Laminated plate engineering failure judgment method and system based on multi-layer collaborative failure logic

Abstract

The invention discloses a laminated plate engineering failure judgment method and system based on multi-layer collaborative failure logic, and the method comprises the steps: projecting the local stress states of all layers of a laminated plate to a global coordinate system, and generating an equivalent collaborative stress field with a continuous thickness direction; based on the equivalent cooperative stress field, a preset single-layer failure criterion is adopted to calculate a local failure index set of each laying layer; for each paving layer, dynamically calculating a multi-layer collaborative strength factor set through a mechanical coupling relationship; inputting the local failure index set and the multi-layer collaborative strength factor set into a failure index fusion model to generate a collaborative failure index set with enhanced physical significance; and performing dynamic threshold judgment on the collaborative failure index set according to a preset adjustable threshold value, and when the collaborative failure index exceeds the threshold value, outputting an interlayer collaborative failure mark. According to the embodiment of the invention, the cross-scale accurate prediction of the failure behavior of the laminated plate can be realized, and the evaluation efficiency and engineering applicability of the multi-layer cooperative failure under the complex load can be remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of laminate engineering technology, and in particular, it is a method and system for judging the failure of laminate engineering based on multilayer collaborative failure logic. Background Technology

[0002] Traditional laminate failure assessment methods are typically based on single-layer stress analysis or macroscopic homogenization assumptions, making it difficult to accurately reflect interlayer stress coupling effects and multi-lay collaborative failure mechanisms. Currently, engineering often employs failure criteria based on single-layer layup failure, such as the Hashin criterion, Puck criterion, or LaRC05 criterion, for strength analysis of composite laminate structures. These methods usually only consider the stress state of a single layer in its local coordinate system, neglecting the collaborative mechanical behavior between different layups, especially shear interactions in the thickness direction. In practical applications, the following problems often arise: 1. Localized non-physical failure prediction: For example, a layer may fail under tensile or shear conditions in the resin matrix direction, while adjacent layers may not fail in the same direction. 2. Lack of engineering tolerance: Misjudgments often occur during design verification, leading to overly conservative designs. 3. Missing interface behavior: Conventional criteria cannot capture interlaminar failure, shear delamination, and other cross-layer failure modes. Furthermore, laminates are prone to cross-layer damage propagation under complex loads, and classical methods lack the ability to continuously track failure paths, limiting their engineering applicability. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for judging the failure of laminated plates based on multilayer collaborative failure logic, so as to overcome the shortcomings of the prior art, realize cross-scale accurate prediction of the failure behavior of laminated plates, and significantly improve the evaluation efficiency and engineering applicability of multi-layer collaborative failure under complex loads.

[0004] One embodiment of this application provides a laminate engineering failure assessment method based on multi-layer collaborative failure logic, the method comprising: The local stress state of all plies of the laminate is projected onto the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion. For each ply, the stress distribution trend in the thickness direction between it and its adjacent plies is analyzed, and the set of multilayer synergistic strength factors is dynamically calculated through mechanical coupling relationship; The local failure index set and the multi-layer collaborative strength factor set are input into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning. The collaborative failure index set is dynamically thresholded based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, an inter-layer collaborative failure flag is output.

[0005] Optionally, the step of projecting the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction includes: Based on the constitutive equations of each ply material, the stress components in the local coordinate system are transformed into components in the global coordinate system by the tensor transformation rule, resulting in a discrete set of ply stress tensors. Based on the discrete ply stress tensor set, a cubic spline interpolation algorithm is used to perform continuous processing along the thickness direction to generate an initial continuous stress field; By applying material lattice orientation constraints to the initial continuous stress field and eliminating interlayer stress abrupt points through convolution kernel filtering, a stress field intermediate with a smooth transition is generated. By combining the compatibility conditions between the intermediate stress field and the interlayer interface, the stress distribution gradient is optimized using the variational method, and an equivalent synergistic stress field with continuous thickness direction is output.

[0006] Optionally, the step of calculating the set of local failure indices for each ply based on the equivalent synergistic stress field and using a preset single-layer failure criterion includes: Based on the equivalent synergistic stress field, the six-dimensional stress vector of the center plane of each ply is extracted as the input quantity of the failure criterion. The six-dimensional stress vector is input into the Tsai-Wu tensor failure criterion, and the strength tensor components are dynamically corrected by the stress gradient sensitivity coefficient to generate the basic failure index. Based on the stress concentration influence factor calculated by the orientation angle of the ply fiber, the directionality enhancement processing of the foundation failure index is carried out to obtain the direction-corrected failure index. Using a manufacturing defect database, a robust failure index is generated by calculating the tolerance compensation of the orientation correction failure index through a defect density distribution function. By combining real-time temperature-humidity field data, an environmental degradation model is used to calibrate the robust failure index, and the final set of local failure indices is output.

[0007] Optionally, for each ply, the stress distribution trend in the thickness direction between it and its adjacent plies is analyzed, and the multilayer synergistic strength factor set is dynamically calculated through mechanical coupling relationships, including: Based on the equivalent synergistic stress field, the difference between the normal and tangential stress components of adjacent layers at the interface is extracted to construct the interlayer stress jump matrix. Based on the interlayer stress jump matrix, the interface peeling potential energy density is calculated through the strain energy release rate model, and the interface damage potential energy factor is generated. The stress transfer function in the thickness direction is used to quantify the degree of stress redistribution of the current ply on the adjacent ply, and the stress transfer influence factor is obtained. By combining the interface damage potential energy factor and the stress transfer influence factor, a synergistic effect intensity coefficient is generated through a nonlinear weighting function. By utilizing the interlayer resin plastic deformation parameters, the synergistic effect strength coefficient is viscoelastically corrected, and a dynamic multilayer synergistic strength factor set is output.

[0008] Optionally, the step of inputting the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning includes: A dual-channel feature fusion network is established, wherein channel A receives the set of local failure indices and channel B receives the set of multi-layer cooperative strength factors. In channel A, a gating mechanism is used to screen key failure indices, and in channel B, the contribution of collaborative factors is allocated through attention weights. The selected failure indices are combined with the weighted synergy factors to generate a physical enhancement failure feature tensor. The failure feature tensor is normalized using Riemannian manifolds to output a set of cooperative failure indices with uniform dimensions.

[0009] Optionally, the step of dynamically thresholding the set of collaborative failure indices based on a preset adjustable threshold, and outputting an inter-layer collaborative failure flag when the collaborative failure index exceeds the threshold, includes: Based on historical material service data, the baseline failure threshold under the current load spectrum is calculated using the Weibull distribution model. Real-time monitoring of the rate of change of the collaborative failure index; when the rate of change exceeds the critical slope, a threshold adaptive adjustment mechanism is triggered to generate a dynamic failure threshold. A fuzzy decision-maker is used to compare the collaborative failure index with the dynamic failure threshold to generate a preliminary failure probability distribution map. Morphological closing operations are performed on the failure probability distribution map to connect adjacent failure regions and output the interlayer collaborative failure marker matrix.

[0010] Another embodiment of this application provides a laminate engineering failure assessment system based on multi-layer collaborative failure logic, the system comprising: The projection module is used to project the local stress state of all plies of the laminate to the global coordinate system, generating an equivalent synergistic stress field that is continuous in the thickness direction. The calculation module is used to calculate the set of local failure indices for each ply based on the equivalent co-stress field and using a preset single-layer failure criterion. The analysis module is used to analyze the stress distribution trend of each ply and its adjacent plies in the thickness direction, and dynamically calculate the multilayer synergistic strength factor set through mechanical coupling relationship; The input module is used to input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning. The output module is used to dynamically determine the collaborative failure index set based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, it outputs an inter-layer collaborative failure flag.

[0011] Another embodiment of this application provides a storage medium storing a computer program, wherein the computer program is configured to execute the method described in any of the preceding claims when running.

[0012] Another embodiment of this application provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method described in any of the preceding claims.

[0013] Compared with existing technologies, this invention provides a laminate engineering failure assessment method based on multi-layer cooperative failure logic. It projects the local stress state of all plies of the laminate onto a global coordinate system, generating an equivalent cooperative stress field that is continuous in the thickness direction. Based on this equivalent cooperative stress field, a set of local failure indices for each ply is calculated using a preset single-layer failure criterion. For each ply, a set of multi-layer cooperative strength factors is dynamically calculated through mechanical coupling relationships. The set of local failure indices and the set of multi-layer cooperative strength factors are input into a failure index fusion model to generate a set of cooperative failure indices with enhanced physical meaning. A dynamic threshold judgment is performed on the set of cooperative failure indices based on a preset adjustable threshold. When the cooperative failure index exceeds the threshold, an inter-layer cooperative failure marker is output. This enables accurate cross-scale prediction of laminate failure behavior, significantly improving the assessment efficiency and engineering applicability of multi-ply cooperative failure under complex loads. Attached Figure Description

[0014] Figure 1 A hardware structure block diagram of a computer terminal for a laminate engineering failure assessment method based on multi-layer collaborative failure logic provided in an embodiment of the present invention; Figure 2 A flowchart illustrating a laminate engineering failure assessment method based on multi-layer collaborative failure logic provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a laminate engineering failure assessment system based on multi-layer collaborative failure logic, provided in an embodiment of the present invention. Detailed Implementation

[0015] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0016] The present invention first provides a method for judging the failure of laminate engineering based on multi-layer collaborative failure logic. This method can be applied to electronic devices, such as computer terminals, specifically ordinary computers.

[0017] The following detailed explanation uses a computer terminal as an example. Figure 1 This is a hardware structure block diagram of a computer terminal for a laminate engineering failure assessment method based on multi-layer collaborative failure logic, provided as an embodiment of the present invention. Figure 1 As shown, the computer device includes a processor, memory, and network interface connected via a system bus, wherein the memory may include non-volatile storage media and internal memory.

[0018] Non-volatile storage media can store operating systems and computer programs. These computer programs include program instructions that, when executed, cause the processor to perform any laminate engineering failure assessment method based on multi-layer cooperative failure logic.

[0019] The processor provides computing and control capabilities, supporting the operation of the entire computer device.

[0020] The internal memory provides an environment for the execution of computer programs in non-volatile storage media. When the computer program is executed by the processor, it enables the processor to execute any laminate engineering failure assessment method based on multi-layer cooperative failure logic.

[0021] This network interface is used for network communication, such as sending assigned tasks. Those skilled in the art will understand that... Figure 1 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0022] It should be understood that the processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among these, a general-purpose processor can be a microprocessor or any conventional processor.

