A method for generating a finite element model of a porous composite material based on CT identification or random generation of near-spherical reinforcing bodies

Abstract

A kind of near-spherical reinforcement porous composite finite element model generation method based on CT identification or random generation, it relates to a kind of porous composite finite element model generation method.To solve the problems of the existing near-spherical porous composite three-dimensional model generation method and finite element modeling process, such as not closely connected, tedious intermediate geometric reconstruction step, need to build additional multi-software collaborative environment, software dependence, long data conversion chain, insufficient degree of automation and so on.The present application can reduce the geometric complexity, improve the stability of finite element solution, take into account a variety of application scenarios, realize the high flexibility modeling of spherical reinforcement porous composite, and be applied to structure-property relationship research, finite element solution and engineering design optimization.The present application is suitable for modeling of composite materials containing near-spherical cavities, or containing spherical particles, hollow particles, spherical inclusions and other near-spherical reinforcements or structural units, and is compatible with different material types, different geometric sizes and complex spatial distribution characteristics.

Description

Technical Field

[0001] This invention relates to a method for generating finite element models of porous composite materials. Background Technology

[0002] Porous composite materials are a class of composite materials characterized by lightweight, high specific strength, good energy absorption performance, and strong structural designability. They typically contain numerous near-spherical pores, hollow particles, hollow microspheres, or other near-spherical structural units. These materials have broad application prospects in lightweight protective structures, buffer energy-absorbing components, porous functional materials, and multi-scale composite structures.

[0003] For this type of material, there is a close relationship between its macroscopic mechanical properties and microstructure. The spatial distribution, size composition, shell thickness, local aggregation characteristics, boundary truncation state, and positional relationship between the spherical structural units and the matrix all significantly affect the stress transfer, crack propagation, damage evolution, energy absorption capacity, and overall deformation mode of the material under compression, impact, and bending loads. Therefore, establishing a three-dimensional model that can reflect the main statistical characteristics of the material's internal structure and is suitable for finite element analysis is an important foundation for conducting numerical simulation research and structural optimization design of this type of material.

[0004] In the existing technology, the modeling methods for the internal structure of this type of material mainly include the following two categories.

[0005] The first category is reverse reconstruction methods based on microscopic images or CT data. These methods typically begin by acquiring slice images or 3D volumetric data of the sample's interior. Then, through image segmentation and surface reconstruction, the geometric morphology of pores, spherical particles, or hollow structural units is obtained. Subsequently, solid geometry is constructed based on voxel models or complex surface models, and finally, the data is imported into finite element software for analysis. The advantage of this type of method is its ability to better preserve the distribution characteristics of the actual internal structure of the sample. However, it generally suffers from the following drawbacks: First, the reconstructed target boundaries are usually irregular and have complex curved surfaces, which is detrimental to subsequent mesh generation and computational stability. Second, adjacent targets are prone to adhesion, making it difficult to accurately separate them using traditional segmentation methods. Third, the identification results, geometric reconstruction, and finite element modeling often belong to different software platforms, resulting in a long data conversion chain, numerous manual steps, and a low overall level of automation.

[0006] The second category is stochastic modeling methods based on statistical parameters. These methods typically pre-determine the number of spheres, particle size distribution, wall thickness or pore size parameters, matrix dimensions, and container boundary conditions. They then automatically generate idealized sphere and matrix models using random point placement and collision detection. The advantages of this type of method are high modeling efficiency, controllable parameters, and ease of conducting batch parameter studies and sensitivity analyses. However, its internal structure is usually derived from an ideal statistical distribution rather than the identification results of real samples, making it difficult to guarantee the consistency between the model and the actual material's internal structure in terms of spatial distribution and dimensional statistical characteristics. Summary of the Invention

[0007] To address the problems of existing methods for generating 3D models of near-spherical porous composite materials, such as poor integration with the finite element modeling process, cumbersome intermediate geometric reconstruction steps, the need to construct additional multi-software collaborative environments, numerous software dependencies, long data conversion chains, and insufficient automation, this invention provides a method for generating finite element models of near-spherical reinforced porous composite materials based on CT recognition or random generation. This method balances structural feature preservation, parameter controllability, process automation, and simple environment deployment.

[0008] The present invention provides a method for generating finite element models of porous composite materials with near-spherical reinforcements based on CT identification, which follows these steps:

[0009] S1, CT Data Acquisition

[0010] Two-dimensional cross-sectional images of the interior of the hollow microsphere-reinforced metal matrix porous composite material sample were obtained by scanning the sample with a CT scanning device.

[0011] S2. Three-dimensional volume data establishment and voxel size calibration

[0012] Import the sliced ​​image obtained in step S1 into the 3D image visualization and analysis software. During the import, a 3D volume data object is created, and the voxel size parameter is set in the object properties. Finally, the 3D volume data of the sliced ​​image is obtained.

[0013] S3, Volume Data Preprocessing

[0014] The three-dimensional volume data obtained in step S2 are sequentially subjected to three-dimensional nonlocal mean filtering, local contrast enhancement or gamma adjustment to obtain preprocessed volume data that balances smoothing image noise and maintaining edge sharpness.

