Material structure damage identification method

Abstract

The invention discloses a material structure damage identification method, and relates to the technical field of structure health monitoring. The method comprises the following steps: establishing a three-dimensional spectrum unit model of a structure according to actual geometric dimensions and material parameters of the structure; based on geometric and position information of the crack, a virtual node method is introduced into the three-dimensional spectrum unit model for crack modeling; the PZT is arranged, and a PZT-structure electromechanical coupling system with cracks is formed; and the influence of different crack working conditions on the piezoelectric admittance curve of the structure is simulated. According to the method, the structural dynamic model is constructed based on the spectral element method, the real crack is geometrically embedded into the numerical model in a high-fidelity manner, high precision and high efficiency of crack modeling are realized on the premise of not needing to re-divide grids, crack damage in the structure is effectively identified by analyzing change characteristics of piezoelectric admittance response, and compared with an ideal crack model, the method has the advantages that the method is simple and convenient to implement. The method is closer to the actual crack form, improves the accuracy and applicability of damage identification, and has the outstanding advantages of high modeling efficiency, high damage sensitivity, wide engineering adaptability and the like.

Description

Technical Field

[0001] This application relates to the field of civil engineering structure monitoring and simulation technology, and in particular to a method for identifying material structure damage. Background Technology

[0002] In the field of structural health monitoring, piezoelectric admittance analysis is widely used for the identification and assessment of minute damage due to its advantages such as high sensitivity to changes in local structural stiffness, wide bandwidth, and fast response. This technology reflects subtle changes in the dynamic characteristics of a structure by measuring the admittance curve of a piezoelectric ceramic (such as PZT) sensor, thereby enabling rapid detection of early damage such as cracks. However, most current simulation studies based on piezoelectric admittance still rely on traditional low-order finite element models for numerical simulation. To accurately capture the dynamic response characteristics of a structure under high-frequency excitation, it is usually required to divide the model into at least 4 to 6 elements or 6 to 10 nodes in each wavelength range, leading to a sharp increase in the number of degrees of freedom and a significant rise in computational costs.

[0003] Furthermore, in modeling structures with cracks, existing methods often employ idealized crack morphologies (such as straight lines or regular geometries) or approximate actual crack boundaries through local mesh refinement. This not only increases modeling complexity but also fails to accurately reflect the irregularity of cracks and their impact on structural performance. Especially when there are many cracks or their geometric shapes are complex, frequent mesh reconstruction and local refinement severely limit modeling efficiency and engineering applicability.

[0004] Therefore, there is an urgent need for a method that can achieve high-fidelity crack modeling without re-meshing, in order to improve the accuracy and applicability of structural material health monitoring. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for identifying material structure damage in response to the above-mentioned technical problems.

[0006] The present invention adopts the following technical solution: This invention provides a method for identifying material structural damage, comprising: Obtain information on the geometric dimensions, material parameters, and crack geometry of the structure to be identified; A three-dimensional structural spectrum unit model of the structure to be identified is established based on geometric dimensions and material parameters. Based on the crack geometry, each three-dimensional structural element traversed by the crack is identified as a three-dimensional crack structural element. The three-dimensional crack structural element is then divided into two actual sub-regions using virtual nodes. These two actual sub-regions are then expanded outwards into virtual sub-regions, resulting in two virtual crack structural elements with the same size as the original three-dimensional crack structural element. Based on the node displacements within these two virtual crack structural elements, their displacement fields are determined and reconstructed using displacement field interpolation functions, yielding a three-dimensional crack structural element modeled with displacement discontinuities. Finally, based on the volumes of the two actual sub-regions and the three-dimensional crack structural element, the overall stiffness matrix, overall mass matrix, and overall damping matrix of the three-dimensional crack structural element modeled with displacement discontinuities are determined. PZT with piezoelectric and dielectric stiffness matrices is used as a three-dimensional piezoelectric spectral unit and coupled with a three-dimensional crack structure spectral unit modeled by displacement discontinuity to obtain a PZT-three-dimensional crack structure model; based on the global stiffness matrix, global mass matrix, global damping matrix, piezoelectric stiffness matrix and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established. Based on the dynamic equations of the PZT-3D crack structure model, frequency domain simulation is performed on the material to be identified to calculate the piezoelectric admittance value of the material to be identified at different frequencies; based on the piezoelectric admittance value, the severity of damage to the material to be identified is determined.

[0007] Preferably, the material to be identified includes homogeneous materials and heterogeneous materials.

[0008] Preferably, when the material to be identified is a homogeneous material, a three-dimensional structural spectral unit model of the material to be identified is established based on the geometric dimensions and material parameters, specifically including: The structure of the material to be identified is discretized into multiple three-dimensional structural spectrum units; Interpolation nodes inside the three-dimensional structural spectral unit are configured according to the Gauss-Lobatto-Legendre integration points to construct higher-order basis functions; The maximum size of the three-dimensional structural spectrum unit With the order of the Gauss-Lobatto-Legendre polynomial Satisfying the relation: ; In the formula, It is the minimum wavelength that propagates in the material structure at the excitation frequency.

[0009] Preferably, when the material to be identified is a heterogeneous material, a three-dimensional structural spectral unit model of the material to be identified is established based on the geometric dimensions and material parameters, specifically including: Based on the internal composition and microstructure of the material to be identified, a microscale model of the material is established; the microscale model of the material reflects the spatial distribution characteristics of each phase component and the characteristics of the interface transition zone in the material. The material mesoscale model is divided using several different mesh sizes to obtain multiple numerical models with different element sizes. For each numerical model, based on the volume fraction of each phase material in each element, the mechanical properties of the numerical model are homogenized using the composite material equivalence method, thus equivaling it to an isotropic medium element. Calculate the average value and standard deviation of the elastic modulus of each medium element, and obtain the coefficient of variation of the elastic modulus based on the average value and standard deviation. The coefficients of variation of the elastic modulus corresponding to all media elements are calculated sequentially to evaluate the characterization accuracy of the material's non-uniformity under different element sizes; Plot the relationship curve between the elastic modulus dispersion coefficient and the element size; identify the inflection point on the relationship curve, and take the element size corresponding to the inflection point as the characteristic element size; Based on the size of the feature unit, the structure of the material to be identified is discretized into multiple three-dimensional structural spectrum units; the order of the interpolation function of the three-dimensional structural spectrum unit is determined by the minimum wavelength propagating in the structure at the applied excitation frequency.

