A high-fidelity scalable random crack metal mesh digital modeling method

Abstract

This invention proposes a high-fidelity and scalable digital modeling method for random crack metal mesh gratings, comprising the following steps: preprocessing microscopic images of experimental crack samples to obtain a vector representation of the crack network; extracting multi-dimensional feature vectors of the crack network based on the vector representation; initializing a random crack growth model and driving crack growth through a set of parameter vectors; optimizing the crack growth model using an iterative optimization algorithm with the extracted multi-dimensional feature vectors as the optimization objective to obtain the optimal parameter vectors; generating multiple random crack element networks in batches based on the optimal parameter vectors; and finally, stitching together multiple random crack element networks into a large-area random crack network. This invention integrates experimental observation, physical mechanism modeling, and engineering scalability, solving the problems of low geometric fidelity and poor engineering scalability of existing models, and providing a reliable tool for device design, accurate performance prediction, process optimization, and inversion of random crack mesh gratings.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic metasurface design technology, and in particular to a high-fidelity, scalable digital modeling method for random cracked metal mesh gratings. It is especially suitable for rapid modeling, performance prediction, process optimization, and large-area uniform structure design of metal mesh grating structures prepared based on the crack template method in applications such as aircraft optical windows and flexible electronic devices. Background Technology

[0002] Metamaterials and metasurfaces, as artificially designed composite materials or two-dimensional structures, can achieve remarkable control over the amplitude, phase, and polarization of electromagnetic waves through their subwavelength-scale unit structures ("superatoms" or "supramoleculars") and their arrangement, breaking through the performance limitations of natural materials. Traditional metamaterial / metasurface design typically relies on periodic or quasi-periodic resonant unit structures, such as open rings, metal rods, and nanoblocks; this design method can achieve efficient control at specific frequencies or within narrow bands, but it also has inherent limitations: (1) Periodic structures will produce obvious diffraction effects at specific wavelengths, which is not good for applications such as optical windows; (2) Its electromagnetic response (such as resonant frequency) is highly dependent on the precise geometry and arrangement period of the unit, resulting in a narrow performance bandwidth and extreme sensitivity to manufacturing errors; (3) The low-cost and high-consistency fabrication of complex periodic unit structures on large-area, curved substrates faces challenges.

[0003] To overcome the limitations of periodic structures, the concept of random or aperiodic metasurfaces has attracted attention in recent years. These structures, through carefully designed but aperiodic subwavelength scatterers, can achieve stable electromagnetic responses over a wider frequency band and effectively suppress diffraction. Random cracked metal mesh structures (such as metal networks obtained through the crack template method) can be considered a class of natural, self-assembled two-dimensional random metasurfaces. Their subwavelength-scale metal cracks form a randomly distributed, interconnected conductive network. When electromagnetic waves are incident, they excite complex localized surface plasmon resonances and conduction currents, exhibiting unique equivalent conductivity, equivalent dielectric constant, and electromagnetic shielding / transmission characteristics. Compared to periodic metasurfaces, random cracked metasurfaces offer advantages such as wideband response, angle insensitivity, absence of diffraction patterns, and the potential for large-area fabrication through low-cost self-assembly processes.

[0004] In the prior art, specific processes for preparing such random structures using the crack template method have been disclosed. For example, Chinese invention patent CN103227240A discloses "A method for preparing porous metal thin film transparent conductive electrodes based on the crack template method"; this method uses a specific microcrystalline titanium dioxide sol as a cracking solution to form a cracked thin film template on a substrate, followed by metal deposition and template removal, ultimately obtaining a porous metal thin film electrode with a random crack network structure. This patent details how adjusting process conditions such as sol ratio, spin-coating parameters, and temperature can influence the macroscopic statistical characteristics of cracks (e.g., mesh size of 1-200 μm, metal linewidth of 0.1-15 μm) to a certain extent, and verifies its excellent photoelectric properties. This confirms that self-assembly of random crack structures through physicochemical processes (such as thin film stress release) is a feasible and cost-effective preparation method, providing a technological basis for the practical application of random crack metasurfaces.

[0005] However, there is currently a key bottleneck in applying random crack networks as a designable metasurface: the lack of a precise digital modeling and reverse design bridge between "controllable fabrication" and "performance-oriented design." To accurately predict their optoelectronic properties (such as transmittance, conductivity, and electromagnetic shielding effectiveness) and guide process optimization, it is necessary to establish digital models that include parameters such as linewidth and its evolution, spacing, connectivity, and fractal characteristics.

[0006] Currently, the modeling of random crack structures has the following main shortcomings: (1) Low geometric fidelity: Existing methods focus on the generation of crack centerline (skeleton) and often assume that cracks are grooves of uniform width, ignoring the non-uniformity of line width in the model. In fact, during the propagation process, the width of the crack usually changes non-uniformly from coarse to fine due to energy release. This morphology directly affects the cross-sectional area after metal filling, thus having a key impact on electrical and electromagnetic properties.

[0007] (2) Poor model scalability: Physical mechanism-based models (such as the phase field method) have high computational costs and are difficult to directly generate large-area models. Although geometric statistical methods (such as Voronoi diagrams) can generate large-area patterns, their statistical characteristics are completely random in the global range, making it difficult to guarantee the uniformity and consistency of statistical characteristics in large areas, which is a key requirement for many engineering applications (such as large-area transparent electrodes).

[0008] (3) Lack of effective splicing strategy: Constructing a large-area uniform network by splicing small-sized statistical equivalent networks is an efficient approach, but simple splicing can lead to discontinuities, misalignments or density abrupt changes in cracks at the splicing boundary, which destroys the overall uniformity and physical rationality of the network.