[0015] S4. Local Region Extraction and Binary Segmentation of Holes

[0016] The preprocessed volume data obtained in step S3 is subjected to local region truncation, and the truncated region is subjected to hole binary segmentation; then, the obtained hole binary volume is subjected to morphological cleaning and local boundary smoothing repair; the morphological cleaning includes opening operation, closing operation and small connected component deletion;

[0017] S5, Separation of Adhesion and Cavities

[0018] The binary pore obtained in step S4 is separated into multiple independent pores.

[0019] S6. Hole Connectivity Domain Labeling and Geometric Parameter Statistics

[0020] Connectivity labeling is performed on the separated hole data obtained in step S5, and a unique label is automatically assigned to each independent hole to form a hole label body. After the label body is generated, the statistical analysis module is called to perform statistical analysis on the hole structure parameters. The statistical analysis includes the hole center coordinates, hole volume, hole equivalent sphere diameter, hole spatial enclosing range, and hole sphericity.

[0021] The connected component labeling is implemented using the Connected Components module in the 3D image visualization and analysis software;

[0022] Steps S2-S6 are all performed in 3D image visualization and analysis software, such as Avizo, Dragonfly, or VGSTUDIO MAX.

[0023] S7, CSV parameter table export

[0024] The statistical analysis results obtained in step S6 are exported as a CSV parameter table. The CSV parameter table includes the center coordinates of the hole and the equivalent sphere diameter of the hole. The center coordinates of the hole are used to determine the position of the sphere's center, and the equivalent sphere diameter of the hole is used to determine the inner or outer diameter of the sphere.

[0025] S8. Generation of Sphere Size and Center Parameters

[0026] Import the CSV parameter table obtained in step S7 into the finite element software to generate the sphere size and center parameters; the sphere size and center parameters include the center coordinates, the list of outer diameters of the sphere, the list of inner diameters of the sphere, the grouping results of the outer diameters, and the grouping results of the inner diameters;

[0027] S9, Matrix Establishment

[0028] Import the sphere center parameters obtained in step S8 and establish the matrix geometric model in the finite element software;

[0029] S10, Establishment of Sphere Component Reuse

[0030] Import the outer diameter grouping results and inner diameter grouping results obtained in step S8, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, first count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with that diameter already exists, reuse that component directly. If a spherical component with that diameter does not yet exist, create a new corresponding spherical component. Continue until a spherical component is created for each different diameter value.

[0031] S11, Outer sphere assembly and substrate hole cutting

[0032] Import the sphere center coordinates obtained in step S8 and the outer sphere component obtained in step S10, and complete the outer sphere assembly and base hole cutting in the assembly environment; the sphere center coordinates are the modeling coordinates after local region origin subtraction, unit conversion and container boundary repositioning.

[0033] S12, Hollow spherical shell formation

[0034] The inner sphere component obtained in step S10 is sequentially imported into the outer sphere assembly result obtained in step S11. A hollow sphere shell and an assembly structure of a porous substrate and a hollow sphere shell are generated in the finite element software.

[0035] S13, Material Definition and Section Assignment

[0036] In the finite element software, the porous matrix obtained by cutting holes in the matrix in step S11 and the hollow spherical shell obtained in step S12 are material-defined and cross-section-assigned to obtain the material-assigned model.

[0037] S14, Pressure Plate Establishment and Compression Assembly

[0038] A pressure plate is created in the finite element software, and a compression assembly is completed with the porous matrix and hollow spherical shell assembly structure obtained in step S12 to obtain a compression assembly structure.

[0039] The method for establishing the pressure plate and completing the compression assembly is as follows: the pressure plate adopts a discrete rigid body form, and the geometry of the pressure plate is formed by extruded circular sketches and defined as a rigid loading component through reference points and rigid body constraints; first, draw the circular outline, and then extrude it along the thickness direction to form the pressure plate component; then, remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface, and establish a reference point in the middle of the pressure plate; in the assembly environment, create an upper pressure plate instance and a lower pressure plate instance respectively; translate the upper pressure plate to the outer side of the top of the sample, and translate the lower pressure plate to the outer side of the bottom of the sample to form a compression assembly structure; and further establish rigid body constraints so that the pressure plate surface area is controlled by the corresponding reference point;

[0040] S15, Analysis Step and Output Settings

[0041] Import the compressed assembly structure obtained in step S14, and establish an explicit dynamic analysis step and output settings in the finite element software;

[0042] The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. History output includes the vertical displacement and vertical reaction force of the upper pressure plate reference point, used to output the compression displacement-reaction force curve.

[0043] S16. Contact Relationships and Interaction Settings

[0044] Establish the contact properties and global contact relationships of the compressed assembly structure obtained in step S14 in the finite element software;

[0045] S17, Boundary Conditions and Compression Loading

[0046] In the finite element software, boundary conditions and compression loading are applied to the compressed assembly structure obtained in step S14.

[0047] S18, Mesh Generation

[0048] In the finite element software, the porous substrate obtained in step S11, the hollow spherical shell obtained in step S12, and the pressure plate obtained in step S14 are meshed; the pressure plate is meshed with a coarse mesh, the porous substrate is meshed with a free tetrahedral mesh, and the hollow spherical shell is meshed with a partitioned solid mesh.

[0049] Further, the method for separating holes in step S5 is as follows: First, the Distance Map module is used to perform distance transformation on the binary volume of holes, and the distance value from each hole voxel to the nearest boundary is calculated to form a three-dimensional distance field; then, seed points are generated based on the local peaks in the distance field, and the Watershed module is used to perform three-dimensional watershed segmentation, thereby separating the mutually adhered holes into multiple independent holes.