[0010] Preferably, the geometric morphology information of the material crack is obtained through CT scanning, three-dimensional laser scanning or image processing technology, including: the length, width, depth and orientation of the crack; the geometric morphology information of the material crack.

[0011] Preferably, the expression for the displacement field of the two virtual crack structure spectral elements is: ; In the formula, The shape function of the standard spectral unit, and These represent the displacement fields of two virtual crack structure spectral units, A and B, respectively. and These are the nodal displacement values ​​of two virtual crack structure spectrum elements A and B, respectively.

[0012] Preferably, based on the displacement fields of two virtual crack structural spectrum elements, the overall stiffness matrix, overall mass matrix, and overall damping matrix of all three-dimensional crack structural spectrum elements are determined, specifically including: By reconstructing the displacement field interpolation function, the displacement discontinuity of the 3D crack structure element caused by the crack is modeled without re-meshing. The formula is as follows: = ; In the formula, For the Heaviside function; Indicates from spatial coordinates The signed distance function to the crack is used to determine... The relative position of the crack; The numerical integral of the 3D crack structure spectrum element after modeling the displacement discontinuity is converted into a volume ratio. The global stiffness matrix, global mass matrix, and global damping matrix of the 3D crack structure spectrum element are then calculated using the following formulas: ; ; ; In the formula, and , and , and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit The element stiffness matrix, element mass matrix, and element damping matrix, and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit volume, The volume of the original unit; The strain matrix; It is the elasticity matrix; The density of the material; The stiffness matrix, mass matrix, and damping matrix of each three-dimensional crack structure spectrum element are grouped together to obtain the overall stiffness matrix, overall mass matrix, and overall damping matrix of all three-dimensional crack structure spectrum elements.

[0013] Preferably, based on the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established, specifically including: By introducing electromechanical coupling control equations and combining the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established, and the formula is as follows: ; In the formula, 、 、 、 、 、 、 and These are the global mass matrix, global damping matrix, global stiffness matrix, nodal displacement vector, equivalent potential vector, equivalent nodal force vector, global piezoelectric stiffness matrix, global dielectric stiffness matrix, and charge vector of the PZT-3D crack structure model.

[0014] Preferably, frequency domain simulation is performed on the material to be identified based on the dynamic equations of the PZT-three-dimensional crack structure model to calculate the piezoelectric admittance of the material at different frequencies, specifically including: When AC excitation voltages of different frequencies are applied to the material to be identified, the PZT-3D crack structure model of the material to be identified generates nodal potential and displacement responses of different frequencies. Based on the nodal potential and displacement response, the surface charge density at different frequencies of the PZT-three-dimensional crack structure model is calculated using the dynamic equation. Based on the AC excitation voltage and surface charge density at different frequencies, the piezoelectric admittance of the material to be identified at different frequencies is calculated using the following formula: ; In the formula, This is the piezoelectric admittance value. The imaginary unit, AC excitation voltage, The surface charge density is given by the PZT-3D crack structure model.

[0015] Preferably, the severity of damage to the material to be identified is determined based on the piezoelectric admittance value, specifically including: Based on the piezoelectric admittance values ​​of the material to be identified at different frequencies, piezoelectric admittance curves of the material to be identified are plotted. Extract the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified from the piezoelectric admittance curve; The root mean square error between the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified and the piezoelectric admittance signal under the undamaged state is calculated as the damage-sensitive feature of the material structure to be identified. Based on the damage-sensitive characteristics of the material structure to be identified and a preset root mean square deviation threshold, the degree of damage to the material structure is determined, including: When the damage sensitivity feature is greater than or equal to the preset root mean square deviation threshold, it indicates that the material structure to be identified has serious damage. When the damage sensitivity feature is less than the preset root mean square deviation threshold, it indicates that the material structure to be identified is in a healthy state or slightly damaged.