[0009] Therefore, there is an urgent need for a digital modeling method that can generate real linewidth evolution characteristics and can be flexibly and seamlessly extended into arbitrarily large-area uniform random crack networks to support the entire chain of needs from microscopic mechanism research to macroscopic device design. Summary of the Invention

[0010] This invention proposes a high-fidelity and scalable digital modeling method for random crack metal mesh, which solves the problems of low geometric fidelity, poor model scalability, and lack of effective splicing strategies in existing random crack modeling methods.

[0011] The technical solution of this invention is implemented as follows: This invention provides a high-fidelity, scalable digital modeling method for randomly cracked metal mesh, comprising the following steps: S1: Collect microscopic images of experimental crack samples, and perform binarization, skeletonization, and vectorization processing on the microscopic images to obtain a vector representation of the crack network; S2: Extract multi-dimensional feature vectors of the crack network based on the vector representation. The multi-dimensional feature vectors include: topological features describing the network connection relationship, geometric features describing the overall shape and space filling ability of the network, and line width features describing the geometric features of the crack cross section. S3: Initialize a parameterized stochastic crack growth model based on an improved stochastic walk algorithm, which drives crack nucleation, propagation and termination through a set of parameter vectors; S4: Using the multi-dimensional feature vector extracted in step S2 as the optimization target, the parameter vector of the parameterized random crack growth model is adjusted through an iterative optimization algorithm to obtain the optimal parameter vector; S5: Based on the optimal parameter vector, generate multiple statistically equivalent random crack unit networks in batches; S6: Employs an edge-optimized seamless stitching algorithm to stitch together multiple random crack unit networks to form a large-area random crack network.

[0012] Specifically, in step S1, an adaptive thresholding algorithm is used to convert the grayscale image... Convert to binary image A thinning algorithm is applied to the binary image to obtain a crack centerline skeleton image with a width of one pixel. Convert skeleton images into vector networks ,in V For the set of nodes in the network, E Let be the set of edges of the network.

[0013] Specifically, in step S2: The topological features include a histogram of crack segment length distribution. Histogram of crack intersection angle distribution and network connectivity parameters ; The geometric features include fractal dimension. dough coverage ; The linewidth feature includes a crack width distribution histogram. and width attenuation coefficient .

[0014] Furthermore, the method for calculating the topological features includes: The crack segment length distribution histogram Build it in the following way: For the first defined by vector representation i crack edge Calculate its physical length : ; in, To define the ordered sequence of points along the crack edge, Indicates Euclidean distance; Statistically analyze the distribution of all crack edge lengths and divide them into... For each interval, calculate the normalized frequency of the number of line segments within that interval, and form... dimensional vector , its first j Normalized frequency of each interval for: , ; in, Represents a counting function. Indicates the first j A length interval, This represents the total number of edges in the crack network. Histogram of crack intersection angle distribution Build it in the following way: For each node in the vector representation with a degree ≥ 3, calculate the included angles between all pairs of adjacent edges of that node. ; Statistically analyze these included angles in The distribution within the range is divided into Each interval is calculated and its normalized frequency is formed. dimensional vector , its first k Normalized frequency of each interval for: , ; in, Indicates the firstk An angle range, This represents the total number of all included angles. The network connectivity parameters Calculated in the following way: For vector representation with a mean nodes Its clustering coefficient for of The actual number of edges between adjacent nodes Ratio to the maximum possible number of edges: ; If the average clustering coefficient is used to measure the local connectivity of a network, then the network connectivity parameter... The calculation formula is: ; in, This represents the total number of nodes in the crack network. V This is the set of nodes in the crack network.

[0015] Furthermore, the method for calculating the geometric features includes: The fractal dimension Calculated using the box counting method: Using a series of different side lengths A square grid overlays the crack skeleton image, for each Count the number of meshes containing at least one crack pixel. Linear fitting of the data in a log-log coordinate system yields a line whose slope is the fractal dimension. The linear fit satisfies the following relationship: ; Where ~ indicates that a linear relationship is approximately satisfied. The intercept of the fitted line; The surface coverage Directly from binary images The calculation is as follows: ; in, W , H These are the width and height of the binary image, respectively; This indicates that the binary image is at coordinates... Pixel value at a given pixel; area coverage This represents the proportion of crack pixels to the total number of pixels in the image.

[0016] Furthermore, the method for calculating the linewidth feature includes: The crack width distribution histogram Build it in the following way: For each crack pixel in the crack skeleton image, calculate its shortest Euclidean distance to the background region using distance transform. d The width of the local crack at that point is... W Approximately 2 d ; Statistically analyze the distribution of the width values ​​corresponding to all crack pixels, and divide them into... Each interval is calculated and its normalized frequency is formed. dimensional vector , its first m Normalized frequency of each interval for: , ; in, Represents a counting function. Indicates the first m A width range The total number of crack width values ​​included in the statistics; Width attenuation coefficient Obtain it through the following methods: Extract several complete crack trajectories from the vector representation; for the... j Trajectory Along its arc length s Sampling was performed to obtain a set of corresponding width values. The exponential decay model was used to analyze this trajectory. Data fitting: ; in, To fit the obtained crack trajectory The initial width, This is the width attenuation coefficient of the crack trajectory. e It is a natural constant; For all successfully fitted crack trajectories, calculate their attenuation coefficients. The average value is used as the overall width attenuation coefficient of the sample. : ; in, This represents the total number of successfully fitted crack trajectories.

[0017] Specifically, in step S3, the parameterized random crack growth model iteratively simulates the propagation process of each crack, which includes the following steps: S31, Set the size of the simulation area; S32, based on nucleation probability generate M Nucleation point The coordinates of each nucleation point follow a uniform distribution within the region; S33, assign initial state to each nucleation point: initial direction of each nucleation point. obey Uniformly distributed, with initial linewidth at each nucleation point. From the initial linewidth distribution parameter set Sampling from the defined distribution; S34, for each unterminated crack i Iterative expansion is performed until all cracks cease to propagate; S35, after all cracks have terminated, output a vector network that records the coordinates of each node and the linewidth sequence of each crack segment. and strip binary image .

