;

[0020] The magnetoelectric coupling in magnetostrictive-piezoelectric composite materials is achieved through stress transfer between the magnetostrictive and piezoelectric layers. Based on this principle, a method for calculating the magnetoelectric coefficient α is established. 11 With α 33 Theoretical model of magnetoelectric coefficient.

[0021] Preferably, the nonlinear magnetization constitutive model of the magnetostrictive material in step (4) is as follows:

[0022]

[0023]

[0024] In the formula, m σ ij Indicates the stress in the magnetostrictive layer. m ε kl M represents the strain of the magnetic stretching layer. i E represents the magnetization intensity; E represents the elastic modulus of the magnetic stretching material; ν represents Poisson's ratio; M represents the magnetic stretching material. S λ is the saturation magnetic susceptibility. s χ represents the saturation magnetization. m Let μ0 be the initial magnetic susceptibility, and l(x) be the free permeability; l(x) is a function describing the nonlinear magnetization process. eff H represents the effective magnetic field. dev represents the deviation operator; Hi This represents the applied magnetic field, when calculating α 11 At that time, H i =[H x 0 0] T When calculating α 33 At that time, H i =[0 0 H z ] T .

[0025] Preferably, the linear piezoelectric constitutive model in step (4) is:

[0026] p σ ij = p c ijkl p ε kl -e kij E k

[0027] D i =e kij p ε kl +k ik E k

[0028] In the formula, p σ ij Indicates the stress in the piezoelectric layer. p ε kl E represents the strain of the piezoelectric layer. k Electric field strength, D i Indicates electric displacement. p c ijkl e represents the elastic constant of piezoelectric materials. kij piezoelectric constant, k ik Dielectric constant.

[0029] Preferably, the mechanical boundary conditions used in step (4) are: one end of the magnetostrictive-piezoelectric composite material is fixed, and the other end is free, i.e.:

[0030]

[0031] In the formula, m u1、 m u2、 m u3… m u i , m u i+1 This indicates that the displacement of the first, second, third...i, i+1 layers of magnetostrictive material is zero at x=0. p u1、 p u2、 p u3… p uj-1 , p u j This indicates that the displacement of the 1st, 2nd, 3rd...j-1th, jth layers of piezoelectric material is zero at x=0; m σ ij This indicates that the stress in the magnetostrictive material is zero at x = l. p σ ij This indicates that the stress in the piezoelectric material is zero at x = l.

[0032] Preferably, in step (4), the electrical boundary conditions are as follows: the bottom surface of the magnetostrictive-piezoelectric composite material is grounded, i.e., the bottom surface is a zero potential plane; an open circuit condition is adopted, and there are no free charges on the surface of the piezoelectric layer. The electrical boundary conditions of the piezoelectric layer are expressed as follows:

[0033]

[0034] In the formula, D z This represents the electric displacement in the z-direction of the piezoelectric material. This represents the potential of the composite piezoelectric material.

[0035] Preferably, the magnetoelectric coefficient α is calculated. 11 With α 33 The theoretical model for the magnetoelectric coefficient is as follows:

[0036] (1) Calculate the magnetoelectric coefficient component α 11 The theoretical model applies a DC magnetic field H along the x-direction. dc The magnetostrictive layer is magnetized along the x-direction, and through stress transfer, it drives the piezoelectric layer to polarize along the x-direction. The magnetoelectric coefficient component α 11 :

[0037]

[0038] In the formula, E x H represents the x-direction component of the electric field of the composite material. x This represents a DC magnetic field applied along the x-direction, with a magnitude of H. x =H dc H dc Indicates the magnitude of the applied DC magnetic field;

[0039] (2) Calculate the magnetoelectric coefficient component α 33 The theoretical model applies a DC magnetic field H along the z-direction. dc The magnetostrictive layer is magnetized along the z-direction, and through stress transmission, it drives the piezoelectric layer to polarize along the z-direction. Therefore, the magnetoelectric coefficient component α 33 :

[0040]

[0041] In the formula, E zH represents the z-component of the electric field of the composite material. z This represents the applied DC magnetic field along the z-direction, with a magnitude of H. z =H dc .

[0042] Preferably, in step (4), the dynamic response solution of the magnetostrictive layer is described: the mechanical boundary conditions, magnetostrictive material parameters, external excitation magnetic field and nonlinear magnetostrictive magnetization model are introduced into the elastic field control and magnetic field control equation to complete the solution of the elastic field and magnetic field of the magnetostrictive layer.