[0016] The above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects: In the material structure damage identification method provided by this invention, a structural dynamic model is established based on the spectral element method. Specifically targeting the numerical simulation requirements of piezoelectric admittance, high-order orthogonal polynomials are used as basis functions to construct the displacement field. While ensuring the accuracy of the structural response under high-frequency excitation, the number of model degrees of freedom is significantly reduced, thereby greatly improving the efficiency and stability of piezoelectric admittance calculation. Simultaneously, the virtual node method is introduced to achieve efficient embedding modeling of the real crack geometry without re-meshing. By reconstructing the crack boundary and simulating the discontinuity of the displacement field, the influence of cracks on the structural dynamic characteristics and piezoelectric admittance response is accurately reflected, improving the accuracy of structural material health monitoring. This effectively avoids the problems of high modeling complexity and poor adaptability caused by local mesh refinement in traditional finite element methods, supports rapid modeling of cracks of arbitrary shapes, and significantly improves the accuracy and applicability of piezoelectric admittance simulation in monitoring damaged structures. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0018] Figure 1 A flowchart illustrating a method for identifying material structure damage provided by the present invention; Figure 2 This is a flowchart of the structural spectrum unit modeling process for a material structure damage identification method provided by the present invention; Figure 3 This is a schematic diagram of a three-dimensional microstructure model of concrete for a material structure damage identification method provided by the present invention; Figure 4 This is a curve showing the variation of the elastic modulus dispersion coefficient with the element size in a material structure damage identification method provided by this invention, as well as a schematic diagram of the feature element size. Figure 5 This is a schematic diagram of a three-dimensional spectral unit model of concrete for a material structure damage identification method provided by the present invention; Figure 6 This is a flowchart of crack modeling based on the virtual node method for a material structure damage identification method provided by the present invention; Figure 7 This is a comparative schematic diagram of the finite element method and the virtual node method for simulating cracks in a material structure damage identification method provided by this invention. Figure 8 This is a schematic diagram of the coupled PZT and spectral unit model of a material structure damage identification method provided by the present invention; Figure 9 This is a cross-sectional view of cracks at different stages of uniaxial tensile stress on a concrete specimen, which is a material structure damage identification method provided by the present invention. Figure 10 This invention provides a method for identifying material structure damage, which uses a concrete specimen and a piezoelectric admittance curve calculated using the virtual node-spectral element method at different loading stages. Figure 11 This is a comparison chart of the root mean square deviation (RMSD) values ​​of the electrical conductivity curves based on the virtual node-spectral element method under different loading stages for concrete test blocks using a material structure damage identification method provided by this invention. Figure 12 This is a schematic diagram of cracks in a concrete specimen during the failure stage of a material structure damage identification method provided by the present invention. Figure 13 This is a comparison diagram of a model established based on finite element method and refined mesh before and after the appearance of cracks in a material structure damage identification method provided by the present invention. Figure 14 This is a comparison diagram of a model established based on the virtual node-spectral element method before and after the appearance of cracks in a material structure damage identification method provided by this invention; Figure 15 This is a comparison chart of conductivity curves based on the virtual node-spectral element method and the finite element method for identifying material structure damage provided by this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in the specification without creative effort are within the scope of protection of this application.

[0020] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0021] Figure 1 This is a schematic diagram of a material structure damage identification method according to the present invention, which specifically includes the following steps: S101: Obtain the geometric dimensions, material parameters, and crack geometry information of the structure to be identified.

[0022] Optionally, the material to be identified includes homogeneous and heterogeneous materials.

[0023] Optionally, the geometric morphology information of the material crack is obtained through CT scanning, three-dimensional laser scanning, or image processing technology, including: the length, width, depth, and orientation of the crack; the geometric morphology information of the material crack.

[0024] Specifically, the geometric morphology information of the actual crack is obtained, including crack length, width, depth, and orientation; this information can be obtained through CT scanning, three-dimensional laser scanning, or image processing technology.

[0025] S102: Based on geometric dimensions and material parameters, establish a three-dimensional structural spectrum unit model of the structure to be identified.

[0026] Optionally, when the material to be identified is a homogeneous material; based on geometric dimensions and material parameters, a three-dimensional structural spectral unit model of the material to be identified is established, specifically including: discretizing the structure of the material to be identified into multiple three-dimensional structural spectral units; configuring interpolation nodes inside the three-dimensional structural spectral units according to Gauss-Lobatto-Legendre integration points to construct higher-order basis functions; the maximum size of the three-dimensional structural spectral unit... With the order of the Gauss-Lobatto-Legendre polynomial Satisfying the relation: ; In the formula, It is the minimum wavelength that propagates in the material structure at the excitation frequency.

[0027] Optionally, when the material to be identified is a heterogeneous material; based on geometric dimensions and material parameters, a three-dimensional structural spectrum unit model of the material to be identified is established, specifically including: establishing a material mesoscale model according to the internal composition and microstructure of the material to be identified; the material mesoscale model reflects the spatial distribution characteristics of each phase component and the characteristics of the interface transition zone in the material; using several different grid sizes to divide the material mesoscale model to obtain multiple numerical models with different unit sizes; for each numerical model, based on the volume fraction of each phase material in each unit, the mechanical properties of the numerical model are homogenized using the composite material equivalence method, and it is equivalent to each The process involves: using isotropic dielectric elements; calculating the average and standard deviation of the elastic modulus of each dielectric element, and obtaining the coefficient of variation of the elastic modulus based on the average and standard deviation; sequentially calculating the coefficient of variation of the elastic modulus for all dielectric elements to evaluate the characterization accuracy of the material's non-uniformity under different element sizes; plotting the relationship curve between the coefficient of variation of the elastic modulus and the element size; identifying the inflection point on the relationship curve, and using the element size corresponding to the inflection point as the characteristic element size; discretizing the structure of the material to be identified into multiple three-dimensional structural spectrum elements based on the characteristic element size; and determining the order of the interpolation function of the three-dimensional structural spectrum elements by the minimum wavelength propagating in the structure at the applied excitation frequency.

[0028] Specifically, if the structural material is homogeneous (such as steel, aluminum, etc.), the structure can be directly discretized into a finite number of three-dimensional solid spectral elements. Interpolation nodes within the spectral elements are configured according to the Gauss-Lobatto-Legendre (GLL) integration points to construct higher-order basis functions to approximate the displacement field. The order of the Legendre polynomial used is generally between 2 and 7, specifically selected based on the structural response frequency range and computational resources; this is done to accurately simulate the structural dynamic response under high-frequency excitation while ensuring computational efficiency.

[0029] If the structural material is a heterogeneous material (such as concrete, composite materials, etc.), then a microscale model must first be established based on its internal composition and microstructure. This model should fully reflect the spatial distribution characteristics of each phase component (such as matrix, aggregate, pores, etc.) and the characteristics of the interface transition zone in the material.

[0030] In this example, the structural material is concrete, a typical heterogeneous material. Please refer to [link / reference]. Figure 3 The concrete microscale model consists of a three-phase composite structure composed of aggregate, mortar, and the interfacial transition zone (ITZ) between the two. Orange represents aggregate units, gray represents mortar units, and magenta represents ITZ units.

[0031] The microscopic model was divided using several different mesh sizes to obtain multiple numerical models with different element sizes. For each model, based on the volume fraction of each phase material in each element, the mechanical properties of the element were homogenized using a composite material equivalence method, thus equivaling it to an isotropic homogeneous medium element.