[0018] Furthermore, in step S34, the iterative propagation steps of a single crack include: Location update: 1st i The crack started from the first t Step position , with step size ,direction Expand to t +1 step position The calculation formula is: ; Direction Update: For the first i The first crack t direction of step expansion Generate a random number ,like Less than the preset deflection probability Then the direction of the next expansion will shift. Updated expansion direction for: ; Where mod is the modulo function; Line width update: 1st i The crack in the first t +1 step line width By the t Step line width Calculated based on the exponential decay model: ; in, The linewidth attenuation factor is when Below the preset termination line width threshold At that time, the crack stopped growing; Branching and Termination Determination: Generate random numbers for random termination. ,like Less than the preset random termination probability threshold If the crack growth is terminated, then a random number is generated. ,like If the value is less than a preset threshold, a sub-crack is generated, and the angle between the sub-crack direction and the main crack direction meets the preset range.

[0019] Specifically, in step S4, the iterative optimization algorithm is a genetic algorithm, which searches for the optimal parameter vector by minimizing the multi-dimensional differences between simulation features and experimental features; the constructed objective function... for: ; Where P is the model parameter vector; , , These are the normalized errors for topological features, geometric features, and linewidth features, respectively. , , These are the weighting coefficients; The normalization error of the topological feature The calculation formula is: ; in, This represents the root mean square error, used to calculate the difference in distribution between the simulated histogram and the experimental histogram; , , These represent the crack segment length distribution histogram, crack intersection angle distribution histogram, and network connectivity parameter generated by the model under the drive of vector parameter P, respectively. , , These represent the histogram of experimental crack length distribution, histogram of crack intersection angle distribution, and network connectivity parameters extracted in step S2, respectively. The normalization error of the geometric feature The calculation formula is: ; in, , These represent the fractal dimension and surface coverage of the crack network generated by the model under the drive of vector parameter P, respectively. , These represent the fractal dimension and surface coverage of the experimental crack network extracted in step S2, respectively. The normalization error of the linewidth feature The calculation formula is: ; in, , These represent the crack width distribution histogram and crack linewidth attenuation factor generated by the model under the drive of vector parameter P, respectively. , Let S1 and S2 respectively represent the experimental crack width distribution histogram and crack linewidth attenuation coefficient extracted in step S2. k This is the dimension conversion coefficient.

[0020] Specifically, in step S6, the seamless stitching algorithm based on edge optimization includes the following steps: S61, splicing planning: Based on the size of the target area, plan the splicing array of the unit network; S62, Edge Region Definition and Extraction: Define an internal stable region and a ring-shaped outer edge buffer for each cell network, and extract crack segments of all cell networks within their edge buffers; S63, Buffer Crack Fusion and Re-optimization: During splicing, the edge buffers of adjacent element networks overlap to form overlapping regions. Crack segments from different element networks are fused within these overlapping regions. The fusion process includes: (a) Crack connection: If the distance between the endpoints of two crack segments from different unit networks is less than the connection distance threshold, and the angle difference of their tangent directions is less than the direction difference threshold, then these two segments are connected into a continuous crack. (b) Conflict resolution: For crack segments that are close to or intersect in the overlapping area and do not meet the connection conditions, one of the segments is cut off or deleted according to the preset rules. (c) Density adjustment: Calculate the crack density in the overlapping area. If it is lower than the preset percentage of the density in the stable area of ​​the unit network, then local, small-step random crack growth is started in this area, constrained by the optimal parameter vector obtained in step S4. S64, Crack Integration: Integrate the stable region cracks of each unit network with the overlapping region cracks processed in step S63 to generate the final large-area random crack network.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention provides a complete digital modeling workflow from microscopic feature extraction to macroscopic structure construction. By collecting real sample images and extracting multi-dimensional statistical features including linewidth features, the growth model parameters of the integrated linewidth evolution mechanism are optimized based on these features. Finally, a large-area uniform network is generated through an innovative seamless splicing algorithm. This workflow systematically integrates experimental observation, physical mechanism modeling and engineering scalability. It not only solves the core contradiction of low geometric fidelity and poor engineering scalability of existing models, but also opens up the digital chain of "process-microstructure-large-size device performance". It provides a one-stop efficient and reliable tool for device design, accurate performance prediction, process optimization and inversion of random crack grids.

[0022] (2) This invention integrates a linewidth evolution mechanism into a random crack growth model. When the model simulates crack propagation, the linewidth decreases exponentially according to the physical law of "from thick to thin", thereby generating a "band-shaped" crack geometry with a real cross-sectional shape, rather than the traditional uniform "skeleton line". This allows the digital model to more realistically reflect the change in the cross-sectional area of ​​the conductor after metal filling, significantly improving the accuracy and reliability of subsequent electrical conduction performance and electromagnetic field simulation calculations, and overcoming the performance prediction deviation caused by the neglect of linewidth non-uniformity in existing models.

[0023] (3) By defining a “stable region-buffer zone” for each unit network and performing crack connection, conflict resolution and local density adjustment within the overlapping buffer zone, this invention effectively eliminates the boundary discontinuity and statistical feature mutation problems caused by simple splicing, enabling small-area high-fidelity unit networks to be flexibly and uniformly expanded into crack networks with arbitrarily large areas and consistent statistical features. This solves the engineering problem of balancing the generation efficiency and global uniformity of large-size computational models, and is particularly suitable for the design of large-area optoelectronic devices with stringent requirements for performance uniformity.