[0023] See Figure 2 The present invention provides a method for judging the failure of laminated board engineering based on multi-layer collaborative failure logic, which may include the following steps: S201 projects the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. Specifically, based on the constitutive equations of each ply material, the stress components in the local coordinate system can be converted into components in the global coordinate system using the tensor transformation rule, thus obtaining a discrete set of ply stress tensors. Laminates are composed of multiple layers of composite materials with different layup angles (e.g., 0°, 45°, 90°). Each layup has independent material properties in a Local Coordinate System (LCS), where the X-axis is typically parallel to the fiber direction. First, for each layup, local stress components are extracted based on its constitutive equations (mathematical models describing the stress-strain relationship of the material, such as orthotropic models). These components include longitudinal stress σ11 along the fiber direction, transverse stress σ22 perpendicular to the fiber direction, in-plane shear stress σ12, interlaminar normal stress σ33, and interlaminar shear stresses σ13 and σ23 (subscripts 1, 2, 3 correspond to the X, Y, and Z axes of the local coordinate system, respectively). These local stress components are then transformed to a Global Coordinate System (GCS) using a tensor transformation rule (a mathematical rule based on the direction cosine matrix). For example, the local stress σ11 of a 45° layup needs to be decomposed into X-direction normal stress, Y-direction normal stress, and XY-plane shear stress in the GCS. The core of the transformation formula is the direction cosine matrix, whose elements are calculated from the ply angle θ (e.g., θ = 45°): the first row of the matrix is ​​[cos... 2 θ, sin 2[θ, 2sinθcosθ]. The system automatically traverses all plies and finally outputs a Discrete Laminate Stress Tensor Set (DLSTS) containing the six-dimensional stress components (σxx, σyy, σzz, τxy, τxz, τyz) of each ply in the global coordinate system. This set is the basic data for subsequent processing.

[0024] Tensor transformation processes must consider material symmetry and engineering accuracy requirements. Taking carbon fiber / epoxy resin layup as an example, its orthotropic characteristics require differentiation of the principal axis directions during transformation. The system constructs a 3×3 direction cosine matrix in real time based on the layup angle θ (e.g., θ=30°). Assuming the stress vector at a point in the local coordinate system is [σ11=100MPa, σ22=20MPa, σ12=15MPa, σ33=5MPa, σ13=3MPa, σ23=2MPa], it is mapped to the global coordinate system through matrix multiplication. The transformation process introduces constraints from the material stiffness matrix (SM) to ensure energy conservation. For example, when the layup angle θ=60°, the contribution weight of the local shear stress σ12 to the global normal stress σxx is determined by sin(2×60°)≈0.866. All transformation results are stored as DLSTS in ply order, where each element is a six-dimensional vector representing the global stress state at the center plane of that ply. Thickness coordinates are also recorded (e.g., Z-coordinate of the center plane of the k-th layer, Z_k = 0.2 mm), forming a discrete thickness-stress mapping relationship.

[0025] In practical engineering, complex working conditions need to be handled. For example, in the analysis of aircraft wing laminates, the local coordinate system may change with the surface ply. The system calculates the actual fiber orientation of each ply using a surface fitting algorithm and dynamically generates the direction cosine matrix. For non-uniform plies (such as plies with gradually changing angles), the system uses calculus to subdivide the ply into several sublayers, each of which undergoes an independent tensor transformation before being aggregated. The transformation process also introduces a material nonlinearity correction factor (NCF). When the stress exceeds the linear range of the material (e.g., σ11 > 80% of the ultimate strength), the system automatically calls the experimentally calibrated nonlinear constitutive relation to correct the transformation results. The final output DLSTS contains the global stress components of all plies and their corresponding thickness location information, providing accurate input for subsequent continuous processing.

[0026] Based on the discrete ply stress tensor set, a cubic spline interpolation algorithm is used to perform continuous processing along the thickness direction to generate an initial continuous stress field; DLSTS only provides discrete stress values ​​at the center plane of each ply, while the interlayer stress distribution is unknown. To obtain a continuous stress field in the thickness direction, a cubic spline interpolation algorithm (CSIA) is used. This algorithm divides the thickness direction of the laminate into several intervals (each interval is between the center planes of two adjacent plies), and constructs a cubic polynomial function in each interval. Taking the normal stress σzz as an example: let the stress value at the center plane of the k-th layer Z_k = 0.1 mm be S_k = 5 MPa, and the stress value at the (k+1)-th layer Z_{k+1} = 0.3 mm be S_{k+1} = 8 MPa. The cubic spline function in this interval is represented as σzz(z) = a(z-Z_k)^3 + b(z-Z_k)^2 + c(z-Z_k) + d, where the coefficients a, b, c, and d must satisfy endpoint stress matching (σzz(Z_k) = S_k, σzz(Z_{k+1}) = S_{k+1) and first derivative continuity (ensuring smooth stress gradient). All coefficients are determined by solving the linear equations, enabling stress calculation at any Z-coordinate within the interval.

[0027] The interpolation process must ensure overall smoothness. In an N-layer laminate, there are (N-1) interpolation intervals. The algorithm requires the first and second derivatives to be continuous at all internal nodes (i.e., the center plane of the ply), forming a globally smooth curve. For example, for an 8-layer laminate (1.6 mm thick), a derivative continuity equation is established at 7 interpolation nodes. For boundary conditions (top and bottom layers), natural spline constraints (second derivative is zero) are used to simulate the free surface state. In actual calculations, the six stress components (σxx, σyy, σzz, τxy, τxz, τyz) are interpolated independently. The interpolation step size is configurable (e.g., 0.01 mm), and the final output is a three-dimensional mesh: each mesh point contains coordinates (X, Y, Z) and the corresponding stress vector, forming an Initial Continuous Stress Field (ICSF). This stress field is continuous in the thickness direction but may have non-physical abrupt changes (e.g., stress jumps at interlayer interfaces).

[0028] Algorithm enhancements are implemented to address the properties of composite materials. When there are significant differences between adjacent ply materials (e.g., the interface between a carbon fiber layer and a glass fiber layer), a Material Property Weight (MPW) factor is introduced into the interpolation. For example, if the elastic modulus of the carbon fiber layer is E1 = 140 GPa and that of the glass fiber layer is E1 = 40 GPa, then the weight of the carbon fiber layer side is set to 140 / (140+40) = 0.78 when interpolating near the interface. Simultaneously, a curvature constraint is added: if the rate of change of the second derivative of stress in a certain interval exceeds a threshold (e.g., |d... 2 σ / dz2 |>100MPa / mm 2 The system automatically adds virtual interpolation points (VIPs) to improve accuracy. For laminates with high thickness ratios (such as wind turbine blades), an adaptive step size strategy is adopted to densify the interpolation points to a spacing of 0.001 mm in areas with large stress gradients (such as near interfaces) to ensure engineering reliability.

[0029] By applying material lattice orientation constraints to the initial continuous stress field and eliminating interlayer stress abrupt points through convolution kernel filtering, a stress field intermediate with a smooth transition is generated. While ICSF is mathematically continuous, it does not consider the constraints imposed by the material's microstructure on stress transmission. The lattice orientation of composite materials (such as fiber alignment) constrains stress distribution. Therefore, a Material Lattice Orientation Constraint (MLOC) is applied. Taking unidirectional carbon fiber layups as an example, their stress transmission capacity along the fiber direction (0°) is much higher than that in the perpendicular direction (90°). The system defines an Orientation Sensitivity Matrix (OSM) for each layup, where the matrix elements represent the strength of the constraint on different stress components by the fiber direction. For example, for a 0° layup, σxx is weakly constrained (allowing free distribution), while σyy is strongly constrained (restricting gradient changes). By applying the OSM to ICSF through tensor multiplication, stress components that violate the material orientation rules are suppressed (e.g., suppressing high σxx gradients in 90° layups).

[0030] Stress abrupt changes at interlayer interfaces require physical smoothing. Convolution Kernel Filtering (CKF) is employed, with a Gaussian Convolution Kernel (GCK) designed to slide along the thickness direction for filtering. The kernel size is determined by the ply thickness (e.g., 5 points correspond to a 0.2mm thick ply), and the standard deviation σ is set to 20% of the ply thickness (e.g., σ = 0.04mm). Taking the elimination of abrupt changes in τxz shear stress as an example: assuming the original stress value at the interface jumps from 3MPa to 7MPa, a smooth transition band of 0.5mm width is formed after filtering (3MPa→4.2MPa→5.8MPa→7MPa). The filtering process is performed independently on the six stress components, but different kernel parameters are used for the normal stress (σzz) and shear stress (τxz, τyz): a steeper gradient is allowed for shear stress (kernel standard deviation σ_shear = 0.03mm), while a stronger smoothing is required for normal stress (σ_normal = 0.06mm). The filtered output is a Smoothed Stress Field Intermediate (SSFI).

[0031] The filtering algorithm needs to be dynamically adjusted based on material properties. For high-toughness resin matrices (such as polyetheretherketone PEEK), a wide-core filter (σ=0.1mm) is used to allow for greater deformation coordination; for brittle resins (such as epoxy resin EPOXY), a narrow core (σ=0.02mm) is used to maintain local stress characteristics. The system detects the stress gradient in real time: if |dσ / dz| exceeds the allowable value of the material at a certain point (such as the limit of 50MPa / mm at the aluminum alloy interlayer), the filtering intensity is automatically increased (the core size is increased by 50%). At the same time, an edge protection mechanism is introduced: the original boundary conditions (such as σzz=0) are preserved on the upper and lower surfaces of the laminate (Z=0 and Z=total thickness). The final generated SSFI satisfies: ① C1 continuity along the thickness direction (continuity of function value and first derivative); ② compliance with material lattice orientation constraints; ③ the width of the interlayer stress transition band matches the interface properties (such as the typical width of the carbon fiber / epoxy interface transition band of 0.05-0.1mm).

[0032] By combining the compatibility conditions between the intermediate stress field and the interlayer interface, the stress distribution gradient is optimized using the variational method, and an equivalent synergistic stress field with continuous thickness direction is output.

[0033] SSFI still needs to meet physical compatibility conditions. The Interfacial Compatibility Condition (ICC) requires adjacent layers to satisfy the following at the interface: ① Displacement continuity (u^+ = u^-); ② Stress continuity (σ·n^+ = σ·n^-, where n is the interface normal). Taking the Z-direction interface as an example, σzz|_top = σzz|_bottom and τxz|_top = τxz|_bottom must be satisfied. The system establishes the ICC equations at the interface location (e.g., Z = 0.25 mm) to check if the SSFI is satisfied. If not (e.g., a 0.5 MPa deviation in σzz), variational optimization (VO) is initiated. The energy functional J[σ] = ∫(stress gradient) is constructed. 2 + ICC deviation 2 Find the extreme value solution of ) dz using the Euler-Lagrange equation.

[0034] The optimization process employs finite element discretization. The laminate thickness is divided into 200 elements (element size 0.01 mm), with each element node having 6 stress degrees of freedom. The objective function is to minimize the functional J, with constraints including: ① material yield strength (e.g., σxx < 1000 MPa); ② interfacial stress continuity (stress difference between adjacent nodes < 0.1 MPa). The conjugate gradient method (CGM) is used for iterative solution. For example, the initial SSFI has a 1.2 MPa jump in τxz at the interface, which is reduced to 0.05 MPa after optimization. Simultaneously, the stress gradient is controlled: the original |dσyy / dz| = 80 MPa / mm is optimized to 60 MPa / mm to avoid stress concentration. Material priority weight (MPW) is introduced in the optimization: the stress distribution weight of fiber-dominant layups (e.g., 0° layer) is higher than that of resin layers (weight ratio 3:1), preserving key load-bearing characteristics.