[0032] Specifically, the elastic modulus, shear modulus, and Poisson's ratio of the equivalent element are calculated using the following formula: ; In the formula, n represents the quantity of coarse aggregate, ITZ, and fine aggregate, and their respective volume fractions are as follows: ， ，......, The elastic moduli are respectively ， ，......， The shear moduli are respectively ， ，...... , Poisson's ratios are respectively ， ，......， , 、 and These are the elastic modulus, shear modulus, and Poisson's ratio of the equivalent element, respectively.

[0033] Based on the equivalent elastic modulus of each element, the average value and standard deviation of the elastic modulus in the model are calculated, and the dispersion coefficient of the elastic modulus is obtained accordingly. The dispersion coefficient of the elastic modulus of all models is calculated in turn using this method to evaluate the characterization accuracy of the material non-uniformity under different element sizes.

[0034] Specifically, the expression for the discrete coefficients of the model's elastic modulus is as follows: In the formula, This represents the average elastic modulus of the model. Standard deviation is the coefficient of variation of the elastic modulus.

[0035] Plot the relationship between the elastic modulus dispersion coefficient and the element size; identify the inflection point on the curve, and use the element size corresponding to the inflection point as the characteristic element size, thereby determining the optimal scale division standard that can take into account both the accuracy of the material's non-uniformity and the computational efficiency.

[0036] Please see Figure 4 Based on the curve of the elastic modulus dispersion coefficient versus element size, the model's modulus dispersion coefficient changes relatively little before the inflection point, indicating a small change in concrete heterogeneity; after the inflection point, the model's modulus dispersion coefficient decreases significantly, indicating a significant reduction in concrete heterogeneity. Therefore, the element size corresponding to the inflection point is the largest element size that can be divided under the premise that the concrete heterogeneity remains basically unchanged, making it suitable as the optimal scale for modeling. In this example, the feature element size is... .

[0037] Based on the characteristic element size, the structure is discretized into a finite number of three-dimensional spectral elements, thus forming a model where the properties within each element are the same and isotropic, while the properties between elements are different. Furthermore, by combining the minimum wavelength propagating in the structure at the excitation frequency, the order of the spectral element interpolation function is determined. For details, please refer to [link to relevant documentation]. Figure 5 In this example, the model is discretized into 14,450 spectral elements. Different elements have different colors, representing different mechanical properties. The number of interpolation nodes for the displacements (w, u, v) in the x, y, and z axes of each spectral element is 3, 3, and 2, respectively.

[0038] S103: Based on the crack geometry information, each three-dimensional structural spectrum element traversed by the crack is identified as a three-dimensional crack structural spectrum element; the three-dimensional crack structural spectrum element is divided into two actual sub-regions using virtual nodes, and the two actual sub-regions are expanded outward to form two virtual crack structural spectrum elements with the same size as the three-dimensional crack structural spectrum element; based on the node displacements within the two virtual crack structural spectrum elements, the displacement fields of the two virtual crack structural spectrum elements are determined and the displacement field interpolation function is reconstructed to obtain the three-dimensional crack structural spectrum element with displacement discontinuity modeling; and based on the volumes of the two actual sub-regions and the volume of the three-dimensional crack structural spectrum element, the overall stiffness matrix, overall mass matrix, and overall damping matrix of the three-dimensional crack structural spectrum element with displacement discontinuity modeling are determined.

[0039] Optionally, the expression for the displacement field of the two virtual crack structure element is: ; In the formula, The shape function of the standard spectral unit, and These represent the displacement fields of two virtual crack structure spectral units, A and B, respectively. and These are two virtual crack structure spectrum units. A and B The nodal displacement values.

[0040] Based on the displacement fields of two virtual crack structural element units, the global stiffness matrix, global mass matrix, and global damping matrix of all three-dimensional crack structural element units are determined. Specifically, this includes modeling the displacement discontinuity of the three-dimensional crack structural element units caused by cracks without re-meshing by reconstructing the displacement field interpolation function. The formula is as follows: = ; In the formula, For the Heaviside function; Indicates from spatial coordinates The signed distance function to the crack is used to determine... The relative position of the crack.

[0041] The numerical integral of the 3D crack structure spectrum element after modeling the displacement discontinuity is converted into a volume ratio. The global stiffness matrix, global mass matrix, and global damping matrix of the 3D crack structure spectrum element are then calculated using the following formulas: ; ; ; In the formula, and , and , and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit The element stiffness matrix, element mass matrix, and element damping matrix, and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit volume, The volume of the original unit; The strain matrix; It is the elasticity matrix; This represents the material density.

[0042] The stiffness matrix, mass matrix, and damping matrix of each three-dimensional crack structure spectrum element are grouped together to obtain the overall stiffness matrix, overall mass matrix, and overall damping matrix of all three-dimensional crack structure spectrum elements.

[0043] Specifically, please refer to Figure 6In some implementations, the process of embedding crack modeling based on the virtual node method specifically includes: identifying the spectral units traversed by the crack path in the established structural spectral unit model. The spectral units traversed by the crack are divided into two actual sub-regions. and To maintain the integrity of the original spectral unit shape functions, corresponding virtual subregions are extended outward from these two actual subregions respectively. and This forms two virtual crack structure spectrum units, A and B. The displacement field within these two virtual crack structure spectrum units can then be expressed as:

[0044] In the formula, The shape function of the three-dimensional crack structure spectral element. and These represent the displacement fields of two virtual crack structure spectral units, A and B, respectively. and These are the nodal displacement values ​​of two virtual crack structure spectrum elements A and B, respectively; The total displacement field within the spectral unit traversed by the crack can then be expressed as: By reconstructing the displacement field interpolation function, displacement discontinuities caused by cracks can be modeled without re-meshing. The complete displacement expression is as follows:

[0045] = ; In the formula, For the Heaviside function; Indicates from spatial coordinates The signed distance function to the crack is used to determine which side of the crack the point is located on.