[0043] Step (4) describes the solution of the dynamic response of the piezoelectric layer: Based on the strain transfer achieved by the connection between the magnetostrictive layer and the piezoelectric layer, the mechanical boundary conditions, the electrical boundary, the piezoelectric material parameters, and the linear piezoelectric constitutive model, the elastic field control equation and the electrostatic control equation are introduced to complete the solution;

[0044] The governing equations for the elastic field, magnetic field, and electric field, neglecting body force, body current, and body charge, are expressed as follows:

[0045]

[0046] In the formula, m σ ij Indicates the stress in the magnetostrictive layer. p σ ij B represents the stress in the piezoelectric layer. i D represents the magnetic flux density. i Let denote the electric displacement, and “,j” denotes the partial derivative with respect to j.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] 1. Current research typically assumes homogeneity in composite materials, assuming that their magnetoelectric coefficients remain constant during operation and ignoring scale effects, which is clearly inconsistent with reality. This invention is based on the actual structure of magnetoelectric composite materials, which is more in line with actual production needs.

[0049] 2. The rationality and accuracy of the analytical expression have been improved. Existing analytical expressions for the magnetoelectric coefficient of magnetically stretched piezoelectric composites, derived theoretically, typically impose numerous constraints, thus their rationality needs improvement. By employing the finite element method, considering the scale effect of composite materials, and simulating the real-world working conditions of magnetoelectric composite materials, the resulting analytical expression is more reasonable and possesses strong versatility. Furthermore, extensive simulations have further enhanced its accuracy.

[0050] 3. This invention provides significant assistance for the structural design of electronic components that rely on the coupling properties of magnetoelectric composite materials. Currently, the design of magnetoelectric composite material structures typically requires extensive experimentation or numerical simulation to obtain the expected results. This process is time-consuming, labor-intensive, and requires experienced engineers. The analytical solution provided in this invention can be used to determine the coupling properties of magnetoelectric composite materials, greatly simplifying the electronic component design process. It can also be used as part of the composite material parameters for further research on aspects such as contact performance, cracking, and lifespan. Attached Figure Description

[0051] Figure 1 This is the theoretical model for calculating the magnetoelectric coefficient components of this invention;

[0052] Figure 2 This is a schematic diagram of the discrete mesh of the 7-layer composite material of the present invention;

[0053] Figure 3 This is the finite element model solution process of the present invention;

[0054] Figure 4 This is a diagram showing the electromagnetic field distribution inside the model for calculating different magnetoelectric coefficient components in this invention;

[0055] Figure 5 This is a diagram showing the relationship between the magnetoelectric coefficient and geometric dimensions of the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] Please see Figure 1-5 As shown, the present invention provides a technical solution: a method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials, which is implemented according to the following steps:

[0058] 1. Geometric model creation and mesh generation

[0059] To ensure sufficient accuracy in the finite element method (FEM) calculations, a hexahedral mesh was used to discretize the theoretical model, and mesh independence was verified. The mesh's degrees of freedom reached 2.4 × 10⁻⁶. 6 When the calculation requirements are met, this rule is followed for mesh discretization in subsequent calculations. Figure 2 A schematic diagram of the discrete mesh of a 7-layer composite material is given.

[0060] 2. Material parameters

[0061] Magnetoelectric composite materials include: Terfenol, CoFe2O4, Ni, Fe, and Co. The main parameter determining the performance of magnetically conductive composite materials is the magnetostriction coefficient λ. S The main raw materials for piezoelectric materials are piezoelectric ceramics: BaTiO3, PZT, and PMN-PT. The piezoelectric constant e is the parameter that determines the piezoelectric properties of the material. ij Both factors determine the magnetoelectric coupling performance α of the composite material. ij (i = j = 1, 2, 3). Typical materials were used in the study, and the material parameters are shown in Tables 1 and 2: E represents the elastic modulus, v represents Poisson's ratio, ρ represents density, M... S χ represents the saturation magnetization. m λ represents the initial magnetic susceptibility, and λs represents the saturation magnetic material scaling factor; e ij k represents the piezoelectric constant. ij This represents the dielectric constant.