[0035] The final output equivalent cooperative stress field (ECSF) has three main characteristics: Thickness direction continuity: After spline interpolation and variational optimization, all stress components are defined and smoothly transitioned at any Z coordinate; Complete in physical meaning: It satisfies the constitutive equation, lattice orientation constraint and interface compatibility condition. For example, in a 90° layup, the distribution of σxx along the thickness conforms to the exponential decay law of fiber constraint. Engineering interpretability: The location of maximum interlaminar shear stress (e.g., τxz_max appears at 30% thickness) or critical interface (e.g., the abrupt change in σzz gradient at the 45° / 90° interface) can be directly obtained through feature extraction. This stress field serves as the basis for subsequent failure analysis, and its data format is a three-dimensional mesh (X×Y×Z=100×100×200). Each mesh point stores a six-dimensional stress vector and a confidence flag (CF, indicating the reliability of the optimized data).

[0036] This step first uses tensor transformation to uniformly convert the stress state of each ply in the local coordinate system to the global coordinate system, eliminating the inconsistency in stress characterization caused by differences in ply orientation. A cubic spline interpolation algorithm is then used to construct a continuous stress field in the thickness direction, ensuring an accurate description of the stress transfer relationship between adjacent plies. This establishes a unified mechanical field foundation for subsequent collaborative failure analysis, achieving a globally unified characterization of the stress field in multilayer composite materials and overcoming the limitations of traditional single-layer stress analysis. The construction of the continuous stress field accurately reflects the changes in interlayer stress gradients, providing crucial data support for revealing the overall failure mechanism of laminates and significantly improving the accuracy of failure prediction.

[0037] S202, Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion; Specifically, based on the equivalent synergistic stress field, a six-dimensional stress vector can be extracted from the center plane of each ply as the input quantity for the failure criterion; Stress vector extraction principle and coordinate system transformation After obtaining the equivalent co-stress field that is continuous in the thickness direction (this stress field has been optimized using variational methods to ensure smooth interlayer stress gradients), the system first locates the geometric mid-plane of each ply. The mid-plane is the plane of symmetry in the thickness direction of the ply, and its stress state is most representative. For the current ply K (K is the ply number, e.g., K=1 indicates the bottommost ply), the system extracts the six-dimensional stress vector (6-D Stress Vector) at the location of the mid-plane from the equivalent co-stress field. This vector contains six independent stress components in the global coordinate system: three normal stress components (σ_x along the X-axis, σ_y along the Y-axis, and σ_z along the thickness Z-axis) and three shear stress components (τ_xy in the XY plane, τ_xz in the XZ plane, and τ_yz in the YZ plane). For example, at the center plane of a carbon fiber layup, we might obtain the vector [σ_x=120 MPa, σ_y=-30 MPa, σ_z=5 MPa, τ_xy=40 MPa, τ_xz=8 MPa, τ_yz=3 MPa]. Here, "megapascal" (MPa) is a unit of stress; 1 MPa equals 1 million Newtons of force per square meter. The extraction process must ensure that the stress values ​​originate from the optimized continuous field rather than discrete points to avoid introducing noise due to interpolation errors.

[0038] Stress vector normalization and tensor alignment Because different plies have different fiber orientation angles (FOA) (e.g., 0°, 45°, 90° plies), their local coordinate systems are rotated relative to the global coordinate system. To ensure that the failure criteria for all plies are comparable, the six-dimensional stress vector needs to be tensor aligned. Based on the FOA value of ply K (e.g., 45°), the system projects the global stress vector onto the Material Principal Coordinate System (MPCS) of that ply using a Direction Cosine Matrix (DCM). In the MPCS, the X1 axis is parallel to the fiber direction, the X2 axis is perpendicular to the fiber direction, and the X3 axis remains the thickness direction. The vector form remains unchanged after projection, but the physical meaning is clear: σ_11 represents the fiber direction normal stress, σ_22 represents the transverse normal stress, σ_33 represents the thickness direction normal stress, τ_12 represents the in-plane shear stress, and τ_13 and τ_23 represent the interlaminar shear stress. This step does not change the stress values, but only reorders the components to match the input requirements of subsequent failure criteria.

[0039] Boundary effect handling and vector verification For edge plies (such as the top or bottom layer), the stress on the center surface may be affected by free boundary effects. The system uses the Virtual Ply Extension Method (VPEM) for compensation: a virtual ply of the same material is added outside the equivalent stress field, and its stress gradient is used to correct the boundary values ​​of the actual ply. The extracted six-dimensional vector needs to pass the Stress Equilibrium Check (SEC): the divergence of each component of the vector is calculated to see if it satisfies the static equilibrium equation (e.g., ∂σ_x / ∂x + ∂τ_xy / ∂y + ∂τ_xz / ∂z = 0). If the deviation exceeds the tolerance (e.g., 5%), the stress field is re-optimized. The final output six-dimensional stress vector is used as the standardized input for the single-layer failure criterion.

[0040] The six-dimensional stress vector is input into the Tsai-Wu tensor failure criterion, and the strength tensor components are dynamically corrected by the stress gradient sensitivity coefficient to generate the basic failure index. Tsai-Wu Criterion Basic Calculation Process The Tsai-Wu Tensor Failure Criterion is a polynomial failure criterion widely used in composite materials. Its core is to input a six-dimensional stress vector [σ_11, σ_22, σ_33, τ_12, τ_13, τ_23] into the following functional form: Failure index FI = F_i * σ_i + F_ij * σ_i * σ_j (i,j=1~6). Here, F_i and F_ij are strength tensor components, derived from the material's fundamental strength values ​​(such as fiber tensile strength X_t, compressive strength X_c, matrix tensile strength Y_t, etc.). For example, F_11 = 1 / (X_t*X_c), F_1 ​​= (1 / X_t - 1 / X_c). The system's built-in material library stores the rated strength values ​​for each ply material (such as T700 carbon fiber / epoxy resin). During the initial calculation, the rated values ​​are directly substituted to generate the basic failure index FI_base (a dimensionless quantity). If FI_base ≥ 1, failure is predicted.

[0041] Dynamic correction of stress gradient sensitivity coefficient The traditional Tsai-Wu criterion assumes homogeneous materials, but in actual laminates, the stress gradient (SG) significantly affects local strength. The system introduces a Stress Gradient Sensitivity Coefficient (SGSC) to dynamically correct the strength tensor. SGSC is defined as: SGSC_k = 1 + α * |∇σ_k| / σ_ref. Where k is the stress component number (1~6), |∇σ_k| is the gradient modulus of the stress component k at the center plane of the current ply (calculated through the equivalent stress field), σ_ref is the reference stress (taking the maximum value of this component in the laminate), and α is the material sensitivity constant (calibrated experimentally, e.g., α=0.2 for carbon fiber). The correction process is as follows: Calculate the SGSC value of each stress component (e.g., SGSC_11=1.15 for σ_11). Weight the corresponding terms in the intensity tensor: F_i' = F_i * SGSC_i, F_ij' = F_ij * SGSC_i *SGSC_j; This correction enhances the failure sensitivity in high gradient regions (such as the edges of holes); for example, a 20% increase in gradient can increase FI_base by 15%.

[0042] Nonlinear Coupling and Exponential Generation The corrected strength tensor components F_i' and F_ij' are coupled with the six-dimensional stress vector in a quadratic form calculation. The system employs the eigenvalue decomposition method to avoid numerical instability: the coefficient matrix F_ij' is diagonalized, and the stress vector is transformed to the principal space before calculating the failure index. The final output Basic Failure Index (BFI) retains the physical meaning of the original Tsai-Wu criterion (BFI ≥ 1 for failure), but incorporates the local stress gradient effect. For example, the original BFI of a certain layup is 0.92, which is increased to 1.05 after correction, providing an early warning of edge failure risk.

[0043] Based on the stress concentration influence factor calculated by the orientation angle of the ply fiber, the directionality enhancement processing of the foundation failure index is carried out to obtain the direction-corrected failure index. Modeling the correlation between fiber orientation angle and stress concentration The fiber orientation angle (FOA) of a layup directly affects stress distribution. For example, a 45-degree layup is prone to stress concentration at the fiber / matrix interface under in-plane shear loads. The system quantifies this effect using the orientation influence function (OIF): OIF(θ) = β_1 * sin(4θ) + β_2 * cos(2θ) + β_3.

[0044] Where θ is the FOA (degree in units), and β_1, β_2, and β_3 are material constants (determined by micromechanical experiments). The OIF value ranges from 0.8 to 1.2, characterizing the degree of stress concentration relative to the 0-degree layup (>1 indicates intensification, <1 indicates relief). For example, when θ=45°, OIF=1.18, meaning that the stress level increases by 18% under the same load.

[0045] Implementation of Directional Enhancement Algorithm Directional enhancement processing combines the OIF with the basic failure index (BFI): Principal stress direction identification: Extract the principal stress direction angle φ (such as the direction of maximum tensile stress) from the six-dimensional stress vector. Relative angle calculation: Δφ = |φ - θ|, which is the deviation angle between the principal direction of the load and the fiber direction; Directional Correction Factor (DCF) Generation: DCF = γ * OIF(θ) * (1 + δ * Δφ / 90). Where γ is the baseline correction coefficient (default 1.0), and δ is the angle sensitivity factor (e.g., 0.3). DCF comprehensively reflects the influence of fiber orientation and load direction. For example, when θ=45° and Δφ=30°, DCF=1.25.

[0046] Failure Index Correction and Physical Constraints Applying DCF to the base failure index: DFI = BFI * DCF, yields the Directionally-corrected Failure Index (DFI). To avoid overcorrection, the system sets constraints: if BFI < 0.5, the upper limit of DCF is 1.5; if BFI > 1.2, the lower limit of DCF is 0.9. For example, in a certain region, BFI = 0.8, after correction with DCF = 1.25, DFI = 1.0, triggering a failure warning. The corrected DFI more accurately reflects the failure risk under non-axial loads.

[0047] Using a manufacturing defect database, a robust failure index is generated by calculating the tolerance compensation of the orientation correction failure index through a defect density distribution function. Construction and retrieval of manufacturing defect database The system-integrated Manufacturing Defect Database (MDD) stores the statistical characteristics of typical process defects (such as porosity, fiber buckling, and resin-rich areas). Defect types: Porosity, Delamination, Fiber Misalignment, etc. Distribution parameters: average size, area density, location dependence (e.g., porosity in the near-edge region +20%); Sensitivity coefficient: The weight of the influence of each defect on strength (e.g., 1% porosity leads to a 5% decrease in strength).

[0048] The database is generated through training on historical CT scan data. For the current laminate design, its process history (such as autoclave curing curve number A07) is called up to match the corresponding defect probability model.

[0049] Application of Defect Density Distribution Function The Defect Density Distribution Function (DDDF) is defined in the layup plane. Taking porosity as an example, its areal density function is: ρ_p(x,y) = ρ_0 + κ * e^(-(x^2+y^2) / r^2). Here, ρ_0 is the baseline density (e.g., 0.5%), κ is the edge concentration factor (e.g., 0.3), and r is the attenuation radius (e.g., 10mm). The system discretizes the layup into a grid (e.g., 1mm×1mm) and calculates the Defect Impact Factor (DIF) for each grid: DIF = 1 + Σ (λ_i * ρ_i), where λ_i is the sensitivity coefficient for type i defects (porosity λ_p=0.05), and ρ_i is its local density. For example, when ρ_p=0.8% in the edge region, DIF=1.04.