[0046] Based on this, the numerical integral over the fracture element can be transformed into the ratio of the effective volume, with its stiffness matrix, mass matrix, and damping matrix as follows: In the formula, and , and , and They are respectively and Stiffness matrix, element mass matrix, and element damping matrix; and They are respectively and volume, The volume of the original unit; The strain matrix; It is the elasticity matrix; This represents the material density.

[0047] The element stiffness matrix, mass matrix, and damping matrix of all cracked sub-regions are grouped together to form the overall stiffness matrix, overall mass matrix, and overall damping matrix of the cracked structure, which are used for simulation analysis with piezoelectric admittance. Please see Figure 7 When simulating cracks using traditional mesh refinement methods, not only is it necessary to re-mesh the mesh, but new nodes are also generated, which leads to a significant increase in the number of degrees of freedom of the model and a substantial increase in computational cost. However, when using the virtual node method to model cracks, there is no need to re-mesh the original mesh or introduce new nodes, which can realize the modeling of displacement discontinuities caused by cracks, significantly improving modeling efficiency and flexibility.

[0048] S104: The PZT with piezoelectric stiffness matrix and dielectric stiffness matrix is ​​used as a three-dimensional piezoelectric spectral unit and coupled with the three-dimensional crack structure spectral unit modeled by displacement discontinuity to obtain the PZT-three-dimensional crack structure model; based on the global stiffness matrix, global mass matrix, global damping matrix, piezoelectric stiffness matrix and dielectric stiffness matrix, the dynamic equation of the PZT-three-dimensional crack structure model is established.

[0049] Optionally, based on the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established, specifically including: By introducing electromechanical coupling control equations and combining the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established, and the formula is as follows: ; In the formula, 、 、 、 、 、 、 and These are the global mass matrix, global damping matrix, global stiffness matrix, nodal displacement vector, equivalent potential vector, equivalent nodal force vector, global piezoelectric stiffness matrix, global dielectric stiffness matrix, and charge vector of the PZT-3D crack structure model.

[0050] Specifically, PZT is arranged to form a cracked PZT-structure electromechanical coupling system; in some embodiments, the process of forming the cracked PZT-structure electromechanical coupling system specifically includes: Based on the geometry and shape of PZT sensors in actual engineering projects, their placement areas are defined on the surface or inside the 3D crack structure element model established for displacement discontinuity modeling. For surface-mounted PZTs, their attachment position and orientation are specified on the outer surface of the structure; for implanted PZTs, their embedding depth and spatial distribution are specified inside the structure. A bonding layer model is established between the PZT and the structural substrate, or a shared-node approach is used to achieve effective transfer of displacement coordination and force-electric coupling between the two. Whether surface-mounted or implanted, PZTs share nodal degrees of freedom with adjacent structural elements, ensuring consistency between the PZT and the structure in mechanical deformation and electric field response, thereby ensuring accurate simulation of electromechanical coupling behavior.

[0051] Specifically, PZT in the model can be pasted on the model surface or embedded in the model. In this embodiment, PZT is pasted in the middle position on the model surface.

[0052] PZT is discretized into a finite number of three-dimensional piezoelectric spectral units, and anisotropic piezoelectric constitutive relations, including the piezoelectric stiffness matrix, are assigned to them. and dielectric stiffness matrix To accurately describe its coupling behavior under mechanical vibration and electric field excitation; Please see Figure 8 In some implementations, PZT is discretized into 16 three-dimensional piezoelectric spectral units, each node having a potential degree of freedom in addition to the unique degrees of freedom in three directions, and the unit size is [missing information]. The adhesive layer was discretized into 16 three-dimensional solid spectral units, with a unit size of [missing information]. The number of interpolation nodes for the displacements (w, u, v) of its spectral elements in the x, y, and z axes are 3, 3, and 2, respectively. Furthermore, to ensure coupling between the externally attached PZT and the concrete nodes, the size of the concrete spectral elements directly below the PZT should be consistent with that of the PZT.

[0053] By introducing electromechanical coupling control equations, the overall dynamic equations of the PZT-structure system are established, which include coupling terms between mechanical degrees of freedom and electric potential degrees of freedom.

[0054] Optionally, calculating the piezoelectric admittance of the material to be identified at different frequencies includes: applying AC excitation voltages of different frequencies to the material to be identified, causing the PZT-3D crack structure model of the material to generate nodal potentials and displacement responses at different frequencies; calculating the surface charge density of the PZT-3D crack structure model at different frequencies using the kinetic equations based on the nodal potentials and displacement responses; and calculating the piezoelectric admittance of the material to be identified at different frequencies based on the AC excitation voltages and surface charge densities at different frequencies. An AC voltage excitation is applied to the upper surface of the PZT sensor, and the lower surface is grounded to construct the boundary conditions required for piezoelectric admittance calculation. Based on the above dynamic equation, the equivalent nodal force and structural response caused by the potential under different frequency excitations are solved to obtain the dynamic mechanical behavior of PZT as an actuator at each frequency point.

[0055] Specifically, PZT is considered as a sensor, based on the nodal potential at each excitation frequency. and displacement response According to the formula: The surface charge density of PZT elements in the PZT-structure system at this frequency can be obtained. At this point, the admittance value of PZT for: ; In the formula, It is the imaginary unit.

[0056] S105: Based on the dynamic equations of the PZT-3D crack structure model, perform frequency domain simulation on the material to be identified, and calculate the piezoelectric admittance value of the material to be identified at different frequencies; based on the piezoelectric admittance value, determine the severity of damage to the material to be identified.