[0050] Furthermore, the method for assembling the outer sphere and cutting holes in the substrate in step S11 is as follows: In the assembly environment, an outer sphere instance is created sequentially for each sphere, and the outer sphere instance is translated to the corresponding center coordinate position; after all the outer sphere instances are arranged, Boolean cut operation is performed sequentially with the substrate instance as the cut object and all the outer sphere instances as the cutting object, and finally a new porous substrate entity is generated; for the outer sphere instances located at the boundary, the Boolean cut retains its real intersection relationship with the substrate to reflect the boundary truncation characteristics.

[0051] Further, the method for generating the hollow spherical shell in step S12 is as follows: a corresponding inner sphere instance is created for each sphere, and the inner sphere instance has the same center coordinates as the corresponding outer sphere instance in the assembly environment; then, Boolean difference operation is performed with the re-instantiated outer sphere as the cutting object and the corresponding inner sphere as the cutting object, thereby obtaining the hollow spherical shell entity.

[0052] Further, the method for defining the material and assigning the cross-section in step S13 is as follows: import the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material; adopt the constitutive model of brittle material for the hollow spherical shell material; then establish the homogeneous solid cross-section of the matrix and the homogeneous solid cross-section of the spherical shell respectively, and assign the matrix cross-section to the porous matrix component, and assign the spherical shell cross-section to all hollow spherical shell components one by one.

[0053] The method for generating a randomly generated finite element model of a near-spherical reinforced porous composite material according to the present invention is carried out according to the following steps:

[0054] S1. Random Modeling Parameter Settings

[0055] In the finite element software, set the basic parameters required for the randomly generated model; the basic parameters required for the model include matrix shape parameters, distribution pattern parameters, distribution type parameters, sphere distribution parameters, matrix half-width, matrix height, total number of spheres, total analysis time, maximum time increment, compression ratio, number of history output points, pressure plate mesh size, matrix mesh size, and hollow spherical shell mesh size;

[0056] S2, Sphere size is randomly generated.

[0057] Import the sphere distribution parameters set in step S1 to randomly generate sphere sizes and form a sphere size list; the sphere size list includes a list of sphere outer diameters, a list of sphere inner diameters, outer diameter grouping results, and inner diameter grouping results;

[0058] S3, Random placement of sphere centers and overlap check

[0059] The list of sphere outer diameters obtained in step S2 is used to randomly place the sphere centers and perform overlap checks. When randomly placing the sphere centers, candidate sphere center positions are generated based on the half-width of the base, the height of the base, and the current radius of the sphere. When checking for overlap, it is determined whether the sphere corresponding to the candidate sphere center position overlaps with the spheres already placed in the base space. If there is no overlap, the candidate sphere center position is accepted. If there is an overlap, the candidate sphere center positions are regenerated until all spheres are placed, and finally a list of sphere placement points is generated. The list of sphere placement points includes the sphere center coordinates and outer diameter.

[0060] S4. Generation of Sphere Size and Center Parameters

[0061] Import the sphere size list obtained in step S2 and the sphere point list obtained in step S3 into the finite element software to form the sphere size and sphere center parameters required for subsequent finite element modeling; the sphere size and sphere center parameters include the outer diameter of the sphere, the inner diameter of the sphere, the coordinates of the sphere center, the grouping results of the outer diameter, and the grouping results of the inner diameter;

[0062] S5, Matrix Establishment

[0063] Import the base shape parameters, base half-width and base height set in step S1, and establish the base geometric model in the finite element software by sketch extrusion;

[0064] S6, Establishment of Sphere Component Reuse

[0065] Import the outer diameter grouping results and inner diameter grouping results obtained in step S4, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with the same diameter already exists, reuse the component directly. If a spherical component with the same diameter does not yet exist, create a new corresponding spherical component.

[0066] S7, Outer sphere assembly and substrate hole cutting

[0067] Import the sphere center coordinates obtained in step S4 and the outer sphere component obtained in step S6, and complete the outer sphere assembly and base hole cutting in the assembly environment;

[0068] S8, Hollow spherical shell formation

[0069] Import the inner sphere component obtained in step S6 and the outer sphere assembly result obtained in step S7, and generate a hollow spherical shell in the finite element software;

[0070] S9. Material Definition and Section Assignment

[0071] In the finite element software, the material definition and section assignment are performed on the porous matrix obtained by cutting holes in the matrix in step S7 and the hollow spherical shell obtained in step S8 to obtain the material model.

[0072] S10, Pressure Plate Establishment and Compression Assembly

[0073] Based on the material model obtained in step S9, a pressure plate is built in the finite element software, and the pressure plate and the material model are compressed and assembled to obtain a compressed assembly structure.

[0074] S11. Analysis Step and Output Settings

[0075] In the finite element software, establish the explicit dynamic analysis step and output settings for the compression assembly structure obtained in step S10;

[0076] The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. History output includes the vertical displacement and vertical reaction force (U3 and RF3) of the upper pressure plate reference point, used to output the compression displacement-reaction force curve.