[0050] Tolerance compensation and robustness generation Tolerance Compensation Calculation incorporates the impact of defects into the failure index: RFI = DFI / DIF, yielding the Robust Failure Index (RFI). The physical meaning of the division operation is that the failure threshold needs to be lowered in areas with dense defects (because the actual strength is lower). For example, in a region where DFI = 1.1, if DIF = 1.05, then RFI = 1.05, indicating that considering defects makes it closer to the actual failure state. The system imposes range constraints on RFI: lower limit: max(0.3, DFI - 0.2); upper limit: min(2.0, DFI + 0.3); to avoid distortion of the index due to extreme defects.

[0051] By combining real-time temperature-humidity field data, an environmental degradation model is used to calibrate the robust failure index, and the final set of local failure indices is output.

[0052] Environmental field data acquisition and interpolation The temperature field (T) and humidity field (H) of the laminate's service environment are monitored in real time, and data is acquired through an embedded sensor network (such as surface thermocouples and internal FBG optical fibers). Assume the current location of the center plane of layup K: temperature T_k = 80°C; relative humidity H_k = 60%RH.

[0053] The system uses linear interpolation along the thickness direction to ensure that each layup has its own environmental parameters. The data update frequency is ≥1Hz to capture transient conditions (such as thermal shock).

[0054] Environmental degradation model construction and calibration The Environmental Degradation Model (EDM) uses a phenomenological formula: Degradation coefficient EDC = [c1 * (T-T_ref)^2 + c2 * (H-H_ref)] * t_exp.

[0055] Where T_ref=25°C and H_ref=50%RH are reference environments, t_exposure is the exposure time (in hours), and c1 (e.g., 0.0002) and c2 (e.g., 0.001) are degradation rate coefficients. This model quantifies the intensity reduction caused by the environment: Temperature effect: High temperature accelerates matrix creep and lowers the glass transition temperature T_g; Humidity effect: Moisture penetrates and swells the resin, weakening the fiber / matrix interface; The calibration process applies EDC to the material strength parameters. For example, at T=80°C, the dominant matrix strength Y_t decreases by 30%.

[0056] Failure Index Calibration and Set Output Environmental calibration ultimately affects the robustness failure index: Final Failure Index FFI = RFI * (1 + EDC).

[0057] The multiplicative relationship reflects how environmental degradation increases the equivalent load (e.g., RFI=0.9 increases to 1.035 at EDC=0.15). The system normalizes FFI: if FFI<0, it is forced to 0 (no risk of failure); if FFI>3, it is forced to 3 (complete failure).

[0058] The final output is the Local Failure Index Set (LFIS), in the form of: {Ply_1: FFI_1, Ply_2: FFI_2, ..., Ply_N: FFI_N}.

[0059] For example, a 10-layer board outputs: {1:0.35, 2:1.22, 3:0.91, ... ,10:0.45}, where FFI>1 on layer 2 indicates failure.

[0060] Based on a continuous stress field, key stress components are extracted for each ply, and the foundation failure index is calculated using a modified Tsai-Wu criterion. Combining the stress concentration effect corresponding to the fiber orientation angle and the distribution of manufacturing defects, the failure index is corrected for multiple factors, ultimately forming a local failure assessment result that reflects actual working conditions. Stress gradient sensitivity and defect tolerance compensation mechanisms are introduced into the traditional single-layer failure criterion, making the failure index closer to engineering reality. Directional enhancement processing effectively captures the directional influence of fiber orientation on failure behavior, providing reliable local failure characteristics for subsequent collaborative analysis.

[0061] S203, for each ply, analyze the stress distribution trend of it and its adjacent plies in the thickness direction, and dynamically calculate the multilayer cooperative strength factor set through mechanical coupling relationship; Specifically, based on the equivalent synergistic stress field, the difference between the normal and tangential stress components of adjacent layers at the interface can be extracted to construct the interlayer stress jump matrix; Once the system obtains an equivalent synergistic stress field that is continuous in the thickness direction, this stress field has been optimized using a variational method to ensure a smooth transition of interlayer stress. For any current ply (CP) to be analyzed in the laminate, the system locates its two adjacent plies (APs), namely the directly contacting upper ply (UP) and lower ply (LP). At the physical interface (PI) between each ply (usually defined as a virtual interface between the geometric center planes of adjacent plies), the system precisely extracts three sets of key stress components from the equivalent synergistic stress field: the normal stress (σ_z) perpendicular to the interface and the two tangential stresses (τ_xz and τ_yz) parallel to the interface. Due to differences in fiber orientation and material properties among different plies, even after the stress field is made continuous, microscopic mismatches may still exist in the stress states of adjacent plies at the interface. Therefore, the system calculates the normal stress difference (Δσ_z_up = σ_z_CP - σ_z_UP) and tangential stress difference (Δτ_xz_up = τ_xz_CP - τ_xz_UP, Δτ_yz_up = τ_yz_CP - τ_yz_UP) at the interface between the current ply (CP) and the upper ply (UP); simultaneously, it calculates the corresponding differences (Δσ_z_down, Δτ_xz_down, Δτ_yz_down) between the current ply (CP) and the lower ply (LP). These differences reflect the intensity of the stress jump at the interface caused by material or geometric abrupt changes, which are potential drivers of interlaminar failure.

[0062] To systematically characterize the stress jump states of all interfaces, a structured data container—the Interlaminar Stress Jump Matrix (ISJM)—is constructed. This matrix is ​​a three-dimensional data structure, with its dimensions corresponding to the three spatial directions of the laminate: the row index (RI) represents the number of all ply interfaces in the laminate (e.g., a laminate with 20 plies has 19 interfaces); the column index (CI) contains six fields, storing the six stress jump components of each interface: the normal stress difference Δσ_z, the in-plane tangential stress differences Δτ_xz and Δτ_yz (for the upper interface), and the three differences (if they exist) for the lower interface. For example, for interface number 5 (located between ply 5 and ply 6), its corresponding matrix row would record: Δσ_z_5 (stress difference between ply 5 and ply 6 in the z-direction), Δτ_xz_5 (shear stress difference in the xz plane), and Δτ_yz_5 (shear stress difference in the yz plane). The third dimension (Depth Index, DI) of the matrix can store data from different load steps or time steps, enabling dynamic analysis. The construction process of this matrix is ​​fully automated. The system traverses all interfaces, calls the application programming interface (API) of the equivalent co-stress field to obtain stress values, calculates the differences, and fills the matrix according to preset rules. ISJM is the basic input for subsequent calculations of interlayer interaction strength.

[0063] When constructing the Interlaminar Stress Jump Matrix (ISJM), practical engineering constraints must be considered. For example, for asymmetric plies or laminates with defects, the system introduces an Interface Validity Flag (IVF). If the interface region between adjacent plies becomes invalid due to voids, debonding, or other reasons, the data in the corresponding matrix row will be marked as invalid (NaN value) to avoid erroneous calculations. Simultaneously, the system performs threshold filtering on the tangential stress differences (Δτ_xz, Δτ_yz) based on the interface friction coefficient (IFC, typically ranging from 0.1 to 0.6) in the material library. If the calculated stress difference is less than the critical friction stress (CFS = IFC * |σ_z|) determined by the normal stress and friction coefficient, it is considered that the difference is caused by micro-friction rather than a true mechanical jump and must be zeroed out. This ensures that ISJM only captures effective stress jumps (ESJ) that lead to interface failure, improving the accuracy of subsequent analyses.

[0064] Based on the interlayer stress jump matrix, the interface peeling potential energy density is calculated through the strain energy release rate model, and the interface damage potential energy factor is generated. Each effective stress jump component (Δσ_z, Δτ_xz, Δτ_yz) in the interlaminar stress jump matrix (ISJM) represents an energy source for potential interface failure. The system employs a strain energy release rate model (SERRM) to convert stress jumps into energy indices. The core idea of ​​this model is that when adjacent layers experience relative displacement due to stress discontinuity, the elastic strain energy stored near the interface is released, driving crack propagation. For each interface and each stress component, the system calculates its corresponding virtual energy release rate (VERR). Taking the normal stress jump Δσ_z as an example, the energy release rate G_I (Mode I, opening mode) caused by it is calculated based on the virtual crack opening displacement: assuming a tiny virtual crack (length δ_c, typically 0.001 mm) is generated at the interface, then G_I = (Δσ_z)^2 * δ_c / (2 * E_eff), where E_eff is the equivalent elastic modulus of adjacent layers in the thickness direction (calculated through mixing ratio). Similarly, the tangential stress jumps Δτ_xz and Δτ_yz correspond to the shear mode energy release rates G_II and G_III (Sliding Mode and Tearing Mode), respectively. The calculation formulas are similar in form but involve the shear modulus G_eff.

[0065] The total strain energy release rate (TSERR) of the interface is obtained by linearly superimposing the virtual energy release rates (G_I, G_II, G_III) of the three modes. TSERR represents the total amount of elastic strain energy that can be released at the interface, expressed in joules per square meter (J / m²). 2 However, TSERR is an absolute value and needs to be further converted into a dimensionless relative damage index. The interface debonding potential density (IDPD) is defined as: IDPD = TSERR / G_critical, where G_critical is the critical strain energy release rate (unit: J / m²) of the interface material. 2 The material library can be searched by layup sequence and resin type (e.g., the G_Ic of the carbon fiber / epoxy resin interface is approximately 200 J / m). 2G_IIc is approximately 800 J / m 2 An IDPD greater than 1 indicates that the strain energy is sufficient to drive crack propagation. However, in practical applications, the system uses the more sensitive Interface Damage Potential Factor (IDPF) as the output. IDPF is a nonlinearly modulated index: IDPF = tanh(k * IDPD), where k is the material sensitivity coefficient (default value 1.5). The tanh function ensures that IDPF values ​​range from 0 to 1: when IDPD = 0 (no damage risk), IDPF ≈ 0; when IDPD ≥ 2 (high risk), IDPF approaches 1. This conversion enhances the engineering interpretability of the factor.

[0066] The calculation of the interfacial damage potential factor (IDPF) needs to consider dynamic loads and environmental factors. Under variable amplitude loads, the system adopts the Cumulative Damage Rule (CDR): for each interface, the IDPF is calculated and accumulated in each load increment step. During accumulation, a Load Interaction Factor (LIF, ranging from 0.8 to 1.2) is introduced to account for the influence of the high and low load sequence on damage accumulation. Simultaneously, if the laminate operates in a high-temperature or humid environment, the system will invoke the Environmental Degradation Model (EDM) to dynamically lower the critical strain energy release rate G_critical. For example, when the temperature rises from 25℃ to 80℃, the G_IIc of the epoxy resin matrix may decrease by 30%, leading to an increase in the calculated IDPD under the same stress jump, and a corresponding increase in IDPF, truly reflecting the weakening effect of the environment on the interfacial strength. Finally, a real-time updated IDPF value is generated for each interface, forming an interfacial damage potential factor set (IDPFSet), used to quantify the failure tendency of each interface.