[0024] (4) The present invention adopts a parameter optimization strategy of multi-dimensional feature matching, which not only matches topological and geometric features, but also takes line width distribution and decay law as key optimization targets. Through iterative methods such as genetic algorithms, the growth model parameters are highly consistent with the micro-statistical features of real samples. This reverse optimization based on multi-dimensional experimental features ensures that the established parameterized model can accurately reproduce the micro-structural features under specific preparation processes, laying a solid foundation for the quantitative correlation and reverse design of "process parameters-microstructure-macro performance". Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating a high-fidelity, scalable digital modeling method for random cracked metal mesh according to the present invention.

[0027] Figure 2 This is an image of an experimental crack sample from an embodiment of the present invention.

[0028] Figure 3 These are six typical crack element network images selected from the element network library generated in this embodiment of the invention.

[0029] Figure 4 This is a diagram illustrating the effect of a large-area uniform crack network formed by splicing in an embodiment of the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0031] This embodiment uses the digital modeling of a large-area random cracked metal mesh for an aircraft's photoelectric detection window as an application scenario. It achieves the construction of a high-fidelity random cracked metal mesh model with dimensions of 400mm × 400mm and a hemispherical substrate with a curvature radius of 150mm. The model needs to meet the following requirements: linewidth 0.2~8μm, surface coverage 6%~8%, fractal dimension 1.5~1.7, and large-area statistical feature uniformity error ≤5%. This provides accurate digital support for subsequent process fabrication and photoelectric performance simulation. Before starting the embodiment, a random cracked metal mesh sample is first prepared using the crack template method. Specific process parameters are referred to in Embodiment 1 of Chinese Patent (Publication No.: CN103227240A), and a random crack template is obtained as the experimental crack sample.

[0032] Reference Figure 1 This invention provides a high-fidelity, scalable digital modeling method for random cracked metal mesh, comprising the following steps: Step S1: Acquire microscopic images of three groups of experimental crack samples from different regions (e.g., Figure 2As shown, each set of images contains 5 non-overlapping fields of view to ensure the statistical representativeness of feature extraction. The microscopic image is binarized, skeletonized, and vectorized to obtain a vector representation of the crack network. Specifically, this includes the following steps: Binarization: Adaptive thresholding algorithms (such as the Otsu algorithm) are used to perform binarization on grayscale images. Perform binary segmentation to obtain a binary image. In this process, the crack pixel value is 1 (or 255), and the background pixel value is 0; isolated noise points are removed by morphological opening operations (structuring element is a 3×3 square); Skeletonization: A thinning algorithm (such as the Zhang-Suen algorithm) is applied to extract the skeleton from the binary image to obtain a single-pixel-wide crack centerline skeleton image. This ensures that the skeleton is free of branch breaks and redundant pixels; Vectorization: The Douglas-Peucker algorithm is used to approximate the skeleton contour with polygons, and a vector network is constructed. ,in V It is the set of nodes in the network (crack intersections and endpoints). E The set of edges in the network (crack segments connecting nodes), where each edge is composed of an ordered sequence of coordinate points. The coordinate precision is defined to be retained to 0.1μm.

[0033] Step S2: Based on the vector representation Extracting multi-dimensional feature vectors from crack networks, the multi-dimensional feature vectors Includes: topological features describing network connectivity. Geometric features describing the overall morphology and space-filling ability of a network and linewidth features describing the geometry of the crack cross section. ; Specifically, in this embodiment: The topological features include a histogram of crack segment length distribution. Histogram of crack intersection angle distribution and network connectivity parameters ; The geometric features include fractal dimension. dough coverage ; The linewidth feature includes a crack width distribution histogram. and width attenuation coefficient .

[0034] Furthermore, the topological features The calculation methods include: The crack segment length distribution histogram Build it in the following way: For the first defined by vector representation i crack edge Calculate its physical length : ; in, To define the ordered sequence of points along the crack edge, Indicates Euclidean distance; Statistically analyze the distribution of all crack edge lengths and divide them into... Each interval (in this embodiment) ), calculate the normalized frequency of the number of line segments within each interval, and form dimensional vector , its first j Normalized frequency of each interval for: , ; in, Represents a counting function. Indicates the first j A length interval, This represents the total number of edges in the crack network; this feature reflects the scale distribution of crack propagation.

[0035] Histogram of crack intersection angle distribution Build it in the following way: For each node with a degree ≥ 3 in the vector representation (a total of 186 nodes / intersections with a degree ≥ 3 in this embodiment), calculate the included angles between all pairs of adjacent edges of that node. ; Statistically analyze these included angles in The distribution within the range is divided into Each interval (in this embodiment) (Each interval is 20°) and the normalized frequency is calculated to form... dimensional vector (In this embodiment, and These two intervals have the highest frequency), and their... k Normalized frequency of each interval for: , ; in, Indicates the first k An angle range, This represents the total number of all statistical angles; this feature reflects the tendency of crack branching (e.g., whether it tends to intersect perpendicularly).

[0036] In this embodiment, "degree" is a concept in graph theory, representing the number of edges connected to a node. In this scenario, a "node with degree ≥ 3" specifically refers to a point where at least three crack segments intersect, i.e., a branch or intersection point of the crack. If a crack segment terminates at this node, the degree of the node is 1; if a crack segment passes through this node (i.e., the node is a point on the segment), the degree of the node is 2 (because an edge has two endpoints, and this node is one of them).