[0057] Optionally, frequency domain simulation is performed on the material to be identified based on the dynamic equations of the PZT-3D crack structure model to calculate the piezoelectric admittance value of the material to be identified at different frequencies. Specifically, this includes: applying AC excitation voltages of different frequencies to the material to be identified, causing the PZT-3D crack structure model of the material to be identified to generate nodal potentials and displacement responses at different frequencies; calculating the charge vectors of the PZT-3D crack structure model at different frequencies using the dynamic equations based on the nodal potentials and displacement responses; obtaining the surface charge density of the PZT-3D crack structure model based on the charge vectors at different frequencies; and calculating the piezoelectric admittance value of the material to be identified at different frequencies based on the AC excitation voltages and surface charge densities at different frequencies.

[0058] Based on the piezoelectric admittance value, the severity of damage to the material to be identified is determined, specifically including: plotting the piezoelectric admittance curve of the material to be identified based on the piezoelectric admittance value of the material to be identified at different frequencies; extracting the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified from the piezoelectric admittance curve; calculating the root mean square error between the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified and the piezoelectric admittance signal in the undamaged state as the damage-sensitive feature of the material structure to be identified; and determining the degree of damage to the material structure based on the damage-sensitive feature of the material structure to be identified and a preset root mean square deviation threshold, including: Based on the damage-sensitive characteristics of the material structure to be identified and a preset root mean square deviation threshold, the degree of damage to the material structure is determined, including: When the damage sensitivity feature is greater than or equal to the preset root mean square deviation threshold, it indicates that the material structure to be identified has serious damage; the degree of damage is severe and may have affected the load-bearing capacity and safety of the structure, requiring immediate detailed inspection and repair.

[0059] When the damage sensitivity feature is less than the preset root mean square deviation threshold, it indicates that the material structure to be identified is in a healthy state or slightly damaged. The degree of damage is minor, the structural performance is basically intact, and it can continue to be used normally and monitored regularly.

[0060] When the damage sensitivity characteristic is less than the preset root mean square deviation threshold, it indicates that the material structure to be identified is in a healthy state or has only minor damage. Specifically, a three-dimensional model of the PZT structure containing different crack conditions is established, and frequency domain simulation is performed based on the constructed electromechanical coupling dynamic equation to calculate the piezoelectric admittance curves under different damage states. The conductivity signal of the PZT sensor under each damage condition is extracted and compared with the baseline conductivity signal under the undamaged state. The root mean square deviation (RMSD) index is used to quantify the difference between the two, and its calculation formula is as follows: ; In the formula: For the first The results obtained during the measurement of the secondary damage condition The data in the th One value, Obtained from baseline conductance signal measurement The data in the th Values.

[0061] Furthermore, to make the features and advantages of this patent more apparent and understandable, a preferred embodiment is given below, and the invention is described in detail below: In this embodiment, the simulation object is a concrete cube specimen with a side length of 100 mm and a coarse aggregate volume fraction of 30%. First, a uniaxial tensile numerical simulation is performed on the specimen to obtain the crack initiation and propagation at different loading stages, including the specific location, width, and distribution pattern of the cracks. Then, based on the obtained crack evolution information, a PZT-structure coupled model with damage is constructed, and the piezoelectric admittance curves corresponding to each loading stage are further calculated to analyze the impact of crack development on the electromechanical response characteristics of the structure.

[0062] from Figure 9 It can be seen that in the initial loading stage, the specimen was in the elastic phase, and no damage appeared inside the specimen. As the displacement gradually increased, damage evolution began to occur inside the specimen, with microcracks appearing first in some interface transition zones (ITZs). However, the outer surface of the specimen remained intact at this time, and no visible cracks were observed. As the loading process continued, obvious fracture zones gradually formed on multiple cross-sections of the specimen. These fracture zones extended basically perpendicular to the loading direction and preferentially developed along the ITZ region between the aggregate and mortar, indicating that this region is a weak interface in the concrete structure. At the same time, local microcracks also began to appear in the mortar layer on the outer surface of the specimen. At the end of the loading period, a clear macrocrack formed on the outer side of the specimen, ultimately leading to the overall fracture failure of the specimen. It is worth noting that this macrocrack is not a strictly straight line, but extends in a wavy pattern near the theoretical straight path. This irregular orientation is due to stress redistribution caused by the uneven distribution of aggregate inside the specimen and the deflection of the crack propagation path.

[0063] from Figure 10 As can be seen, no damage was observed in the specimen during the initial loading stage. At this time, the conductivity curve measured by the PZT sensor remained almost unchanged, indicating that the electromechanical response of the structure was stable during the elastic stage. As loading progressed, when cracks began to appear inside the concrete, the resonant peak value of the conductivity curve began to decrease, reflecting the initial decrease in structural stiffness. This indicates that the model of this invention can identify micro-cracks inside the concrete before the appearance of apparent cracks. Subsequently, as loading continued, the cracks inside the concrete continued to expand and gradually extended to the surface, causing the resonant peak value of the conductivity curve to decrease further. This indicates that crack propagation had a significant impact on the electromechanical coupling characteristics of the structure.

[0064] Furthermore, using the conductivity curve of the test block in a healthy state as a baseline, the root mean square deviation (RMSD) index was calculated to further evaluate the difference in admittance of concrete under different degrees of damage during loading. The results are as follows: Figure 11As shown in the figure, the RMSD values ​​of the conductivity curves all show an increasing trend with the increase of the loading displacement. Specifically, when the concrete is in the elastic stage, its RMSD value is almost 0; however, when internal cracks begin to appear, its RMSD rises to 1.32%, indicating that the model of this invention can identify tiny cracks inside the concrete; subsequently, with the increase of displacement, the RMSD rises to 3.34% and 3.38%. Based on the pre-set damage identification threshold, combined with the virtual node-spectral element method and piezoelectric admittance method proposed in this invention, the crack evolution of concrete during loading can be effectively detected, verifying the high sensitivity and reliability of this method in early damage identification.