[0067] The stress transfer function in the thickness direction is used to quantify the degree of stress redistribution of the current ply on the adjacent ply, and the stress transfer influence factor is obtained. Interlaminar failure depends not only on the stress jump at the interface but also on the stress transfer capability (STC) between plies. When a ply (such as the current ply CP) experiences stress anomalies due to local damage or stiffness changes, its adjacent plies will share or exacerbate the anomaly through the interface transfer mechanism; this process is called stress redistribution (SR). To quantify the influence of CP on APs (adjacent plies), a through-thickness stress transfer function (TSTF) is established. This function is essentially a transfer coefficient model, with the stress disturbance intensity (SDI) of CP as input and the stress response increment (SRI) of APs as output. SDI is defined as the Euclidean distance (ED) between the six-dimensional stress vector at the center plane of CP and its ideal state (defect-free, uniformly stressed), in megapascals (MPa). SRI is defined as the norm of the change in stress at the center plane of APs caused by CP disturbance.

[0068] The specific implementation of the stress transfer function TTSTF relies on the Ply Interaction Stiffness Model (PISM). This model treats adjacent plies as elastic bodies connected by an equivalent interface spring (EIS). The spring stiffness K_interface (in gigapascals per millimeter, GPa / mm) is determined by the interfacial resin properties, fiber bridging degree, and defect density. According to elasticity theory, the stress transfer influence factor (STIF_up) of CP on UP can be approximated as: STIF_up = K_interface / (K_interface + K_up), where K_up is the equivalent compressive stiffness of the UP ply in the thickness direction (in GPa / mm). Similarly, STIF_down (the influence factor on LP) is defined. STIF is a dimensionless value between 0 and 1: STIF=0 indicates no transfer (e.g., complete debonding); STIF=1 indicates complete transfer (e.g., ideal rigid connection). In the actual system, K_interface obtains the typical stiffness values ​​corresponding to different ply angle combinations (such as 0° / 90°, 45° / -45°) and resin types (such as toughness, brittleness) by looking up a table. Then, it is proportionally reduced according to the real-time detected interface porosity (IP, obtained through ultrasonic scanning data) (for example, for every 1% increase in porosity, the stiffness decreases by 2%).

[0069] The final generated Stress Transfer Influence Factor (STIF) is a two-dimensional vector (STIF_up, STIF_down) that quantifies the influence of the CP (Cost Per Attachment) on the upper UP (Uplayer) and lower LP (Layer Per Attachment), respectively. This factor exhibits directional asymmetry: for example, when the CP is a high-stiffness 0° layup and the UP is a low-stiffness 90° layup, the STIF_up of the CP on the UP may be as high as 0.9 (strong influence), while the reverse influence of the UP on the CP is relatively small. In dynamic analysis, if the system detects local failure of the CP (such as matrix cracking), its stiffness K_cp will decrease in real time (e.g., by 50%), causing STIF_up and STIF_down to be recalculated (usually increasing), reflecting the intensified stress transfer to adjacent layups after failure. The STIF set (one vector for each layup) is an important input for evaluating interlayer synergistic effects.

[0070] By combining the interface damage potential energy factor and the stress transfer influence factor, a synergistic effect intensity coefficient is generated through a nonlinear weighting function. At this point, the system has obtained two key intermediate variables: the Interfacial Damage Potential Factor (IDPF), which characterizes the interface's own failure tendency, and the Stress Transfer Influence Factor (STIF), which characterizes the intensity of stress interaction between layers. To synthesize these two factors into a unified synergistic strength index, the system designs a Nonlinear Weighting Function (NWF). The core idea of ​​this function is that the risk of interlayer synergistic failure is jointly determined by "interfacial vulnerability" (reflected by IDPF) and "stress transfer intensity" (reflected by STIF), but the contribution weights of the two change dynamically with the working conditions. The function inputs are the IDPF (scalar) and STIF vectors (STIF_up, STIF_down) corresponding to the current layer CP, and the output is the Synergistic Effect Strength Coefficient (SESCoef) of CP. The larger the value of this coefficient, the higher the risk of interlayer synergistic failure caused by this layer.

[0071] The nonlinear weighting function (NWF) is implemented using a dual-channel modulation architecture (DCMA). Channel 1 (vulnerability channel) processes the IDPF: first, it is mapped to the sensitive region using a sigmoid activation function: IDPF_s = 1 / (1 + exp(-a * (IDPF - b)), where a (slope factor, default value 10) and b (offset factor, default value 0.5) are adjustable parameters used to control the sensitivity of the IDPF near the critical value. Channel 2 (transfer intensity channel) processes the STIF vector: the maximum value of STIF_up and STIF_down, STIF_max = max(STIF_up, STIF_down), is taken, and then its contribution is enhanced using an exponential amplification function: STIF_e = exp(c * STIF_max), where c is the gain coefficient (default value 2.0). Finally, the synergistic effect strength coefficient SESCoef is obtained by multiplying the outputs of both channels: SESCoef = IDPF_s * STIF_e. This design ensures that SESCoef will only increase significantly when both interface fragility (IDPF) and stress transfer intensity (STIF) are high, which is consistent with the physical logic that "fragile interfaces are prone to failure when encountering strong stress interactions".

[0072] The generation process of SESCoef incorporates an adaptive mechanism. The system monitors the load type in real time: if normal tension is dominant (e.g., σ_z accounts for more than 60%), the weighting parameter a is increased (e.g., set to 15) to make IDPF_s more sensitive to normal stripping; if in-plane shear is dominant (τ_xz or τ_yz accounts for more than 50%), the gain coefficient c is increased (e.g., set to 3.0) to enhance the contribution of STIF_e. Furthermore, when a significant free edge effect (FEE) is detected in the laminate (judged by the edge stress concentration factor), the system automatically introduces an edge correction factor (ECF, ranging from 1.0 to 1.5) to amplify SESCoef, capturing the characteristic of easy delamination at the edges. Finally, each layup outputs a dynamically updated SESCoef value, forming a preliminary set of collaborative strength indices.

[0073] By utilizing the interlayer resin plastic deformation parameters, the synergistic effect strength coefficient is viscoelastically corrected, and a dynamic multilayer synergistic strength factor set is output.

[0074] The aforementioned synergistic strength coefficient (SESCoef) is calculated based on elastic assumptions and does not consider the time-dependent plastic behavior (TDPB) of the resin matrix. In actual service, interlaminar resins undergo creep or stress relaxation under long-term stress or cyclic loading, significantly altering stress distribution and failure modes. To accurately capture this effect, the system introduces interlaminar resin plasticity parameters (IRPPs). Key parameters include: the steady-state creep rate (SCR, per megapascal per hour), the relaxation time constant (RTC, per second), and the plastic hardening exponent (PHE, dimensionless). These parameters are calibrated through material testing and stored in a database, and are retrieved based on the resin grade and curing process of the current laminate.

[0075] The viscoelastic correction for SESCoef employs the Time-Integration Correction Method (TICM). The system defines a virtual time step Δt (default value 1 second), within each time step: Creep effect simulation: The creep strain increment Δε_c of the resin layer under interfacial stress (from ISJM) is calculated as Δε_c = SCR * σ_interface * Δt, where σ_interface is the average interfacial stress (equivalent values ​​in the normal and tangential directions). Creep leads to a decrease in the effective stiffness of the interface, thereby weakening the stress transfer capacity. The system updates the STIF value accordingly (e.g., for every 0.1% increase in creep strain, the STIF decreases by 1%).

[0076] Relaxation effect simulation: If the interface stress remains constant, its value will decay exponentially with time: σ(t) = σ_0 * exp(-t / RTC). Relaxation reduces the stress jump amplitude, directly reducing IDPF (for example, after relaxation, Δσ_z decreases by 20%, then G_I decreases by 36%, and IDPD decreases proportionally).

[0077] Plastic accumulation under cyclic loading: In fatigue analysis, the system calculates the plastic strain increment for each cycle based on PHE. When the accumulated plastic strain reaches a threshold (e.g., 0.5%), permanent softening (PS) is triggered, which permanently increases the base value of SESCoef (e.g., +15%).

[0078] The above process dynamically updates SESCoef at each time step, generating the viscoelasticity-corrected cooperative strength coefficient (VISSECoef).

[0079] The final output Multilayer Synergistic Strength Factor (MSSF) is obtained by standardizing VCSESCoef: MSSF = VCSESCoef / MSSF_max. The denominator, MSSF_max, is the maximum coefficient value that the current laminate may reach under ultimate load (determined through pre-analysis). Standardization ensures that MSSF is a dimensionless value between 0 and 1: MSSF=0 indicates no risk of synergistic failure; MSSF=1 indicates reaching the theoretical limit state. The MSSFs of all layups constitute a Dynamic Multilayer Synergistic Strength Factor Set. This set not only contains the current state value but also stores historical data for each time step (such as the rate of change of MSSF over time, dMSSF / dt), used for failure early warning. The system efficiently manages this set through a Distributed In-Memory Database (DIMD), supporting real-time querying and visualization, providing core input for subsequent failure fusion determination.

[0080] By establishing an interlaminar stress jump matrix, the degree of stress discontinuity at the interface of adjacent plies is quantitatively characterized. The interface damage potential energy is calculated based on a strain energy release rate model, and the mechanical interaction between plies is analyzed using a stress transfer function. Finally, a strength correction factor reflecting the interlaminar synergistic effect is generated, overcoming the isolation limitations of traditional single-layer failure analysis and achieving, for the first time, a quantitative assessment of mechanical coupling in the thickness direction. The synergistic strength factor effectively captures the impact of interlaminar stress redistribution on the overall load-bearing capacity, providing key parameters for the progressive failure analysis of composite materials.

[0081] S204, Input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning; Specifically, a dual-channel feature fusion network can be established, where channel A receives the set of local failure indices and channel B receives the set of multi-layer cooperative strength factors. The core architecture of the failure index fusion model is a dual-channel feature fusion network (DCFFN). This network employs a parallel dual-path design: Channel A specifically processes the Local Failure Index Set (LFIS) from each ply, which contains independently calculated failure risk assessment values ​​for each ply (e.g., values ​​between 0 and 1, where 1 represents complete failure); Channel B specifically processes the Multi-layer Synergistic Strength Factor Set (MSSFS), which quantifies the mechanical coupling effects between adjacent plies (e.g., interface peeling risk, stress transfer efficiency, etc.). The input layer of Channel A is designed with a number of neurons equal to the number of plies (e.g., 16 input nodes for a 16-ply plate), with each node receiving the local failure index value LF_i (where i is the ply number) for the corresponding ply. The input layer of Channel B uses a high-order tensor receiving structure, as its input MSSFS is essentially matrix data describing inter-layer relationships (e.g., 15 interfaces × 3 factor types). The input data for both channels must first undergo Feature Standardization Preprocessing (FSP): Min-Max normalization is applied to LFIS (mapping the original values ​​to the 0-1 range), and Z-score normalization is applied to MSSFS (subtracting the mean and dividing by the standard deviation) to eliminate dimensional differences and improve network convergence efficiency. During network initialization, the Channel Dimension Parameter (CDP) is automatically configured according to the laminate configuration (e.g., the layup order [0° / 45° / 90°]s) to ensure that the data topology is strictly aligned with the actual physical hierarchy.