[0037] The network connectivity parameters Calculated in the following way: For vector representation with a mean nodes Its clustering coefficient for of The actual number of edges between adjacent nodes Ratio to the maximum possible number of edges: ; If the average clustering coefficient is used to measure the local connectivity of a network, then the network connectivity parameter... The calculation formula is: ; in, The total number of nodes in the crack network (in this embodiment, ...). ), V For the set of nodes in a crack network; A higher value indicates that the network is more locally connected. In this embodiment, ; Furthermore, the geometric features The calculation methods include: The fractal dimension Calculated using the box counting method: Using a series of different side lengths A square grid overlays the crack skeleton image, for each Count the number of meshes containing at least one crack pixel. Linear fitting of the data in a log-log coordinate system yields a line whose slope is the fractal dimension. It reflects the complexity of the crack and its space-filling ability; the linear fitting satisfies the following relationship: ; Where ~ indicates that a linear relationship is approximately satisfied. The intercept of the fitted line; The smaller the size, the fewer grids are needed. The more, the better; in this embodiment, ; The surface coverage Directly from binary images The calculation is as follows: ; in, W , H These are the width and height of the binary image, respectively; This indicates that the binary image is at coordinates... Pixel value at a given pixel; area coverage This represents the proportion of the total number of cracked pixels to the total number of pixels in the image. The metal filler content is directly related to the material's conductivity and optical transparency; in this embodiment, .

[0038] Furthermore, the linewidth feature The calculation methods include: The crack width distribution histogram Build it in the following way: For each crack pixel in the crack skeleton image, calculate the shortest Euclidean distance to the background region (pixel value 0) using distance transform. d The width of the local crack at that point is... W Approximately 2 d (Assuming the crack boundary is symmetrical); statistically analyze the distribution of the width values ​​corresponding to all crack pixels, and divide them into... Each interval (in this embodiment, And calculate the normalized frequency to form dimensional vector , its first m Normalized frequency of each interval for: , ; in, Represents a counting function. Indicates the first m A width range This represents the total number of crack width values ​​included in the statistics; this feature directly affects the cross-sectional area and resistance of the metallized conductor.

[0039] Width attenuation coefficient Obtain it through the following methods: Crack tracing: Extract several complete crack trajectories (30 in this implementation) with a length ≥ 5 μm from the vector representation; Width-arc length mapping: for the first arc length j Trajectory Along its arc length s (From the starting point) s Starting from 0, sampling is performed (width value is sampled every 0.2μm) to obtain a set of corresponding width values. (Obtained by interpolating the aforementioned distance transformation results); Exponential fitting: The trajectory is fitted using an exponential decay model. Data fitting: ; in, To fit the obtained crack trajectory The initial width, This is the width attenuation coefficient of the crack trajectory. e It is a natural constant; Statistical averaging: Calculate the attenuation coefficient for all successfully fitted crack trajectories. The average value is used as the overall width attenuation coefficient of the sample. : ; in, This represents the total number of successfully fitted crack trajectories; this feature quantifies the physical tendency of cracks to "narrow" along the propagation direction. A larger value indicates a faster decrease in crack width as it propagates, which is physically related to the severity of stress release in the thin film; in this embodiment, .

[0040] Finally, by concatenating all the above feature scalars or vectors in a predetermined order, a unique "fingerprint" feature vector representing the experimental sample is formed. This vector provides a clear, multi-dimensional optimization objective for the subsequent parametric growth model, ensuring that the generated digital model is highly consistent with the real sample in terms of topological, geometric, and physical details, thus laying a reliable morphological foundation for its prediction and reverse design of electromagnetic properties as a metasurface.

[0041] Step S3: Initialize a parameterized stochastic crack growth model, which is based on an improved stochastic walk algorithm and drives the nucleation, propagation and termination of cracks through a set of parameter vectors P; In this embodiment, the controllable parameter vector of the model is:

[0042] The parameters are explained in Table 1 below: Table 1. Description of Model Parameter Vectors

[0043] Specifically, in this embodiment, the parameterized random crack growth model iteratively simulates the propagation process of each crack. When simulating each step of crack propagation, the model not only updates the position and direction but also adjusts the current linewidth. and attenuation factor Calculate the line width for the next step. This achieves the generation of banded geometry for crack trajectories, rather than single-line generation; specifically, it includes the following steps: S31, set the simulation area size to 10mm×10mm and the pixel resolution to 0.1μm / pixel, consistent with the experimental image in step S1; S32, based on nucleation probability Generate within the simulation area M 150 nucleation sites (in this embodiment) The coordinates of each nucleation point follow a uniform distribution within the region; S33, assign initial state to each nucleation point: initial direction of each nucleation point. obey Uniformly distributed, with initial linewidth at each nucleation point. From the initial linewidth distribution parameter set Sampling is performed within the defined normal distribution; S34, for each unterminated crack i Iterative expansion is performed until all cracks cease to propagate; The iterative propagation steps of a single crack include: Location update: 1st i The crack started from the first t Step position , with step size ,direction Expand to t +1 step position The calculation formula is: ; Direction Update: For the first i The first crack t direction of step expansion Generate a random number ,like Less than the preset deflection probability (In this implementation, If so, the direction of the next expansion will shift. (In this embodiment, ), updated expansion direction for: ; Where mod is the modulo function; Line width update: 1sti The crack in the first t +1 step line width By the t Step line width Calculated based on the exponential decay model: ; in, The linewidth attenuation factor (in this embodiment, ), step size ;when Below the preset termination line width threshold At that time, the crack stopped growing; Branching and Termination Determination: Generate random numbers for random termination. ,like Less than the preset random termination probability threshold (In this implementation, If the crack grows to the specified value, then the growth of that crack will be terminated; generate random numbers. ,like If the value is less than the preset threshold of 0.04, a sub-crack is generated and an initial state is assigned. The angle between the sub-crack direction and the main crack direction meets the preset range (±60°~±120°), and the initial linewidth is 0.6~0.8 times that of the main crack.