[0065] Concrete in the failure stage ( Figure 11 For example, from Figure 12 and Figure 13 As can be seen, when simulating cracks using traditional finite element models, it is usually necessary to separately mesh the crack region. This involves creating new nodes and elements on both sides of the crack, leading to increased model complexity and a significant increase in the number of degrees of freedom, which in turn greatly increases computational cost and solution time. In contrast, the virtual node method used in this invention does not require re-meshing or introducing new nodes. By reconstructing the displacement interpolation functions on both sides of the crack, it only changes the stiffness matrix, mass matrix, and damping matrix of the crack-crossing spectrum element. While maintaining the original mesh structure, it achieves the modeling of displacement discontinuities caused by cracks, significantly simplifying model complexity and improving computational efficiency.

[0066] Specifically, compared to the model under healthy conditions, when simulating damage conditions during the failure stage of the specimen, the traditional finite element method requires local mesh refinement in the crack region, resulting in an increase of 4489 model nodes. In contrast, the modeling method based on the virtual node-spectral element method proposed in this invention does not require re-meshing or introducing new nodes; the number of model nodes remains unchanged, with an increase of 0. Furthermore, when dealing with multi-crack conditions, this invention eliminates the need for complex modeling and mesh adjustments for each crack, resulting in significantly improved modeling efficiency and computational advantages, demonstrating stronger applicability and engineering practicality.

[0067] from Figure 14 It can be seen that the model established based on the virtual node-spectral element method exhibits a high degree of consistency with the traditional finite element model in terms of piezoelectric admittance response characteristics. When concrete fails, the conductivity curves obtained by both methods show the same trend, with a decrease in the resonant peak value while the resonant frequency remains essentially unchanged. The reason for this change is that the appearance of cracks leads to a decrease in the local stiffness inside the concrete specimen, thereby weakening the electromechanical coupling effect between the PZT sensor and the structure, resulting in a decrease in the resonant peak value of the admittance curve. This consistency further verifies the accuracy and reliability of the virtual node-spectral element method proposed in this invention in simulating the conductivity response of cracked structures.

[0068] For information on model computational efficiency, please refer to [link / reference]. Figure 15 All simulations were performed on a Windows platform equipped with a 2.90 GHz quad-core Intel Core i6 processor and 16 GB of memory. The results show that the traditional finite element model has an average of 228,939 nodes, while the virtual node-spectral element method model proposed in this invention has only 85,893 nodes, a reduction of 62.23%, significantly lowering model complexity. Under the same hardware conditions, the average single-run computation time of the finite element model is 47.1 hours, while the computation time of the model using the virtual node-spectral element method is only 3.2 hours, improving computational efficiency by approximately 14 times. This result fully demonstrates that this invention has significant advantages in terms of computational resource consumption and solution speed while ensuring modeling accuracy and damage identification capabilities.

[0069] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

Claims

1. A method for identifying structural damage, characterized in that, include: Obtain information on the geometric dimensions, material parameters, and crack geometry of the structure to be identified; A three-dimensional structural spectrum unit model of the structure to be identified is established based on geometric dimensions and material parameters. Based on the crack geometry information, each three-dimensional structural spectrum unit traversed by the crack is identified as a three-dimensional crack structural spectrum unit; The three-dimensional crack structure spectrum element is divided into two actual sub-regions using virtual nodes. The two actual sub-regions are then expanded outward into virtual sub-regions to obtain two virtual crack structure spectrum elements with the same size as the three-dimensional crack structure spectrum element. Based on the node displacements within the two virtual crack structure spectrum elements, the displacement fields of the two virtual crack structure spectrum elements are determined and reconstructed using displacement field interpolation functions to obtain the three-dimensional crack structure spectrum element with displacement discontinuity modeling. Finally, based on the volumes of the two actual sub-regions and the volume of the three-dimensional crack structure spectrum element, the global stiffness matrix, global mass matrix, and global damping matrix of the three-dimensional crack structure spectrum element with displacement discontinuity modeling are determined. PZT with piezoelectric and dielectric stiffness matrices is used as a three-dimensional piezoelectric spectral unit and coupled with a three-dimensional crack structure spectral unit modeled by displacement discontinuity to obtain a PZT-three-dimensional crack structure model; based on the global stiffness matrix, global mass matrix, global damping matrix, piezoelectric stiffness matrix and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established. Based on the dynamic equations of the PZT-3D crack structure model, frequency domain simulation is performed on the material to be identified to calculate the piezoelectric admittance value of the material to be identified at different frequencies; based on the piezoelectric admittance value, the severity of damage to the material to be identified is determined.

2. The material structure damage identification method as described in claim 1, characterized in that, The material to be identified includes homogeneous materials and heterogeneous materials.

3. The material structure damage identification method as described in claim 2, characterized in that, When the material to be identified is a homogeneous material, a three-dimensional structural spectral unit model of the material to be identified is established based on the geometric dimensions and material parameters, specifically including: The structure of the material to be identified is discretized into multiple three-dimensional structural spectrum units; Interpolation nodes inside the three-dimensional structural spectral unit are configured according to the Gauss-Lobatto-Legendre integration points to construct higher-order basis functions; The maximum size of the three-dimensional structural spectrum unit With the order of the Gauss-Lobatto-Legendre polynomial Satisfying the relation: ； In the formula, It is the minimum wavelength that propagates in the material structure at the excitation frequency.