[0077] S12. Contact Relationships and Interaction Settings

[0078] Establish the contact properties and global contact relationships of the compression assembly structure obtained in step S10 in the finite element software;

[0079] S13, Boundary Conditions and Compressive Loading

[0080] Boundary conditions and compressive loading are applied to the compressed assembly structure obtained in step S10 in the finite element software.

[0081] S14, Mesh Generation

[0082] In the finite element software, the porous matrix and hollow spherical shell obtained in step S9 and the pressure plate obtained in step S10 are meshed.

[0083] Furthermore, the method for assembling the outer sphere and cutting holes in the substrate in step S7 is as follows: create an outer sphere instance for each sphere in sequence and translate the outer sphere instance to the corresponding center coordinate position; after all the outer sphere instances are arranged, take the substrate instance as the object to be cut and all the outer sphere instances as the cutting objects, and perform Boolean cut operation in sequence to finally obtain a new porous substrate entity.

[0084] Further, the method for generating a hollow spherical shell in step S8 is as follows: a corresponding inner sphere instance is created for each sphere, and the inner sphere instance and the corresponding outer sphere instance have the same center coordinates; then, Boolean difference operation is performed with the re-instantiated outer sphere as the cutting object and the corresponding inner sphere as the cutting object, thereby obtaining the hollow spherical shell entity.

[0085] Further, the method for defining materials and assigning cross sections in step S9 is as follows: import the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material; then establish the homogeneous solid cross section of the matrix and the homogeneous solid cross section of the spherical shell respectively, and assign the matrix cross section to the porous matrix component, and assign the spherical shell cross section to all hollow spherical shell components one by one.

[0086] Further, the method for establishing the pressure plate and completing the compression assembly in step S10 is as follows: the pressure plate adopts a discrete rigid body form, the geometry of the pressure plate is formed by extruded circular sketch, and defined as a rigid loading component through reference points and rigid body constraints; first, draw the circular outline, and then extrude it along the thickness direction to form the pressure plate component; then remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface, and establish a reference point in the middle of the pressure plate; in the assembly environment, create an upper pressure plate instance and a lower pressure plate instance respectively; translate the upper pressure plate to the outer side of the top of the sample, and translate the lower pressure plate to the outer side of the bottom of the sample to form a compression assembly structure; further establish rigid body constraints so that the pressure plate surface area is controlled by the corresponding reference point.

[0087] The present invention has the following beneficial effects:

[0088] 1. Automated Parametric Modeling Based on CT Recognition Parameter Tables. This invention provides a technical solution for directly driving finite element modeling using parameter tables for holes or particles obtained from CT recognition. 3D image processing software is used to preprocess CT data, segment target regions, separate adhered regions, label connected components, and statistically analyze geometric parameters to obtain the center coordinates, volume, and equivalent diameter of each independent target, which are then exported as a CSV parameter table. Finite element modeling reads this parameter table through programming and generates sphere, hollow spherical shell, and porous matrix models based on the sphere's center coordinates and size parameters. Simultaneously, a fixed wall thickness mode or an inner-outer diameter ratio mode can be used to calculate the sphere's dimensions. This solution eliminates the need for complex surface reconstruction and intermediate CAD conversion, achieving fully automated processing from CT recognition to finite element models, improving modeling efficiency, consistency, and traceability, while preserving the main spatial distribution and dimensional statistical characteristics of the material's internal structure.

[0089] 2. Randomized Parametric Modeling Based on Preset Parameters Without a Parameter Table. This invention also provides a method for generating a finite element model without a CT parameter table, using preset matrix dimensions, sphere size distribution, and random point placement rules. The sphere dimensions are generated based on a normal or other statistical distribution, and the sphere center is obtained through a random point placement algorithm with overlap checks, forming a sphere point placement list and size parameters. Subsequently, spheres, hollow spherical shells, and porous matrix structures are generated in the finite element software. Material definition and section assignment, pressure plate establishment, analysis step settings, contact definition, boundary condition application, and mesh generation are completed to obtain a complete finite element model. This scheme is suitable for idealized structure modeling, parameter sensitivity analysis, and the construction of control models.

[0090] 3. Reduce geometric complexity and improve the stability of finite element solutions. This invention does not directly reconstruct complex irregular surfaces, but instead performs regularized parameter modeling based on realistically identified or randomly generated spherical structural elements. While preserving the main distribution characteristics and dimensional statistical features as much as possible, it significantly reduces geometric complexity and improves the quality of subsequent mesh generation and the stability of finite element solutions.

[0091] 4. Suitable for multiple application scenarios. The two methods of this invention (CT parameter table driven and stochastic parameterization) can be applied to reverse modeling based on real material structures and the construction of idealized parameter models, respectively. This achieves highly flexible modeling of near-spherical reinforced porous composite materials, which can be applied to structure-performance relationship studies, finite element solutions, and engineering design optimization.

[0092] 5. Wide range of applications. This invention is applicable to modeling composite materials containing near-spherical cavities, or containing near-spherical reinforcements or structural units such as spherical particles, hollow particles, and spherical inclusions, and is compatible with different material types, different geometric dimensions, and complex spatial distribution characteristics. Attached Figure Description

[0093] Figure 1 The image shown is the non-local mean filtering processed in step S3 of Example 1 (left) and the separation result of adhesion holes in step S5 (right).