[0062] Table 1. Material parameters of the magnetostrictive material Terfenol

[0063]

[0064] Table 2 Material parameters of PZT piezoelectric material

[0065]

[0066]

[0067] 3. Influence of composite material dimensions on magnetoelectric coefficient

[0068] like Figure 1 As shown, the magnetostrictive-piezoelectric composite material has a total length of l, a width of w, and a total number of layers of n; ① MA-PE-MA…MA-PE structure, Figure 1 As shown in (a) and (c), the total number of magnetostrictive layers is i+1, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j, and the thickness of the j-th layer is k. p ② PE-MA-PE…PE-MA structure, Figure 1 As shown in (b) and (d), the total number of magnetostrictive layers is i, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j+1, and the thickness of the j-th layer is k. p The magnetization direction of the magnetic stretching layer is denoted by M, and the polarization direction of the piezoelectric layer is denoted by P;

[0069] like Figure 1 As shown in (a)(b), a DC magnetic field H is applied along the x-direction. dc The magnetostrictive layer is magnetized along the x-direction, and through stress transfer, it drives the piezoelectric layer to polarize along the x-direction. The magnetoelectric coefficient component α is calculated.11 ;

[0070] Calculate the magnetoelectric coefficient component α 33 Theoretical models, such as Figure 1 As shown in (c)(d), a DC magnetic field H is applied along the z-direction. dc The magnetostrictive layer is magnetized along the z-direction, and through stress transfer, it drives the piezoelectric layer to polarize along the z-direction. The magnetoelectric coefficient component α is calculated. 33 ;

[0071] like Figure 4 , 5 As shown, the magnetoelectric coefficient of the composite material exhibits a strong size effect. Based on the finite element model established in step 6, the length l, width w, and layer thickness t = t of the composite material are varied. m =t p Finite element method was used to solve for the number of layers n to obtain the influence of a single parameter on the magnetoelectric coupling coefficient; the image was plotted using Origin 2022 software.

[0072] 4. Formula Fitting

[0073] An empirical formula for fitting the magnetoelectric coefficient of composite materials with respect to geometric dimensions was developed. The influence of individual parameters on the magnetoelectric coefficient of the composite material was obtained by varying the composite material's geometric dimensions: length l, width w, layer thickness t, and number of layers n. Figure 5 As shown. Denoted as: L = l / l0, W = w / w0, T = t / t0, H * =H / H0, where l0, w0, t0 = t m =t p H0, n.

[0074] Fitting the magnetoelectric coefficient α of the composite material ij The relationship between the geometric dimensions is as follows:

[0075]

[0076] In the formula, i = j = 1, 2;

[0077] a1 = -0.6046T 2 +1.1623T-0.28793

[0078] b1 = 0.62753L -0.61456

[0079] c1=-18.2384+8661.3837·0.09054 n

[0080] d1 = 8.95538W 2 -9.38054W +56.71288

[0081] In the formula, when i = j = 3;

[0082] a3 = 0.04459 - 0.2462 × 0.01096 T

[0083] b3 = 1.86281L + 10.60515

[0084] c3 = -29.71012 × (1-n) -1.19458 )

[0085] d3 = 1.65933W 2 -2.118W +20.13967

[0086] in conclusion:

[0087] Based on the properties of magnetostrictive-piezoelectric composite materials, a theoretical model for calculating the magnetoelectric coefficient of multilayer composite materials was established and solved using the finite element method. The differences in electromagnetic field distribution within the model used to calculate different magnetoelectric coefficient components were investigated. Through extensive numerical simulations, the laws governing the magnetoelectric coefficient of the composite material with respect to scale effects were summarized and finally presented in the form of analytical solutions, as shown in the following formula:

[0088]

[0089] In the formula, i = j = 1, 2;

[0090] a1 = -0.6046T 2 +1.1623T-0.28793

[0091] b1 = 0.62753L -0.61456

[0092] c1=-18.2384+8661.3837·0.09054 n

[0093] d1 = 8.95538W 2 -9.38054W +56.71288

[0094] In the formula, when i = j = 3;

[0095] a3 = 0.04459 - 0.2462 × 0.01096 T

[0096] b3 = 1.86281L + 10.60515

[0097] c3 = -29.71012 × (1-n) -1.19458 )

[0098] d3 = 1.65933W 2 -2.118W +20.13967.

[0099] This formula intuitively illustrates the relationship between the magnetoelectric coupling coefficient of a composite material and its geometric dimensions (length l, width w, layer thickness t, and number of layers n). The magnetoelectric coefficient of the material can be calculated based on its structure and dimensions without the need for experiments or numerical simulations.