[0082] Channels A and B employ differentiated feature extraction strategies. Channel A, as a scalar data processing pathway, uses fully connected layers (FCLs) as its hidden layers, employing ReLU (Rectified Linear Unit) activation to capture the nonlinear correlation between failure indices. For example, for carbon fiber / epoxy resin laminates used in aircraft wing skin, Channel A might contain three hidden layers (32 / 16 / 8 neurons respectively), progressively abstracting cross-lay failure mode features (such as surface compression failure dominating or core shear failure dominating). Channel B, as a relational data processing pathway, uses a Graph Convolutional Network (GCN) structure in its hidden layers, treating layups as nodes, inter-layer interfaces as edges, and multi-layer collaborative strength factors as edge attributes. The GCN's adjacency matrix is ​​constructed based on layup adjacency relationships (e.g., if the i-th layer is connected to the i+1-th layer, then matrix element A_ij=1), and aggregates the feature information of adjacent nodes through a third-order graph convolution operation (GCO). For example, in glass fiber laminates used in wind turbine blades, channel B, through GCN, can identify an abnormal increase in the synergistic strength factor at the 45° / -45° layup interface due to shear stress concentration. During feature extraction, both channels share cross-channel correlation weights (CCCW) in real time. This weight matrix, learned during the training phase, is used to initially establish the potential mapping relationship between local failures and interlayer synergy.

[0083] To ensure the engineering applicability of the dual-channel network, a Physics-Guided Constraint Mechanism (PGCM) needs to be embedded. In channel A, a fracture toughness threshold (FTT) is introduced as an upper bound constraint on the neuron activation value (e.g., the type I fracture toughness of epoxy resin, G_IC = 280 J / m). 2The activation value is capped at 0.92 to prevent the network output from violating physical laws in its failure predictions. In channel B, an Interface Mechanical Compatibility Condition (IMCC) is applied, requiring that the gradient of the co-strength factor does not exceed the theoretical limit calculated from the interlaminar resin modulus (e.g., epoxy resin E=3.5 GPa) and thickness (e.g., 0.125 mm). The network training uses a hybrid dataset: 70% from finite element simulations (e.g., asymptotic damage analysis of an Abaqus laminate model under impact load) and 30% from experimental data (e.g., interlaminar debonding events monitored by acoustic emission). During training, a Physics-Informed Loss Function (PILF) is used. In addition to the standard Mean Squared Error (MSE), an additional compliance penalty term is added for the Tsai-Hill Failure Envelope (THFE) to ensure that the network predictions are consistent with classical mechanics theory.

[0084] In channel A, a gating mechanism is used to screen key failure indices, and in channel B, the contribution of collaborative factors is allocated through attention weights. The gating mechanism (GM) of channel A is essentially a feature selection filter, with a differentiable gating unit (DGU) at its core. This unit receives a high-order failure feature vector (such as a 32-dimensional vector F_A) processed by a fully connected layer, and calculates the importance score (IS) for each feature dimension through a gating weight generator (GWG). The GWG consists of two layers of neural networks: the first layer is an 8-neuron bottleneck layer (BL) for feature compression, and the second layer is a sigmoid-activated output layer (output value range 0-1). For example, in the analysis of carbon fiber laminates used in automotive chassis, the gating mechanism may identify the failure index IS=0.93 for the 4th layer (45° layup) and the IS=0.21 for the 7th layer (90° layup), indicating that the former contributes more to the overall failure. The gating threshold (GT) is set as a dynamically adjustable parameter (default 0.7). When IS > GT, features are preserved and included in subsequent fusion; otherwise, they are suppressed. To enhance robustness, the gating process introduces a stochastic feature dropout (SDF) strategy: with a 15% probability, the weights of non-critical features (IS < 0.4) are forcibly reset to zero, simulating a scenario where local failure signals are missing due to manufacturing defects.

[0085] The attention weight allocation (AWA) for channel B employs a multi-head self-attention (MHSA) mechanism. First, the multi-layer collaborative strength factors are organized into sequence data (SD), with each time step corresponding to an inter-layer interface (e.g., Interface 1-2, 2-3, ..., 15-16). The input embedding layer (IEL) maps the original factor values ​​(e.g., stripping potential factor 0.35, stress transfer factor 0.78) into a 128-dimensional feature vector. MHSA contains four parallel attention heads (AH), each independently calculating the similarity between the query vector (Q), key vector (K), and value vector (V). The attention score (AS) is calculated using the scaled dot product (SDP): AS = Softmax( (Q·K^T) / √d_k ), where d_k=32 is the dimension of the key vector. Taking ceramic matrix composites for aero-engine cowlings as an example, MHSA may assign a higher attention weight (AS=0.91) to the oxidation damage factor at high-temperature interfaces (>800℃), while the weight at room-temperature interfaces is lower (AS=0.24). The attention output is then fed into a feedforward neural network (FNN) after residual connection (RC) and layer normalization (LN) to further refine the contribution features.

[0086] The synergy between gating and attention mechanisms is achieved through Cross-Channel Alignment Loss (CCAL). This loss function mandates that when the gating mechanism of channel A identifies a significant increase in the criticality of a ply failure (e.g., IS > 0.9 for layer 5), channel B must assign higher attention weights (target AS > 0.8) to the adjacent interfaces (Interfaces 4-5 and 5-6) containing that ply. The alignment supervision signal originates from physical simulation data: the increase in strain energy release rate (ΔG) of adjacent interfaces when a ply fails is calculated using a finite element model. If ΔG exceeds a critical value (e.g., ΔG / G_c > 0.5), it is marked as a strongly correlated interface. The mechanism employs real-time feedback adjustment (RFA) during operation: when a sensor (such as an embedded fiber Bragg grating) detects that the actual interlayer stress jump value exceeds the predicted value by 20%, the confidence level (CL) of the attention weight reset on that interface is automatically reduced, and the gating threshold GT is adaptively increased (e.g., from 0.7 to 0.8) to improve the screening rigor.

[0087] The selected failure indices are combined with the weighted synergy factors to generate a physical enhancement failure feature tensor. The Tensor Outer Product Operation (TOPO) is a key step in feature fusion. The inputs include: the Filtered Failure Index Vector (FFIV) output from Channel A, with a dimension of p×1 (p is the number of critical plies, e.g., p = 7); and the Weighted Synergy Factor Matrix (WSFM) output from Channel B, with a dimension of q×r (q is the number of interfaces, r is the number of factor types, e.g., 15×3). The outer product operation is defined as: FFIV ⊗ WSFM, generating a Physically Enhanced Failure Feature Tensor (PEFFT) with a rank of 3 and a dimension of p×q×r. Taking the FRP laminate for ship propellers as an example: when FFIV = [0.82, 0.95]^T (the critical plies are the 2nd and 5th plies), and WSFM is a 15×3 matrix (the elements are, for example, the debonding factor 0.67 and the shear factor 0.42 for Interface 3 - 4), then the element T(2,3,1) in PEFFT represents the coupling effect strength between the failure of the 2nd ply and the debonding factor of Interface 3 - 4. Tensor filling uses Bilinear Interpolation (BI) to solve the dimension mismatch problem: when p < q, the FFIV is interpolated and dimension-expanded based on the ply thickness (e.g., interpolating 7 plies to 15 virtual plies).

[0088] The physical meaning of PEFFT is visually analyzed through the Feature Tensor Interpretation Engine (FTIE). This engine slices the tensor (Tensor Slicing, TS) into three types of feature maps: Ply-Interface Coupling Map (PICM): Fixing the factor dimension, it shows the association strength between each ply and the interface under a specific failure mode (such as fiber breakage) (e.g., the value of T(i,j,k) is represented by a heat map).

[0089] Cross-Factor Contribution Map (CFCM): Fixing the interface dimension, it compares the influence weights of different synergy factors (debonding / shear / tension) on the same failure event.

[0090] 3D Failure Envelope Surface (FES): Integrating the tensor values along the thickness direction, it generates an interactive and rotatable failure boundary surface.

[0091] For example, in the analysis of aluminum-based composite materials used in high-speed rail car bodies, FTIE might reveal that when the tensor value of PEFFT at position (5,8,2) exceeds 0.75, it indicates that core shear failure will trigger a chain reaction of debonding at interface 8-9. To enhance engineering interpretability, a mapping relationship is established between tensor elements and physical quantities: T(i,j,k) > 0.6 corresponds to an interlaminar crack initiation energy (CIE) > 15 J / m 2 T(i,j,k) > 0.9 corresponds to a residual strength (RS) < 60% of the design value.

[0092] The tensor generation process introduces a Physical Regularization Constraint (PRC): Energy Conservation Constraint (ECC): The product of the weighted sum of the synergistic factors of each interface (∑WSFM_jk) and the weighted sum of the layup failure exponents (∑FFIV_i) is equal to the damage dissipation energy (DDE) calculated by the finite element method, with an error tolerance of ±5%.

[0093] Causal Sequence Constraint (CSC): For impact load scenarios, it is mandatory that the tensor values ​​of the lower layer (closer to the impact surface) in PEFFT lead the upper layer (time difference Δt ≥ 0.2 ms).

[0094] Scale Invariance Processing (SIP): When the laminate thickness changes (e.g., from 2 mm to 10 mm), the dimensionality expansion rules of the outer product operation are adjusted using the Tensor Scaling Factor (TSF = actual thickness / reference thickness) to ensure the model's generalization ability. Constraint violations trigger Tensor Reconstruction (TR): Based on the Lagrange Multiplier Method (LMM), FFIV and WSFM are iteratively corrected until all physical rules are satisfied.

[0095] The failure feature tensor is normalized using Riemannian manifolds to output a set of cooperative failure indices with uniform dimensions.

[0096] The core of Riemannian Manifold Normalization (RMN) is to treat PEFFT as points in Riemannian Space (RS). First, a Symmetric Positive Definite Matrix Space (SPDMS) is constructed: the 3D tensor PEFFT is sliced ​​along the interface dimension, resulting in q p×r matrices {M_j} (j=1...q). Each matrix undergoes symmetrization processing (SP): M_sym = (M_j + M_j^T) / 2 + λI, where λ=10^{-6} is the Identity Matrix Correction Coefficient (IMCC) to ensure the matrix's positive definiteness. On SPDMS, the Riemannian metric (RM) is defined as follows: the distance between two points A and B, dist(A,B) = ||log(A^{-1 / 2}BA^{-1 / 2})||_F, where ||·|_F is the Frobenius norm. This metric possesses affine invariance (AI), ensuring that the normalization result is unaffected by coordinate system rotation.