[0094] Figure 2 A comparative cross-sectional view showing the same hole position in step S11 of Example 1;

[0095] Figure 3 This is a diagram of the compression assembly structure obtained in step S14 of Example 1;

[0096] Figure 4 The diagram shows the mesh division and cross-sectional view of the compression assembly structure in Example 1.

[0097] Figure 5 The diagram shows the mesh division and cross-sectional view of the compression assembly structure in Example 2. Detailed Implementation

[0098] Example 1:

[0099] This embodiment is based on a CT-based parameter table-driven method for generating a three-dimensional model of a near-spherical reinforced porous composite material suitable for finite element solution. Given CT scan data and a parameter table for hollow microsphere-reinforced metal matrix porous composite material samples, the method collaboratively establishes both a realistic three-dimensional model and a finite element model using scripts from 3D image visualization and analysis software and finite element software (Abaqus / CAE software). This embodiment uses the pores within the hollow microspheres as the CT recognition target, and through pore recognition, geometric parameter statistics, parameter table export, and parameter table-driven modeling, automatically generates the porous matrix and hollow spherical shell structure.

[0100] This embodiment uses the following steps to generate a finite element model of a near-spherical reinforced porous composite material based on CT identification:

[0101] S1, CT Data Acquisition

[0102] Two-dimensional cross-sectional images of the interior of the hollow microsphere-reinforced metal matrix porous composite material sample were obtained by scanning the sample with a CT scanning device.

[0103] In this embodiment, hollow microsphere-reinforced metal-based porous composite material samples were first obtained by wire cutting. The sample size was 2 mm × 2 mm × 3 mm. The samples were then scanned using a CT scanning device (Xradia 520 Versa) to obtain two-dimensional slice images of the sample interior. The slice images were saved in a lossless image format (TIFF format), with a single image resolution of 1004 × 1024 pixels. A total of 1016 images were acquired along the Z-axis, and the image data type was ushort.

[0104] S2. Three-dimensional volume data establishment and voxel size calibration

[0105] Import the sliced ​​image obtained in step S1 into the 3D image visualization and analysis software. During the import, a 3D volume data object is created, and the voxel size parameter is set in the object properties. Finally, the 3D volume data of the sliced ​​image is obtained.

[0106] In this embodiment, the dimensions of the voxels in the X, Y, and Z directions (Voxel Size X, Voxel Size Y, and Voxel Size Z) are calibrated to 5.108033 μm, thereby establishing the correspondence between image pixels and real spatial dimensions.

[0107] S3, Volume Data Preprocessing

[0108] The three-dimensional volume data obtained in step S2 are sequentially subjected to three-dimensional nonlocal mean filtering, local contrast enhancement, or gamma adjustment to obtain preprocessed volume data that balances smoothing image noise and maintaining edge sharpness.

[0109] Performing 3D nonlocal mean filtering on the original 3D volume data (implemented through the Non-Local Means Filter module) can reduce the impact of scanning noise on hole boundary identification and preserve hole boundaries and metal matrix details; performing local contrast enhancement or gamma adjustment can reduce grayscale fluctuations between different slices and enhance the grayscale difference between the hole area and the matrix area; after preprocessing, the data is observed through orthogonal slice views to confirm that the hole boundaries are continuous and the contrast is clear;

[0110] S4. Local Region Extraction and Binary Segmentation of Holes

[0111] The preprocessed volume data obtained in step S3 is subjected to local region truncation, and the truncated region is subjected to hole binary segmentation; then the obtained hole binary volume is subjected to morphological cleaning and local boundary smoothing repair.

[0112] The morphological cleaning process includes opening operations, closing operations, and deletion of small connected components;

[0113] In this embodiment, the voxel size of the cropped region is 100×100×150 voxels, corresponding to a physical space size of 510.8033 μm×510.8033 μm×766.20495 μm. During the hole binary segmentation, the image segmentation module (Threshold module) is called in the 3D image visualization and analysis software. Based on the difference between the hole region and the matrix region in the gray-level histogram, the gray-level range corresponding to the hole is selected to generate the hole binary. The hole region is assigned a value of 1, and the non-hole region is assigned a value of 0. After obtaining the hole binary, morphological cleaning is performed to remove mis-segmented regions, isolated noise points, and local small voxel clusters. After smoothing and repairing the local boundaries, the cleaned hole binary is obtained. The small connected component deletion process sets the voxel number threshold to 20 voxels to remove isolated noise regions with too small a volume.

[0114] S5, Separation of Adhesion and Cavities

[0115] The binary pore obtained in step S4 is separated into multiple independent pores.

[0116] The method for separating holes is as follows: First, the Distance Map module is used to perform distance transformation on the binary volume of holes, and the distance value from each hole voxel to the nearest boundary is calculated to form a three-dimensional distance field; then, seed points are generated based on the local peaks in the distance field, and the Watershed module is used to perform three-dimensional watershed segmentation, thereby separating the mutually adhered holes into multiple independent holes.

[0117] Figure 1 The images shown are the left and right images of the S3 non-local mean filtering processed image and the S5 adhesion hole separation result image in Example 1. This illustrates that adjacent holes are transformed from the original adhesion state (left image) into multiple independently identifiable target regions (right image), providing a basis for subsequent connected component labeling and statistical analysis.