[0100] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials, characterized in that, The calculation of the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials is achieved by writing a finite element program. That is, the magnetostrictive material with magnetostrictive effect is deformed under the drive of an external magnetic field. The piezoelectric material is driven to generate an electric polarization reaction through strain transfer between the contact surfaces, thus realizing magnetoelectric coupling. The process of calculating the magnetoelectric coefficient, which describes the strength of the magnetoelectric coupling performance, is also described. The specific steps are as follows: Step (1): The magnetostrictive-piezoelectric composite material is composed of a magnetostrictive material with a magnetostrictive effect and a piezoelectric material with a piezoelectric effect; based on the properties of the magnetostrictive-piezoelectric composite material, the constitutive equation of the magnetoelectric coefficient of the magnetostrictive-piezoelectric composite material is given; Step (2): Based on the conclusion in step (1), establish the solution for the magnetoelectric coefficient components. With magnetoelectric coefficient component Theoretical model; Step (3): Discretize the theoretical model established in step (2); Step (4): Based on the magnetoelectric coefficient established in step (2), solve for the magnetoelectric coefficient. and Theoretical model, write finite element program, complete the solution of magnetoelectric coefficient components in step (1), the specific solution steps of finite element program are as follows: step A nonlinear magnetic-mechanical coupling model of the magnetostrictive material is established to solve the dynamic response of the magnetostrictive material. The dynamic response of the magnetostrictive material is driven by an external magnetic field. First, a nonlinear magnetic-mechanical coupling model is established. In order to accurately describe the magnetization process of the magnetostrictive material, a nonlinear magnetization constitutive model is adopted. The dynamic response of the magnetostrictive material is solved. During the solution, the elastic field control equation, the magnetic field control equation and the mechanical boundary conditions are introduced. step Establish a linear force-electric coupling model to solve for the force and electric fields of piezoelectric materials; The dynamic response of the piezoelectric layer is driven by the strain transmitted by the magnetostrictive material phase through the interface. It is assumed that the piezoelectric layer and the magnetostrictive layer are ideally connected. Considering that the strain of the piezoelectric layer is driven by the magnetostrictive layer and is within the linear elastic range, a linear piezoelectric constitutive model is adopted. To solve for the electric and elastic fields of piezoelectric materials, it is necessary to introduce the electric field governing equations and electrical boundary conditions. The elastic field governing equations and mechanical boundary conditions for piezoelectric materials are then determined through the following steps. Maintain consistency; step For steps The solved electric field is stored, and the magnetoelectric coefficient is calculated using the magnetoelectric coefficient component calculation formula given in step (1). step For the steps The calculation results are then evaluated for convergence. If convergence is achieved, the results are recorded. If convergence is not achieved, the above steps are checked until convergence is achieved. Step (5): Change the structure and geometry of the magnetostrictive-piezoelectric composite material, repeat step (4), and perform a large number of finite element numerical simulations; Step (6): Summarize the finite element simulation results from step (5) and perform formula fitting; Step (1) specifically includes the following steps: Step 1.1: The selected magnetostrictive material is a multilayer composite material, which is composed of alternating nonlinear magnetostrictive and piezoelectric materials; parameters are used to describe the magnetoelectric coupling performance between the magnetically stretched phase and the piezoelectric phase of the magnetostrictive-piezoelectric composite material. Represented as: ； In the formula, Represents the magnetic field components. Indicates the electric field components; Current subscript hour, Establish a rectangular coordinate system (x, y, z). If we assume that xy is an isotropic plane, then... ; under current subscript hour, ; Step 1.2: Based on the conclusions in Step 1.1, establish... and The theoretical model was used to solve the constitutive equation for the magnetoelectric coefficient of the magnetostrictive-piezoelectric composite material. The total length of the magnetostrictive-piezoelectric composite material is l, the width is w, and the total number of layers is n; the total number of magnetostrictive layers is i+1, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j, and the thickness of the j-th layer is k. p The total number of magnetostrictive layers is i, and the thickness of the i-th layer is t. m The total number of piezoelectric layers is j+1, and the thickness of the j-th layer is k. p The magnetization direction of the magnetic stretching layer is denoted by M, and the polarization direction of the piezoelectric layer is denoted by P; The magnetoelectric coupling in magnetostrictive-piezoelectric composite materials is achieved through stress transfer between the magnetostrictive and piezoelectric layers. Based on this principle, a calculation method for the magnetoelectric coefficient is established. and Theoretical model of magnetoelectric coefficient.

2. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: The nonlinear magnetization constitutive model of the magnetostrictive material in step (4) is as follows: ； ； In the formula, Indicates the stress in the magnetostrictive layer. This indicates the strain of the magnetic stretching layer. The magnetization intensity is represented by E; the elastic modulus of the magnetic stretching material is represented by E. Represents Poisson's ratio. The saturation magnetic susceptibility, Indicates saturation magnetization. The initial magnetic susceptibility, Indicates the permeability of free space; Functions describing the nonlinear magnetization process Indicates the effective magnetic field. , Represents the deviation operator; Represents the magnetic field components, when calculating hour, When calculating hour, .

3. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: The linear piezoelectric constitutive model for step (4) is as follows: ； In the formula, Indicates the stress in the piezoelectric layer. Indicates the strain of the piezoelectric layer. electric field strength, Indicates electric displacement. This represents the elastic constant of piezoelectric materials. piezoelectric constant, Dielectric constant.

4. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: The mechanical boundary conditions used in step (4) are as follows: one end of the magnetostrictive-piezoelectric composite material is fixed, and the other end is free, i.e.: ； In the formula, This indicates that the magnetostrictive material in layers 1, 2, 3...i, i+1 is in... The displacement is zero at that point. This indicates that the 1st, 2nd, 3rd...j-1,jth layers of piezoelectric material are in... The displacement is zero at that point; Indicating magnetostrictive materials in The stress is zero at that point. Indicates that piezoelectric materials are in The stress at that point is zero.

5. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: The electrical boundary conditions in step (4) are as follows: the bottom surface of the magnetostrictive-piezoelectric composite material is grounded, that is, the bottom surface is a zero potential plane; an open circuit condition is adopted, and there are no free charges on the surface of the piezoelectric layer. The electrical boundary conditions of the piezoelectric layer are expressed as follows: ； In the formula, This represents the electric displacement in the z-direction of the piezoelectric material. This represents the potential of the composite piezoelectric material.

6. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: Calculate the magnetoelectric coefficient and The theoretical model for the magnetoelectric coefficient is as follows: (1) Calculate the magnetoelectric coefficient components The theoretical model applies a DC magnetic field H along the x-direction. dc The magnetostrictive layer is magnetized along the x-direction, and through stress transfer, it drives the piezoelectric layer to polarize along the x-direction. (Magnetoelectric coefficient component) : ； In the formula, This represents the x-direction component of the electric field of the composite material. This represents the DC magnetic field applied along the x-direction, with a magnitude of , Indicates the magnitude of the applied DC magnetic field; (2) Calculate the magnetoelectric coefficient components The theoretical model applies a DC magnetic field H along the z-direction. dc The magnetostrictive layer is magnetized along the z-direction, and through stress transmission, it drives the piezoelectric layer to polarize along the z-direction. Therefore, the magnetoelectric coefficient component... : ； In the formula, The z-component of the electric field of the composite material is represented. This represents the DC magnetic field applied along the z-direction, with a magnitude of .

7. The method for calculating the magnetoelectric coefficient of multilayer nonlinear magnetostrictive and piezoelectric composite materials according to claim 1, characterized in that: Step (4) describes the solution of the dynamic response of the magnetostrictive layer: introduce the mechanical boundary conditions, magnetostrictive material parameters, external excitation magnetic field and nonlinear magnetostrictive magnetization model into the elastic field control and magnetic field control equation to complete the solution of the elastic field and magnetic field of the magnetostrictive layer. Step (4) describes the solution of the dynamic response of the piezoelectric layer: Based on the strain transfer achieved by the connection between the magnetostrictive layer and the piezoelectric layer, the mechanical boundary conditions, the electrical boundary, the piezoelectric material parameters, and the linear piezoelectric constitutive model, the elastic field control equation and the electrostatic control equation are introduced to complete the solution; The governing equations for the elastic field, magnetic field, and electric field, neglecting body force, body current, and body charge, are expressed as follows: ； In the formula, Indicates the stress in the magnetostrictive layer. Indicates the stress in the piezoelectric layer. Indicates magnetic flux density. Let denote electric displacement, and ",j" denotes taking the partial derivative with respect to j.

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