[0044] S35, after all cracks have terminated (iteration steps ≤ 5 × 10) 4 (Step), outputting a 10mm×10mm vector network that records the coordinates of each node and the linewidth sequence of each crack segment. and strip binary image For strip-shaped binary images The pixel value of the crack area is 1 (or 255), and the background is 0, which is consistent with the experimental image format in step S1.

[0045] Step S4: Using the multi-dimensional feature vector extracted in step S2 as the optimization target, adjust the parameter vector of the parameterized random crack growth model through an iterative optimization algorithm to obtain the optimal parameter vector; Specifically, in this embodiment, the iterative optimization algorithm is a genetic algorithm, which searches for the optimal parameter vector by minimizing the multi-dimensional differences between simulation features and experimental features, thereby quantifying the degree of matching between simulation features and experimental features; the constructed objective function... for: ; Where P is the model parameter vector; , , These are the normalized errors for topological features, geometric features, and linewidth features, respectively. , , These are the weighting coefficients; The normalization error of the topological feature The calculation formula is: ; in, This represents the root mean square error, used to calculate the difference in distribution between the simulated histogram and the experimental histogram; , , These represent the crack segment length distribution histogram, crack intersection angle distribution histogram, and network connectivity parameter generated by the model under the drive of vector parameter P, respectively. , , These represent the histogram of experimental crack length distribution, histogram of crack intersection angle distribution, and network connectivity parameters extracted in step S2, respectively. To ensure the local connectivity matching of the network, the absolute error between the simulated network connectivity parameters and the experimental network connectivity parameters is calculated.

[0046] The normalization error of the geometric feature The calculation formula is: ; in, , These represent the fractal dimension and surface coverage of the crack network generated by the model under the drive of vector parameter P, respectively. , These represent the fractal dimension and surface coverage of the experimental crack network extracted in step S2, respectively. The normalization error of the linewidth feature The calculation formula is: ; in, , These represent the crack width distribution histogram and crack linewidth attenuation factor generated by the model under the drive of vector parameter P, respectively. , Let S1 and S2 respectively represent the experimental crack width distribution histogram and crack linewidth attenuation coefficient extracted in step S2. k These are the dimension conversion coefficients. The first term is the root mean square error of the width distribution histogram, ensuring the statistical regularity of the line width matches; the second term is the line width attenuation factor. With experimental attenuation coefficient The relative error of the mapping value ensures the physical authenticity of the dynamic evolution law of the linewidth.

[0047] Considering the critical impact of linewidth characteristics on subsequent electromagnetic and electrical performance simulations, and the differentiated importance of each feature in describing crack morphology, differentiated weights are assigned to features of different dimensions. In this embodiment, the weight vector is set to... ,satisfy .

[0048] A genetic algorithm is used as the core optimization algorithm, with a population size of 70, a maximum number of iterations of 180, a crossover probability of 0.75, a mutation probability of 0.04, and a convergence threshold of [missing value]. (Change in objective function value over 25 consecutive generations ≤) (Then the iteration terminates); by optimization, a set of optimal parameters is obtained that makes the simulated network match the experimental network in terms of topology, geometry, and linewidth characteristics. The optimization results of the key parameters are as follows: , , , Verify the error between simulation characteristics and experimental characteristics: , , All parameters meet the design requirements; the above verification process ensures optimal parameters. It can accurately reproduce the multi-dimensional features of experimental samples, providing reliable parameter guarantees for the subsequent generation of statistically equivalent unit networks and large-area seamless splicing.

[0049] Step S5: Based on the optimal parameter vector, generate multiple random crack unit networks that are statistically equivalent in terms of features in batches; Fixed model parameters are Set 800 different random number seeds (seed range 1~800) to ensure that the generated unit networks are statistically equivalent and do not overlap; run the parameterized random growth model in batches to generate 800 random crack unit networks with a size of 10mm×10mm. ,like Figure 3 As shown, six cell networks were selected from the cell network library for illustration; each cell network... In addition to the crack centerline vector data, it also includes the linewidth data at each point along the centerline, forming a complete description of the "centerline + linewidth field".

[0050] Step S6: Employ an edge-optimized seamless stitching algorithm to stitch together multiple random crack element networks to form a large-area random crack network. This includes the following steps: S61, splicing planning: Based on the size of the target area (400mm×400mm), plan the splicing array of the unit network (e.g., a 40×40 array, with each unit network measuring 10mm×10mm); randomly select 1600 qualified unit networks from the unit library to avoid periodic textures after splicing; S62, Edge Region Definition and Extraction: For each cell network Define an inner stable region (a central 8mm × 8mm area) and an annular outer edge buffer (e.g., the buffer width is 10%-20% of the cell network size, such as 1mm wide), and extract crack segments of all cell networks within their edge buffers; S63, Buffer Crack Fusion and Re-optimization: During splicing, the edge buffers of adjacent element networks overlap to form overlapping regions. Crack segments from different element networks are fused within these overlapping regions. The fusion process includes: (a) Crack connection: If the distance between the endpoints of two crack segments from different unit networks is less than the connection distance threshold (15 μm in this embodiment), and the angle difference in their tangent directions is less than the direction difference threshold (12° in this embodiment), then these two segments are connected into a continuous crack; traverse all the endpoints of crack segments in the overlapping area and connect the endpoints of crack segments that meet the above conditions to form a continuous crack segment; (b) Conflict resolution: For crack segments that are too close or intersect in the overlapping area and do not meet the connection conditions, one of the segments is truncated or deleted according to the preset rules (similar to the rules in the growth model); if parallel segments with a spacing of <10μm and do not meet the connection conditions are regarded as "geometric conflicts", the ratio of segment length to line width is calculated, and the shorter segments with smaller ratios are deleted (priority: retain long cracks, wide line width cracks) to avoid structural redundancy; (c) Density adjustment: Calculate the crack density (crack length per unit area) in the overlapping area. If it is lower than 90% of the density of the stable area of ​​the unit network, then, with the optimal parameter vector obtained in step S4 as a constraint, "seed" new crack nuclei in this low-density area (the nucleation probability is 1.2 times that of the stable area) and perform local finite step size (≤100 steps) growth to fill the density unevenness that may be caused by splicing and ensure uniform transition.