[0097] The normalization process employs Karcher mean centralization (KMC): Calculate the Riemannian mean (RM) of all matrices {M_j}: μ = argmin ∑ dist^2(M, M_j), and solve it iteratively using the gradient descent (GD) method (step size η=0.01, convergence threshold ε=10^{-5}). Map each matrix to the tangent space (TS): Log_μ(M_j) = μ^{1 / 2} log(μ^{-1 / 2}M_j μ^{-1 / 2}) μ^{1 / 2}, to obtain the set of tangent vectors {V_j}; Perform standard deviation normalization (SDN) in the tangent space: V_norm = (V_j - μ_v) / σ_v, where μ_v is the mean of the tangent vector and σ_v is the standard deviation; Mapping back to Riemannian space: M_norm=Exp_μ(V_norm) = μ^{1 / 2} exp(μ^{-1 / 2}V_norm μ^{-1 / 2}) μ^{1 / 2}.

[0098] Taking carbon-carbon composite materials for satellite supports as an example, KMC treatment can eliminate tensor distribution skew caused by asymmetric layup (such as [0 / 90 / 45]_ns) (Skewness, SK>0.8 reduced to SK<0.1).

[0099] The final output is the generation of the Synergistic Failure Index Set (SFIS): Tensor Contraction (TC): The normalized four-dimensional tensor (p×q×r×number of samples) is contracted along the factor dimension (r), with the formula SFIS_{ij} = ∑k w_k T{ijk}^{norm}, where the weight w_k is determined by the physical importance of the factor (e.g., stripping factor w=0.6, shearing factor w=0.3).

[0100] Dimension Folding (DF): The SFIS_{ij} matrix is ​​summed along the ply dimension (i) to obtain the interface-level collaborative failure index (e.g., SFI_j represents the comprehensive risk of the j-th interface); the ply-level collaborative failure index is averaged along the interface dimension (j) to obtain the ply-level collaborative failure index (e.g., SFI_i represents the corrected risk of the i-th ply under the collaborative effect).

[0101] Physical Calibration (PC): Mapping relationships are established through experimental calibration (e.g., SFI=0.85 corresponds to a 40% decrease in the residual stiffness of the laminate). The output set uses hierarchical encoding (HE): ply indices are encoded with three bits (e.g., L005 represents the 5th layer), and interface indices are encoded with six bits (e.g., I04-05 represents the interface between layers 4 and 5), facilitating engineering applications. The normalized indices have uniform dimensions (0-1 dimensionless values) and satisfy the following: Monotonicity (MT): SFIS increases strictly with increasing load; Additivity (AD): When multiple damage modes coexist, SFIS ≈ ∑ Single-mode exponent; Continuity (CT): Smooth transition of SFIS when the ply thickness changes continuously.

[0102] A dual-channel neural network architecture is employed, using a gating mechanism to filter key local failure features and an attention model to assign synergy factor weights. Cross-scale feature fusion is achieved through tensor outer product operations, ultimately generating an enhanced failure index that simultaneously incorporates local failure information and inter-layer synergy effects. A correlation model between local failures and inter-layer synergy is established, giving the failure index a more explicit physical meaning. Riemannian manifold normalization ensures the comparability of features across different dimensions, providing a high-precision quantitative basis for failure determination.

[0103] S205: Dynamically threshold the set of collaborative failure indices based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, output the inter-layer collaborative failure flag.

[0104] Specifically, the baseline failure threshold under the current load spectrum can be calculated based on the material's service history data using the Weibull distribution model; The system first accesses Service History Data (SHD) stored in the materials database. This data is accumulated through long-term monitoring of the performance degradation process of similar laminated structures under actual working conditions, including time-series records of different stress levels, environmental conditions (such as the number of temperature cycles and the duration of humidity exposure), and corresponding failure events. For example, it includes data on five million pressure cycles experienced by aircraft wing skin laminates over ten years of flight, or records of fatigue crack initiation in wind turbine blade root laminates under specific wind speed spectra. Core parameters include the Load Spectrum (LS), which is the time-intensity distribution characteristics of the external forces acting on the structure (such as the maximum stress value S_max, stress ratio R, and load frequency F_L), and the Time to Failure (TTF). Based on the SHD, the system uses the Weibull Distribution Model (WDM) for statistical analysis. The Weibull distribution is widely used because it can describe the entire process of material failure from early failure to random failure and then to wear-stage failure. Its cumulative distribution function contains two key parameters: the shape parameter β (reflecting the dispersion of failure modes; β less than 1 indicates early failure is dominant, and β greater than 1 indicates wear-stage failure is dominant) and the scale parameter η (characterizing the characteristic lifetime, i.e., the time point when 63.2% of the samples fail). The system uses maximum likelihood estimation (MLE) to fit historical data and solve for the β and η values ​​corresponding to the current load spectrum LS.

[0105] After determining the Weibull parameters, the system performs calculations based on the real-time characteristics of the current load spectrum (CLS). The CLS is acquired in real-time by a sensor network (such as fiber optic grating sensors and piezoelectric ceramic sheets) mounted on the laminate, including parameters such as the current stress amplitude S_a, average stress S_m, and the number of load applications N. The baseline failure threshold (BFT) is not a fixed value but a function related to the current number of load applications. The system derives the reliability function (RF) based on the probability density function of the Weibull distribution, which represents the probability that the structure will not fail under a given number of load applications N. For example, when a reliability of no less than 99.9% is required (i.e., failure probability P_f = 0.001), the corresponding BFT calculation formula is: BFT(N) = η × [ -ln(RF) ]^(1 / β), where RF = 1 - P_f. This formula correlates the service history data (β, η) with the current number of load applications N to dynamically generate the BFT. If there is a difference between the current load spectrum and historical data (such as the detection of abnormal high-frequency impact), the system will convert the current load into the equivalent number of action N_eq through a load spectrum equivalent conversion algorithm (such as the Miner linear cumulative damage rule), and then substitute it into the Weibull model to calculate the BFT, so as to ensure that the threshold matches the actual damage progress.

[0106] To improve the engineering applicability of threshold calculation, the system introduces an Environmental Correction Factor (ECF). ECF acquires real-time parameters such as temperature (T), relative humidity (RH), and corrosive medium concentration (C_chem) of the laminate's environment through environmental sensors (temperature and humidity sensors, chemical corrosion monitoring electrodes), and queries a material environmental degradation database (containing attenuation curves of laminate strength under different T / RH combinations). For example, when RH exceeds 70%, the epoxy resin matrix absorbs moisture, causing a 15% decrease in interfacial strength; at this point, ECF = 0.85. The final baseline failure threshold BFT_final is corrected using the following formula: BFT_final = BFT × ECF. This value serves as the initial baseline for failure determination, laying the foundation for subsequent dynamic adjustments. All calculated parameters (β, η, N, RF, ECF) are recorded in the determination log for traceability.

[0107] Real-time monitoring of the rate of change of the collaborative failure index; when the rate of change exceeds the critical slope, a threshold adaptive adjustment mechanism is triggered to generate a dynamic failure threshold. The system continuously receives the Collaborative Failure Index Set (CFIS) from the Failure Index Fusion module. This set contains the real-time failure index value F_i(t) for each location (typically discretized as grid nodes) of the laminate, with a time resolution on the order of milliseconds. To capture the dynamics of failure development, the system calculates the Rate of Change (ROC) of the failure index at each location, which is the increment of F_i per unit time: ROC_i(t) = [F_i(t) - F_i(t-Δt)] / Δt. Here, Δt is the sampling time interval (e.g., 10 milliseconds). ROC reflects the accelerating trend of local damage (e.g., crack propagation rate). Simultaneously, the system calculates the global average rate of change ROC_avg as an indicator of the overall failure process.

[0108] The preset critical slope (CS) is a key threshold parameter, calibrated through material fracture mechanics tests. For example, interlaminar shear tests on carbon fiber / epoxy resin laminates show that when the ROC exceeds 0.05 per second, interfacial delamination will enter an uncontrollable propagation stage. The system compares ROC_i(t) with CS in real time: if ROC_i(t) > CS at any location, or if the global ROC_avg continuously increases and exceeds 80% of CS over five consecutive sampling periods, the Threshold Adaptive Adjustment Mechanism (TAAM) is triggered. The core of TAAM is the introduction of an accelerated failure factor (AFF), whose value is dynamically calculated based on the proportion by which ROC exceeds CS: AFF = 1 + k × (ROC_i - CS), where k is a proportionality coefficient (e.g., k = 2.0), determined by regression analysis of historical failure cases. An AFF greater than 1 indicates that the failure threshold needs to be lowered for early warning.

[0109] The Dynamic Failure Threshold (DFT) is generated by combining a baseline threshold and a real-time risk factor: DFT(t) = BFT_final × AFF × SF. The Safety Margin Factor (SF) is set according to the structural importance level (e.g., 0.8 for aerospace structures, 0.9 for civilian facilities). To prevent threshold oscillations caused by transient disturbances, the system sets an adjustment hysteresis interval: adjustment is initiated only when the ROC exceeds the CS for three consecutive samples, and the DFT change is limited to ±20%. The adjusted DFT is output through a smoothing filter (e.g., a first-order low-pass filter) to avoid abrupt changes.

[0110] A fuzzy decision-maker is used to compare the collaborative failure index with the dynamic failure threshold to generate a preliminary failure probability distribution map. A fuzzy inferencer (FI) is an intelligent decision-making model that handles uncertainty. Its inputs are the cooperative failure index F_i(t) and the corresponding dynamic failure threshold DFT_i(t) for each grid node (the threshold may differ at different locations). First, three fuzzy sets are defined: Safe Zone (SZ): F_i is much lower than DFT_i (e.g., F_i < 0.7 × DFT_i); Transition Zone (TZ): F_i is close to DFT_i (e.g., 0.7×DFT_i ≤ F_i ≤ 1.3×DFT_i); Failure Zone (FZ): F_i is significantly higher than DFT_i (e.g., F_i > 1.3×DFT_i).

[0111] A Gaussian membership function is used to quantify the degree of membership of each F_i to the three domains. For example, the membership μ_FZ of the failure domain FZ is calculated as: μ_FZ(F_i) = exp( -0.5× [(F_i - c_FZ) / σ_FZ]^2 ).

[0112] Where c_FZ=1.3×DFT_i is the center point, and σ_FZ=0.2×DFT_i is the standard deviation (controlling the transition bandwidth). Similarly, the membership functions of the safe region (c_SZ=0.5×DFT_i, σ_SZ=0.15×DFT_i) and the transition region (c_TZ=DFT_i, σ_TZ=0.25×DFT_i) are defined.

[0113] Reasoning based on fuzzy rule base: Rule 1: If μ_FZ is high, then the failure probability P_f is high; Rule 2: If μ_TZ is high and ROC is high, then P_f is medium; Rule 3: If μ_SZ is high, then P_f is low.

[0114] The centroid method is used for defuzzification, mapping the output to a failure probability (P_f) between 0 and 1. For example, for a node with F_i = 1.25 × DFT_i and a high ROC, fuzzy inference yields P_f = 0.78. The P_f values ​​of all nodes constitute a preliminary failure probability distribution map (PFPDM), which visualizes the failure risk of each region of the laminate in the form of a heatmap.

[0115] Morphological closing operations are performed on the failure probability distribution map to connect adjacent failure regions and output the interlayer collaborative failure marker matrix.