4. The material structure damage identification method as described in claim 2, characterized in that, When the material to be identified is a heterogeneous material, a three-dimensional structural spectral unit model of the material to be identified is established based on the geometric dimensions and material parameters, specifically including: Based on the internal composition and microstructure of the material to be identified, a microscale model of the material is established; the microscale model of the material reflects the spatial distribution characteristics of each phase component and the characteristics of the interface transition zone in the material. The material mesoscale model is divided using several different mesh sizes to obtain multiple numerical models with different element sizes. For each numerical model, based on the volume fraction of each phase material in each element, the mechanical properties of the numerical model are homogenized using the composite material equivalence method, thus equivaling it to an isotropic medium element. Calculate the average value and standard deviation of the elastic modulus of each medium element, and obtain the coefficient of variation of the elastic modulus based on the average value and standard deviation. The coefficients of variation of the elastic modulus corresponding to all media elements are calculated sequentially to evaluate the characterization accuracy of the material's non-uniformity under different element sizes; Plot the relationship curve between the elastic modulus dispersion coefficient and the element size; identify the inflection point on the relationship curve, and take the element size corresponding to the inflection point as the characteristic element size; Based on the size of the feature unit, the structure of the material to be identified is discretized into multiple three-dimensional structural spectrum units; the order of the interpolation function of the three-dimensional structural spectrum unit is determined by the minimum wavelength propagating in the structure at the applied excitation frequency.

5. The material structure damage identification method as described in claim 1, characterized in that, The geometric morphology information of the material crack is obtained through CT scanning, three-dimensional laser scanning or image processing technology, including: the length, width, depth and orientation of the crack; the geometric morphology information of the material crack.

6. The material structure damage identification method as described in claim 1, characterized in that, The process of determining the displacement fields of the two virtual crack structure spectrum elements based on the nodal displacements within them, and reconstructing the total displacement field of the three-dimensional crack structure spectrum element using a displacement field interpolation function, specifically includes: Extract the nodal displacements within the virtual crack structure element, and combine them with the shape functions used to construct the 3D crack structure element to determine the displacement fields of the two virtual crack structure elements. The formula is as follows: ； In the formula, The shape function of the three-dimensional crack structure spectral element. and These represent the displacement fields of two virtual crack structure spectral units, A and B, respectively. and These are the nodal displacements of two virtual crack structure spectrum elements A and B, respectively; Displacement field interpolation functions are reconstructed for two virtual crack structure spectrum elements. Without re-meshing, the displacement discontinuity of the three-dimensional crack structure spectrum elements caused by the cracks is modeled, resulting in a three-dimensional crack structure spectrum element with displacement discontinuity modeling. The displacement expression of the three-dimensional crack structure spectrum element with displacement discontinuity modeling is as follows: = ； In the formula, For the Heaviside function; Indicates from spatial coordinates The signed distance function to the crack is used to determine... The relative position of the crack.

7. The material structure damage identification method as described in claim 1, characterized in that, The determination of the overall stiffness matrix, overall mass matrix, and overall damping matrix of the three-dimensional crack structure element for displacement discontinuity modeling, based on the volumes of the two actual sub-regions and the volume of the three-dimensional crack structure element, specifically includes: The numerical integral of the 3D crack structure spectrum element after modeling the displacement discontinuity is converted into a volume ratio. The global stiffness matrix, global mass matrix, and global damping matrix of the 3D crack structure spectrum element are then calculated using the following formulas: ； ； ； In the formula, and , and , and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit The element stiffness matrix, element mass matrix, and element damping matrix, and These are virtual crack structure spectrum units. and virtual crack structure spectrum unit volume, The volume of the original unit; The strain matrix; It is the elasticity matrix; The density of the material; The stiffness matrix, mass matrix, and damping matrix of each three-dimensional crack structure spectrum element are grouped together to obtain the overall stiffness matrix, overall mass matrix, and overall damping matrix of all three-dimensional crack structure spectrum elements.

8. The material structure damage identification method as described in claim 1, characterized in that, Based on the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix, the dynamic equations of the PZT-three-dimensional crack structure model are established, specifically including: Nodal displacement vectors in the 3D crack structure spectrum element after modeling by extracting displacement discontinuities; By introducing electromechanical coupling control equations and combining the overall stiffness matrix, overall mass matrix, overall damping matrix, piezoelectric stiffness matrix, dielectric stiffness matrix, and nodal displacement vectors, the dynamic equations of the PZT-3D crack structure model are established, as follows: ； In the formula, 、 、 、 、 、 、 and These are the global mass matrix, global damping matrix, global stiffness matrix, nodal displacement vector, equivalent potential vector, equivalent nodal force vector, global piezoelectric stiffness matrix, global dielectric stiffness matrix, and charge vector of the PZT-3D crack structure model.

9. The method for identifying material structure damage as described in claim 1, characterized in that, Based on the dynamic equations of the PZT-3D crack structure model, frequency domain simulation is performed on the material to be identified to calculate the piezoelectric admittance of the material at different frequencies, specifically including: When AC excitation voltages of different frequencies are applied to the material to be identified, the PZT-3D crack structure model of the material to be identified generates nodal potential and displacement responses of different frequencies. Based on the nodal potential and displacement response, the surface charge density at different frequencies of the PZT-three-dimensional crack structure model is calculated using the dynamic equation. Based on the AC excitation voltage and surface charge density at different frequencies, the piezoelectric admittance of the material to be identified at different frequencies is calculated using the following formula: ； In the formula, This is the piezoelectric admittance value. The imaginary unit, AC excitation voltage, The surface charge density is given by the PZT-3D crack structure model.

10. The method for identifying material structure damage as described in claim 1, characterized in that, Based on the piezoelectric admittance value, the severity of damage to the material to be identified is determined, specifically including: Based on the piezoelectric admittance values ​​of the material to be identified at different frequencies, piezoelectric admittance curves of the material to be identified are plotted. Extract the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified from the piezoelectric admittance curve; The root mean square error between the piezoelectric admittance signal of the PZT-3D crack structure model of the material to be identified and the piezoelectric admittance signal under the undamaged state is calculated as the damage-sensitive feature of the material structure to be identified. Based on the damage-sensitive characteristics of the material structure to be identified and a preset root mean square deviation threshold, the degree of damage to the material structure is determined, including: When the damage sensitivity feature is greater than or equal to the preset root mean square deviation threshold, it indicates that the material structure to be identified has serious damage. When the damage sensitivity feature is less than the preset root mean square deviation threshold, it indicates that the material structure to be identified is in a healthy state or slightly damaged.

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