[0118] S6. Hole Connectivity Domain Labeling and Geometric Parameter Statistics

[0119] Connectivity labeling is performed on the separated hole data obtained in step S5, and a unique label is automatically assigned to each independent hole to form a hole label body. After the label body is generated, the statistical analysis module is called to perform statistical analysis on the hole structure parameters. The statistical analysis includes the hole center coordinates, hole volume, hole equivalent sphere diameter, hole spatial enclosing range, and hole sphericity.

[0120] The connected component labeling is implemented using the Connected Components module in the 3D image visualization and analysis software;

[0121] The center coordinates of the holes are used to characterize the position of each hole in 3D space; the hole volume is used to characterize the size of the hole; the equivalent sphere diameter of the hole is used to generate a sphere model later; the sphericity of the hole is used to determine whether the hole is close to a sphere, so as to filter out abnormal holes when necessary; the spatial enclosing range of the hole is used to help determine whether the spatial range and segmentation of the hole are abnormal; the statistical fields corresponding to the statistical analysis content include the hole center coordinates field (BaryCenter.x, BaryCenter.y, and BaryCenter.z), the hole volume field (Volume3d), the hole equivalent sphere diameter field (EqDiameter), the spatial enclosing range field (BBoxMinX, BBoxMaxX, BBoxMinY, BBoxMaxY, BBoxMinZ, and BBoxMaxZ), and the hole sphericity field (Sphericity).

[0122] Steps S2-S6 are all performed in 3D image visualization and analysis software, such as Avizo, Dragonfly, or VGSTUDIO MAX.

[0123] S7, CSV parameter table export

[0124] The statistical analysis results obtained in step S6 are exported as a CSV parameter table. The CSV parameter table includes the center coordinates of the hole and the equivalent sphere diameter of the hole. The center coordinates of the hole are used to determine the position of the sphere's center, and the equivalent sphere diameter of the hole is used to determine the inner or outer diameter of the sphere.

[0125] In this embodiment, the hole center coordinate fields (CenterOfMassX, CenterOfMassY, and CenterOfMassZ) in the CSV parameter table are obtained by organizing the original statistical fields (BaryCenter.x, BaryCenter.y, and BaryCenter.z) from the 3D image visualization and analysis software. The hole equivalent sphere diameter field (EquivalentDiameter) in the CSV parameter table is obtained by organizing the original statistical fields (EqDiameter) from the 3D image visualization and analysis software. In addition, the parameter table can also include fields such as hole number, hole volume, spatial enclosure range, and sphericity (ID, Volume3d, BBox range, and Sphericity).

[0126] S8. Generation of Sphere Size and Center Parameters

[0127] Import the CSV parameter table obtained in step S7 into the finite element software script to generate the sphere dimensions and center parameters; the sphere dimensions and center parameters include the center coordinates, the list of outer diameters of the sphere, the list of inner diameters of the sphere, the grouping results of the outer diameters, and the grouping results of the inner diameters; this step is implemented by script programming using the Abaqus secondary development interface;

[0128] In this embodiment, the finite element software script pre-sets the CSV file path, coordinate units, diameter units, coordinate reference system, local region physical dimensions, local region physical origin, and target type. After the script starts, it reads the CSV parameter table, obtains the center coordinates and equivalent diameter of each hole line by line, and saves them as a sphere parameter list. The actual modeling unit in the finite element model is uniformly millimeters, so the script automatically converts the read micrometer-level coordinates and diameters to millimeters. When the CSV coordinate reference system is the global physical coordinate system, the script first uses the local region physical origin to convert the hole center coordinates into local coordinates. Then, combined with the final container boundary, it repositions all sphere center coordinates to make them consistent with the base coordinate system in the finite element model.

[0129] In this embodiment, the CSV read control parameter (use_csv_priority) in the script is used to determine whether to prioritize CSV parameter table-driven modeling; the CSV file path parameter (csv_file_path) is used to specify the location of the parameter table file; the coordinate unit parameter (csv_coordinate_unit) and diameter unit parameter (csv_diameter_unit) are used to perform unit conversion; the coordinate reference system parameter (csv_coordinate_reference) is used to determine whether the coordinates in the CSV are global or local coordinates; the grouping precision parameter (csv_group_round_digits) is used to control the grouping precision of the sphere diameter; and the container boundary control parameters (csv_container_padding_um, csv_force_box_container, auto_expand_container_to_fit_spheres, and auto_expand_margin_um) are used to control the base boundary and its expansion method.

[0130] In this embodiment, the CT scan identifies the hollow microsphere's internal cavity pores; therefore, the equivalent sphere diameter of the pores in the CSV parameter table is used as the inner diameter of the hollow spherical shell. The script calculates the outer diameter of the hollow spherical shell based on a preset inner-outer diameter ratio. When the inner-outer diameter ratio is set to 0.9, the outer diameter of the hollow spherical shell is determined according to the following formula:

[0131]

[0132] In the formula, D1 is the outer diameter of the hollow spherical shell, D2 is the inner diameter of the hollow spherical shell, and Diameter_Ratio is the ratio of the inner and outer diameters of the hollow spherical shell;

[0133] If a fixed wall thickness model is adopted, the outer diameter of the hollow spherical shell is determined according to the following formula:

[0134]

[0135] In the formula, D1 is the outer diameter of the hollow spherical shell, D2 is the inner diameter of the hollow spherical shell, and t is the wall thickness of the hollow spherical shell.