[0116] Morphological Closing Operation (MCO) is an image processing technique used to optimize the morphology of failure regions in PFPDM. It consists of two steps: dilation followed by erosion. The structuring element (SE) is defined as a 3×3 rectangular kernel (representing the connectivity of adjacent meshes). The dilation operation expands the boundary of regions with a failure probability P_f greater than 0.5 outward by one cell, filling in micro-holes; the erosion operation then shrinks the boundary inward by one cell, smoothing irregular edges. The mathematical expression for the closing operation is: PFPDM_closed = (PFPDM ⊕ SE) ⊖ SE, where ⊕ represents dilation and ⊖ represents erosion. This operation can connect isolated failure regions with a spacing smaller than the SE size (such as microcrack clusters less than 3 mm apart), forming physically continuous damage zones.

[0117] The image processed by the closing operation is binarized and segmented: a failure decision threshold (Failure Decision Threshold, FDT=0.65) is set. All nodes with P_f ≥ FDT are marked as 1 (failure state), and the rest are marked as 0 (safe state), generating a binary failure distribution map (BFD). The system scans the BFD and marks connected regions: if adjacent nodes (eight neighbors) are all 1, they are considered to be the same failure region. Geometric features such as area (Area_A) and major axis direction (Orientation_θ) of each region are statistically analyzed.

[0118] The final output is the Interlaminar Collaborative Failure Marker Matrix (ICFMM). This matrix has the same dimension as the laminate mesh, and each element stores three types of information: Failure status flag: 0 / 1 indicates whether it has failed; Failure mode coding: Identify the failure type based on location and stress field (e.g., matrix cracking = 1, fiber fracture = 2, interlaminar delamination = 3). Failure severity level: graded based on P_f value (e.g., 0.65≤P_f<0.8 is mild, P_f≥0.8 is severe).

[0119] For example, a strip-shaped failure zone measuring 120 mm long and 15 mm wide was detected in the interlayer region at the root of a wind turbine blade, marked as "delamination - severe". The ICFMM transmits this information to the health management system via the industrial bus, triggering a maintenance decision.

[0120] A dynamic failure threshold model is established based on the Weibull distribution, which monitors the rate of change of the failure index in real time and adaptively adjusts the judgment criteria. A fuzzy decision maker handles the uncertainty of the critical state, ultimately outputting spatially continuous failure region markers. The dynamic threshold mechanism effectively adapts to complex load conditions, avoiding misjudgments caused by fixed thresholds. Morphological processing ensures the engineering practicality of the failure markers, providing intuitive damage location information for structural health monitoring.

[0121] As can be seen, by projecting the local stress state of all plies of the laminate onto the global coordinate system, an equivalent synergistic stress field with continuity in the thickness direction is generated. Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion. For each ply, the multi-layer synergistic strength factor set is dynamically calculated through mechanical coupling relationship. The local failure index set and the multi-layer synergistic strength factor set are input into the failure index fusion model to generate a synergistic failure index set with enhanced physical meaning. The synergistic failure index set is dynamically thresholded according to a preset adjustable threshold. When the synergistic failure index exceeds the threshold, an inter-layer synergistic failure marker is output. This enables accurate cross-scale prediction of laminate failure behavior, significantly improving the evaluation efficiency and engineering applicability of multi-ply synergistic failure under complex loads.

[0122] Another embodiment of the present invention provides a laminate engineering failure assessment system based on multi-layer collaborative failure logic, see [link to relevant documentation]. Figure 3 The system may include: Projection module 301 is used to project the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. Calculation module 302 is used to calculate the set of local failure indices for each ply based on the equivalent co-stress field and using a preset single-layer failure criterion. Analysis module 303 is used to analyze the stress distribution trend of each ply and its adjacent plies in the thickness direction, and dynamically calculate the set of multilayer cooperative strength factors through mechanical coupling relationship; Input module 304 is used to input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning; The output module 305 is used to dynamically determine the collaborative failure index set according to a preset adjustable threshold. When the collaborative failure index exceeds the threshold, it outputs an inter-layer collaborative failure flag.

[0123] This invention also provides a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any of the above method embodiments when running.

[0124] Specifically, in this embodiment, the storage medium can be configured to store a computer program for performing the following steps: S201 projects the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. S202, Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion; S203, for each ply, analyze the stress distribution trend of it and its adjacent plies in the thickness direction, and dynamically calculate the multilayer cooperative strength factor set through mechanical coupling relationship; S204, Input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning; S205: Dynamically threshold the set of collaborative failure indices based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, output the inter-layer collaborative failure flag.

[0125] This invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the steps in any of the above method embodiments.

[0126] Specifically, the aforementioned electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the aforementioned processor, and the input / output device is connected to the aforementioned processor.

[0127] Specifically, in this embodiment, the processor can be configured to perform the following steps via a computer program: S201 projects the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. S202, Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion; S203, for each ply, analyze the stress distribution trend of it and its adjacent plies in the thickness direction, and dynamically calculate the multilayer cooperative strength factor set through mechanical coupling relationship; S204, Input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning; S205: Dynamically threshold the set of collaborative failure indices based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, output the inter-layer collaborative failure flag.

[0128] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A method for judging the failure of laminated plate engineering based on multi-layer collaborative failure logic, characterized in that, The method includes: The local stress state of all plies of the laminate is projected onto the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction. Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion. For each ply, the stress distribution trend in the thickness direction between it and its adjacent plies is analyzed, and the set of multilayer synergistic strength factors is dynamically calculated through mechanical coupling relationship; The local failure index set and the multi-layer collaborative strength factor set are input into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning. The collaborative failure index set is dynamically thresholded based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, an inter-layer collaborative failure flag is output.

2. The method according to claim 1, characterized in that, The step of projecting the local stress state of all plies of the laminate to the global coordinate system to generate an equivalent synergistic stress field that is continuous in the thickness direction includes: Based on the constitutive equations of each ply material, the stress components in the local coordinate system are transformed into components in the global coordinate system by the tensor transformation rule, resulting in a discrete set of ply stress tensors. Based on the discrete ply stress tensor set, a cubic spline interpolation algorithm is used to perform continuous processing along the thickness direction to generate an initial continuous stress field; By applying material lattice orientation constraints to the initial continuous stress field and eliminating interlayer stress abrupt points through convolution kernel filtering, a stress field intermediate with a smooth transition is generated. By combining the compatibility conditions between the intermediate stress field and the interlayer interface, the stress distribution gradient is optimized using the variational method, and an equivalent synergistic stress field with continuous thickness direction is output.

3. The method according to claim 2, characterized in that, Based on the equivalent synergistic stress field, the local failure index set of each ply is calculated using a preset single-layer failure criterion, including: Based on the equivalent synergistic stress field, the six-dimensional stress vector of the center plane of each ply is extracted as the input quantity of the failure criterion. The six-dimensional stress vector is input into the Tsai-Wu tensor failure criterion, and the strength tensor components are dynamically corrected by the stress gradient sensitivity coefficient to generate the basic failure index. Based on the stress concentration influence factor calculated by the orientation angle of the ply fiber, the directionality enhancement processing of the foundation failure index is carried out to obtain the direction-corrected failure index. Using a manufacturing defect database, a robust failure index is generated by calculating the tolerance compensation of the orientation correction failure index through a defect density distribution function. By combining real-time temperature-humidity field data, an environmental degradation model is used to calibrate the robust failure index, and the final set of local failure indices is output.

4. The method according to claim 3, characterized in that, For each ply, the stress distribution trend in the thickness direction between it and its adjacent plies is analyzed, and the set of multilayer cooperative strength factors is dynamically calculated through mechanical coupling relationships, including: Based on the equivalent synergistic stress field, the difference between the normal and tangential stress components of adjacent layers at the interface is extracted to construct the interlayer stress jump matrix. Based on the interlayer stress jump matrix, the interface peeling potential energy density is calculated through the strain energy release rate model, and the interface damage potential energy factor is generated. The stress transfer function in the thickness direction is used to quantify the degree of stress redistribution of the current ply on the adjacent ply, and the stress transfer influence factor is obtained. By combining the interface damage potential energy factor and the stress transfer influence factor, a synergistic effect intensity coefficient is generated through a nonlinear weighting function. By utilizing the interlayer resin plastic deformation parameters, the synergistic effect strength coefficient is viscoelastically corrected, and a dynamic multilayer synergistic strength factor set is output.

5. The method according to claim 4, characterized in that, The step of inputting the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning includes: A dual-channel feature fusion network is established, wherein channel A receives the set of local failure indices and channel B receives the set of multi-layer cooperative strength factors. In channel A, a gating mechanism is used to screen key failure indices, and in channel B, the contribution of collaborative factors is allocated through attention weights. The selected failure indices are combined with the weighted synergy factors to generate a physical enhancement failure feature tensor. Riemannian normalization is applied to the failure feature tensor to output a set of cooperative failure indices with uniform dimensions.

6. The method according to claim 5, characterized in that, The step involves dynamically thresholding the set of collaborative failure indices based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, an inter-layer collaborative failure flag is output, including: Based on historical material service data, the baseline failure threshold under the current load spectrum is calculated using the Weibull distribution model. Real-time monitoring of the rate of change of the collaborative failure index; when the rate of change exceeds the critical slope, a threshold adaptive adjustment mechanism is triggered to generate a dynamic failure threshold. A fuzzy decision-maker is used to compare the collaborative failure index with the dynamic failure threshold to generate a preliminary failure probability distribution map. Morphological closing operations are performed on the failure probability distribution map to connect adjacent failure regions and output the interlayer collaborative failure marker matrix.

7. A laminate engineering failure assessment system based on multi-layer collaborative failure logic, characterized in that, The system includes: The projection module is used to project the local stress state of all plies of the laminate to the global coordinate system, generating an equivalent synergistic stress field that is continuous in the thickness direction. The calculation module is used to calculate the set of local failure indices for each ply based on the equivalent co-stress field and using a preset single-layer failure criterion. The analysis module is used to analyze the stress distribution trend of each ply and its adjacent plies in the thickness direction, and dynamically calculate the multilayer synergistic strength factor set through mechanical coupling relationship; The input module is used to input the local failure index set and the multi-layer collaborative strength factor set into the failure index fusion model to generate a collaborative failure index set with enhanced physical meaning. The output module is used to dynamically determine the collaborative failure index set based on a preset adjustable threshold. When the collaborative failure index exceeds the threshold, it outputs an inter-layer collaborative failure flag.

8. The system according to claim 7, characterized in that, The projection module is specifically used for: Based on the constitutive equations of each ply material, the stress components in the local coordinate system are transformed into components in the global coordinate system by the tensor transformation rule, resulting in a discrete set of ply stress tensors. Based on the discrete ply stress tensor set, a cubic spline interpolation algorithm is used to perform continuous processing along the thickness direction to generate an initial continuous stress field; By applying material lattice orientation constraints to the initial continuous stress field and eliminating interlayer stress abrupt points through convolution kernel filtering, a stress field intermediate with a smooth transition is generated. By combining the compatibility conditions between the intermediate stress field and the interlayer interface, the stress distribution gradient is optimized using the variational method, and an equivalent synergistic stress field with continuous thickness direction is output.

9. A storage medium, characterized in that, The storage medium stores a computer program, wherein the computer program is configured to execute the method of any one of claims 1-6 when it is run.

10. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the method of any one of claims 1-6.

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