[0051] S64, Crack Integration: Integrate the stable region cracks of each unit network with the overlapping region cracks processed in step S63, ultimately generating a large-area random crack network of 400mm×400mm with uniform statistical characteristics and no obvious splicing traces. ,like Figure 4 As shown; the statistical characteristic uniformity error is ≤4%.

[0052] This embodiment also includes: Step S7, Network Geometric Repair and 3D Mapping: The generated large-area network undergoes geometric post-processing. Isolated crack segments with a length <0.3μm (accounting for 2.1% of the total cracks) are deleted. Crack corners are smoothed (corner radius = 0.05μm), and topological connection errors in intersecting cracks (18 in total) are repaired to ensure the rationality of the geometric structure. The target substrate is a hemisphere with a curvature radius of 150mm. A hemispherical projection mapping algorithm is used to map the 2D planar network to a 3D hemisphere.

[0053] Step S8, Digital Model Output and Application: Output the final model in a format that can be used for simulation; since the model contains linewidth information, it can more accurately generate three-dimensional solids or shell meshes for finite element analysis.

[0054] This embodiment successfully constructed a high-fidelity, scalable, large-area random crack metal mesh digital model through the complete above process, achieving the following technical effects: (1) The model linewidth evolution characteristics are highly consistent with the experimental samples, and the physical morphology of the crack "from thick to thin" is replicated with an accuracy of ≥95%, which solves the defect of existing models ignoring the non-uniformity of linewidth; (2) The spliced ​​large-area network has no obvious boundary traces and the statistical characteristic uniformity error is ≤4%, which meets the requirements of flexible electronic devices for large-area performance consistency. (3) The model contains complete geometric and linewidth information, and the simulation accuracy of photoelectric performance is improved by more than 30% compared with traditional models, providing a reliable tool for reverse design of "process-microstructure-performance".

[0055] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A high-fidelity, scalable digital modeling method for random cracked metal mesh, characterized in that, Includes the following steps: S1: Collect microscopic images of experimental crack samples, and perform binarization, skeletonization, and vectorization processing on the microscopic images to obtain a vector representation of the crack network; S2: Extract multi-dimensional feature vectors of the crack network based on the vector representation. The multi-dimensional feature vectors include: topological features describing the network connection relationship, geometric features describing the overall shape and space filling ability of the network, and line width features describing the geometric features of the crack cross section. S3: Initialize a parameterized stochastic crack growth model based on an improved stochastic walk algorithm, which drives crack nucleation, propagation and termination through a set of parameter vectors; S4: Using the multi-dimensional feature vector extracted in step S2 as the optimization target, the parameter vector of the parameterized random crack growth model is adjusted through an iterative optimization algorithm to obtain the optimal parameter vector; S5: Based on the optimal parameter vector, generate multiple statistically equivalent random crack unit networks in batches; S6: Employs an edge-optimized seamless stitching algorithm to stitch together multiple random crack unit networks to form a large-area random crack network.

2. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 1, characterized in that, In step S1, an adaptive thresholding algorithm is used to convert the grayscale image... Convert to binary image A thinning algorithm is applied to the binary image to obtain a crack centerline skeleton image with a width of one pixel. Convert skeleton images into vector networks ,in V For the set of nodes in the network, E Let be the set of edges of the network.

3. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 1, characterized in that, In step S2: The topological features include a histogram of crack segment length distribution. Histogram of crack intersection angle distribution and network connectivity parameters ; The geometric features include fractal dimension. dough coverage ; The linewidth feature includes a crack width distribution histogram. and width attenuation coefficient .

4. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 3, characterized in that, The calculation method for the topological features includes: The crack segment length distribution histogram Build it in the following way: For the first defined by vector representation i crack edge Calculate its physical length : ； in, To define the ordered sequence of points along the crack edge, Indicates Euclidean distance; Statistically analyze the distribution of all crack edge lengths and divide them into... For each interval, calculate the normalized frequency of the number of line segments within that interval, and form... dimensional vector , its first j Normalized frequency of each interval for: ， ； in, Represents a counting function. Indicates the first j A length interval, This represents the total number of edges in the crack network. Histogram of crack intersection angle distribution Build it in the following way: For each node in the vector representation with a degree ≥ 3, calculate the included angles between all pairs of adjacent edges of that node. ; Statistically analyze these included angles in The distribution within the range is divided into Each interval is calculated and its normalized frequency is formed. dimensional vector , its first k Normalized frequency of each interval for: ， ； in, Indicates the first k An angle range, This represents the total number of all included angles. The network connectivity parameters Calculated in the following way: For vector representation with a mean nodes Its clustering coefficient for of The actual number of edges between adjacent nodes Ratio to the maximum possible number of edges: ； If the average clustering coefficient is used to measure the local connectivity of a network, then the network connectivity parameter... The calculation formula is: ； in, This represents the total number of nodes in the crack network. V This is the set of nodes in the crack network.

5. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 3, characterized in that, The calculation method for the geometric features includes: The fractal dimension Calculated using the box counting method: Using a series of different side lengths A square grid overlays the crack skeleton image, for each Count the number of meshes containing at least one crack pixel. Linear fitting of the data in a log-log coordinate system yields a line whose slope is the fractal dimension. The linear fit satisfies the following relationship: ； Where ~ indicates that a linear relationship is approximately satisfied. The intercept of the fitted line; The surface coverage Directly from binary images The calculation is as follows: ； in, W , H These are the width and height of the binary image, respectively; This indicates that the binary image is at coordinates... Pixel value at a given pixel; area coverage This represents the proportion of crack pixels to the total number of pixels in the image.

6. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 3, characterized in that, The method for calculating the linewidth feature includes: The crack width distribution histogram Build it in the following way: For each crack pixel in the crack skeleton image, calculate its shortest Euclidean distance to the background region using distance transform. d The width of the local crack at that point is... W Approximately 2 d ; Statistically analyze the distribution of the width values ​​corresponding to all crack pixels, and divide them into... Each interval is calculated and its normalized frequency is formed. dimensional vector , its first m Normalized frequency of each interval for: ， ； in, Represents a counting function. Indicates the first m A width range The total number of crack width values ​​included in the statistics; Width attenuation coefficient Obtain it through the following methods: Extract several complete crack trajectories from the vector representation; for the... j Trajectory Along its arc length s Sampling was performed to obtain a set of corresponding width values. The exponential decay model was used to analyze this trajectory. Data fitting: ； in, To fit the obtained crack trajectory The initial width, This is the width attenuation coefficient of the crack trajectory. e It is a natural constant; For all successfully fitted crack trajectories, calculate their attenuation coefficients. The average value is used as the overall width attenuation coefficient of the sample. : ； in, This represents the total number of successfully fitted crack trajectories.

7. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 1, characterized in that, In step S3, the parameterized stochastic crack growth model iteratively simulates the propagation process of each crack, specifically including the following steps: S31, Set the size of the simulation area; S32, based on nucleation probability generate M Nucleation point The coordinates of each nucleation point follow a uniform distribution within the region; S33, assign initial state to each nucleation point: initial direction of each nucleation point. obey Uniformly distributed, with initial linewidth at each nucleation point. From the initial linewidth distribution parameter set Sampling from the defined distribution; S34, for each unterminated crack i Iterative expansion is performed until all cracks cease to propagate; S35, after all cracks have terminated, output a vector network that records the coordinates of each node and the linewidth sequence of each crack segment. and strip binary image .

8. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 7, characterized in that, In step S34, the iterative propagation steps of a single crack include: Location update: 1st i The crack started from the first t Step position , with step size ,direction Expand to t +1 step position The calculation formula is: ； Direction Update: For the first i The first crack t direction of step expansion Generate a random number ,like Less than the preset deflection probability Then the direction of the next expansion will shift. Updated expansion direction for: ； Where mod is the modulo function; Line width update: 1st i The crack in the first t +1 step line width By the t Step line width Calculated based on the exponential decay model: ； in, The linewidth attenuation factor is when Below the preset termination line width threshold At that time, the crack stopped growing; Branching and Termination Determination: Generate random numbers for random termination. ,like Less than the preset random termination probability threshold If the crack growth is terminated, then a random number is generated. ,like If the value is less than a preset threshold, a sub-crack is generated, and the angle between the sub-crack direction and the main crack direction meets the preset range.

9. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 1, characterized in that, In step S4, the iterative optimization algorithm is a genetic algorithm, which searches for the optimal parameter vector by minimizing the multi-dimensional differences between simulation features and experimental features; the constructed objective function... for: ； Where P is the model parameter vector; , , These are the normalized errors for topological features, geometric features, and linewidth features, respectively. , , These are the weighting coefficients; The normalization error of the topological feature The calculation formula is: ； in, This represents the root mean square error, used to calculate the difference in distribution between the simulated histogram and the experimental histogram; , , These represent the crack segment length distribution histogram, crack intersection angle distribution histogram, and network connectivity parameter generated by the model under the drive of vector parameter P, respectively. , , These represent the histogram of experimental crack length distribution, histogram of crack intersection angle distribution, and network connectivity parameters extracted in step S2, respectively. The normalization error of the geometric feature The calculation formula is: ； in, , These represent the fractal dimension and surface coverage of the crack network generated by the model under the drive of vector parameter P, respectively. , These represent the fractal dimension and surface coverage of the experimental crack network extracted in step S2, respectively. The normalization error of the linewidth feature The calculation formula is: ； in, , These represent the crack width distribution histogram and crack linewidth attenuation factor generated by the model under the drive of vector parameter P, respectively. , Let S1 and S2 respectively represent the experimental crack width distribution histogram and crack linewidth attenuation coefficient extracted in step S2. k This is the dimension conversion coefficient.

10. The high-fidelity, scalable digital modeling method for random cracked metal mesh as described in claim 1, characterized in that, In step S6, the seamless stitching algorithm based on edge optimization includes the following steps: S61, splicing planning: Based on the size of the target area, plan the splicing array of the unit network; S62, Edge Region Definition and Extraction: Define an internal stable region and a ring-shaped outer edge buffer for each cell network, and extract crack segments of all cell networks within their edge buffers; S63, Buffer Crack Fusion and Re-optimization: During splicing, the edge buffers of adjacent element networks overlap to form overlapping regions. Crack segments from different element networks are fused within these overlapping regions. The fusion process includes: (a) Crack connection: If the distance between the endpoints of two crack segments from different unit networks is less than the connection distance threshold, and the angle difference of their tangent directions is less than the direction difference threshold, then these two segments are connected into a continuous crack. (b) Conflict resolution: For crack segments that are close to or intersect in the overlapping area and do not meet the connection conditions, one of the segments is cut off or deleted according to the preset rules. (c) Density adjustment: Calculate the crack density in the overlapping area. If it is lower than the preset percentage of the density in the stable area of ​​the unit network, then local, small-step random crack growth is started in this area, constrained by the optimal parameter vector obtained in step S4. S64, Crack Integration: Integrate the stable region cracks of each unit network with the overlapping region cracks processed in step S63 to generate the final large-area random crack network.

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