[0136] After the script completes the calculation, it generates an outer diameter list (d1_values) and an inner diameter list (d2_values), and groups them according to different diameter values ​​to form outer diameter grouping results (d1_grouped) and inner diameter grouping results (d2_grouped). This step can be performed on a large number of spheres and multiple files in batches through programming. It can also be done manually in the Abaqus image interface. The relevant parameters can be organized in Excel.

[0137] S9, Matrix Establishment

[0138] Import the sphere center parameters obtained in step S8 and establish the matrix geometric model in the finite element software; this step is implemented using script programming via the Abaqus secondary development interface;

[0139] This embodiment uses a cuboid base to extract the region based on the S4 local area. The base size is determined by the physical dimensions of the extracted region using 3D image visualization and analysis software to define the theoretical boundary. The container boundary is then determined based on the total sphere space range to either completely encompass all spheres or maintain the extracted region boundary. The script uses the local region's physical dimensions (510.8033 μm × 510.8033 μm × 766.20495 μm in this example) and the local region's physical origin (2749.82 μm, 2632.48 μm, and 1918.24 μm in this example) to define the region. The initial cuboid base area is determined by μm; when the automatic container expansion function is enabled, the final cuboid base boundary is the union of the theoretical local region boundary and the sphere space boundary; subsequently, the script draws a rectangular outline in the sketch and forms a three-dimensional cuboid base (Part-1) using the BaseSolidExtrude command; batch analysis and calculation of a large number of spheres in multiple files can be performed through programming, or this step can be completed manually in the Abaqus image interface, and the relevant parameters can be organized in Excel;

[0140] S10, Establishment of Sphere Component Reuse

[0141] Import the outer diameter grouping results and inner diameter grouping results obtained in step S8, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, first count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with that diameter already exists, reuse that component directly; if a spherical component with that diameter does not yet exist, create a new corresponding spherical component. This process continues until a spherical component is created for each different diameter value. This step is implemented using script programming via the Abaqus secondary development interface.

[0142] In this embodiment, during the reuse of the sphere component, the script first constructs a cross-section in the sketch using a semicircular arc with a radius equal to half the diameter and a rotation axis. Then, it uses the BaseSolidRevolve command to rotate the sphere 360° around the axis to generate a three-dimensional solid sphere. The script creates an outer sphere component (D1-Sphere_xxx) and an inner sphere component (D2-Sphere_xxx) respectively. When multiple holes have the same diameter, the same sphere component is instantiated and called only subsequently. The script converts the diameter value to a component name suffix using the diameter name conversion function (diameter_to_name_str) and automatically determines whether a sphere component with the same diameter already exists using the sphere creation function (create_sphere_part). If the sphere component with the same diameter already exists, it is reused directly; if the sphere component with the same diameter does not yet exist, a new sphere component is created.

[0143] S11, Outer sphere assembly and substrate hole cutting

[0144] Import the sphere center coordinates obtained in step S8 and the outer sphere component obtained in step S10, and complete the outer sphere assembly and base hole cutting in the assembly environment; the sphere center coordinates are the modeling coordinates after local region origin subtraction, unit conversion and container boundary repositioning. Figure 2 The images show a comparison of cross-sections with the same hole location in step S11 of Example 1; the left image shows the hole segmentation result in the 3D image visualization and analysis software, and the right image shows the substrate hole cutting result in the finite element software. This step is implemented using script programming via the Abaqus secondary development interface.

[0145] The method for assembling the outer spheres and cutting holes in the substrate is as follows: In the assembly environment, an outer sphere instance is created sequentially for each sphere, and the outer sphere instance is translated to the corresponding center coordinate position; after all outer sphere instances are arranged, the substrate instance (Container_1) is used as the object to be cut, and all outer sphere instances are used as the cutting objects, and Boolean cut operations (InstanceFromBooleanCut) are executed sequentially to finally generate a new porous substrate entity (Perforated_Container); for outer sphere instances located at the boundary, there are two modes: 1. Automatically expand the substrate boundary to completely encompass all spheres; 2. Maintain the boundary of the cut area to preserve its true intersection relationship with the substrate to reflect the boundary cut characteristics; this step is implemented using script programming through the Abaqus secondary development interface;

[0146] S12, Hollow spherical shell formation

[0147] The inner sphere component obtained in step S10 is sequentially imported into the outer sphere assembly result obtained in step S11. A hollow sphere shell and an assembly structure of a porous substrate and a hollow sphere shell are generated in the finite element software.

[0148] The method for generating a hollow spherical shell is as follows: For each sphere, a corresponding inner sphere instance is created, and the inner sphere instance has the same center coordinates as the corresponding outer sphere instance in the assembly environment; then, using the newly instantiated outer sphere as the object to be cut and the corresponding inner sphere as the cutting object, a Boolean difference operation (InstanceFromBooleanCut) is performed to obtain the hollow spherical shell entity (Hollow_Sphere_i); this step is implemented using script programming via the Abaqus secondary development interface.

[0149] Since the inner sphere size in this embodiment is derived from the equivalent sphere diameter of the hole obtained by CT recognition, the resulting hollow spherical shell cavity is consistent with the recognition result. After the hollow spherical shell is established, the script assigns display colors to spherical shells of different diameters according to the outer diameter of the sphere (color assignment is achieved through the colorsys.hsv_to_rgb function) to distinguish different particle size groups in visual inspection. Subsequently, the temporary outer sphere instance, inner sphere instance, and initial matrix instance are deleted to retain the final porous matrix and hollow spherical shell assembly structure. The script can perform batch assembly and Boolean operations on a large number of spheres. The above steps can also be performed manually in Abaqus.

[0150] S13, Material Definition and Section Assignment

[0151] In the finite element software, the porous matrix obtained by cutting holes in the matrix in step S11 and the hollow spherical shell obtained in step S12 are material-defined and cross-section-assigned to obtain the material-assigned model.

[0152] The method for defining materials and assigning sections is as follows: The matrix material adopts the Johnson-Cook hardening and damage constitutive model of 6061 aluminum alloy (the matrix material model is named Material-jc); the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material are imported; the hollow spherical shell material adopts the JH-2 brittle material constitutive model (the spherical shell material model is named abq_jh2_sio2); then, homogeneous solid sections of the matrix and the spherical shell are established respectively, and the matrix section is assigned to the porous matrix component, and the spherical shell section is assigned to all hollow spherical shell components one by one; this step is implemented by script programming using the Abaqus secondary development interface.

[0153] In this embodiment, the matrix material parameters include density, elastic modulus, Poisson's ratio, Johnson-Cook plastic hardening parameters, Johnson-Cook strain rate parameters, damage initiation parameters, and damage evolution displacement parameters; the density is 2.7e-09; the elastic modulus is 70000.0; the Poisson's ratio is 0.33; the plastic hardening parameters are 275.96, 288.39, 0.59, 1.0, 893.0, and 293.0; the strain rate parameters are 0.0064 and 0.001; the damage initiation parameters are 0.362, -4.57e-06, 17.434, 0.0112, 0.0, 893.0, 293.0, and 0.001; and the damage evolution displacement is 0.02.

[0154] S14, Pressure Plate Establishment and Compression Assembly

[0155] A pressure plate is created in the finite element software, and a compression assembly is completed with the porous matrix and hollow spherical shell assembly structure obtained in step S12 to obtain a compression assembly structure. Figure 3 The compressed assembly structure diagram obtained in S14;

[0156] The method for establishing the pressure plate and completing the compression assembly is as follows: The pressure plate adopts a discrete rigid body form, and the geometry of the pressure plate is formed by extruded circular sketches and defined as a rigid loading component through reference points and rigid body constraints; First, draw the circular outline, and then extrude it along the thickness direction to form the pressure plate component (Part-6); Then, remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface (DISCRETE_RIGID_SURFACE), and establish a reference point (ReferencePoint) in the middle of the pressure plate; In the assembly environment, create an upper pressure plate instance (Part-6-1) and a lower pressure plate instance (Part-6-2) respectively; The upper pressure plate is translated to the outer side of the top of the sample, and the lower pressure plate is translated to the outer side of the bottom of the sample to form a compression assembly structure; and further establish rigid body constraints (Rigid-Top and Rigid-Bottom) so that the pressure plate surface area is controlled by the corresponding reference point; This step is implemented using script programming through the Abaqus secondary development interface.

[0157] In this embodiment, the outer diameter of the pressure plate is determined based on the transverse dimension of the sample and the outer expansion distance of the pressure plate; the outer expansion distance of the pressure plate is set to 100.0 μm, and the thickness of the pressure plate is set to 100.0 μm; the rigid body constraint corresponds to the finite element keyword (*RIGID BODY).

[0158] S15, Analysis Step and Output Settings

[0159] Import the compressed assembly structure obtained in step S14, and establish an explicit dynamic analysis step and output settings in the finite element software;

[0160] This step utilizes the Abaqus secondary development interface for script programming. In this embodiment, an explicit dynamics step is established using a script, and the total analysis time and maximum time increment are set. The total analysis time t is set to 1, and the maximum time increment is set to 0.0001. This analysis step is used to simulate the dynamic explicit response during the compression of the specimen by the pressure plate.

[0161] The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. The field output interval is set to 2000. History output includes the vertical displacement and vertical reaction force (U3 and RF3) of the upper pressure plate reference point, used to output the compression displacement-reaction force curve. The number of history output points is set to 1000.

[0162] S16. Contact Relationships and Interaction Settings

[0163] Establish the contact properties and global contact relationships of the compressed assembly structure obtained in step S14 in the finite element software;

[0164] Contact properties for the interaction between the pressure plate and the specimen are established and assigned to global contact or corresponding contact pairs. These contact properties include tangential friction behavior and normal hard contact behavior. Tangential contact uses a penalty friction model with a friction coefficient of 0.5. Normal contact uses hard contact and allows for contact surface separation. Subsequently, an explicit universal contact (ContactExp or Int-1) is established, incorporating all external surface contacts into the global contact and assigning contact properties to global self-contact relationships. The first contact property is named IntProp-1 with a maximum elastic slip ratio of 0.005. The second contact property is named IntProp-2 with a friction coefficient of 0.2, used for other specific contact pairs.

[0165] S17, Boundary Conditions and Compression Loading

[0166] In the finite element software, boundary conditions and compression loading are applied to the compressed assembly structure obtained in step S14.

[0167] The compression ratio of the compression loading is set to 0.7, and the compression loading is completed by Z-axis displacement;

[0168] This step is implemented using script programming via the Abaqus secondary development interface; in this embodiment, the script is used to establish an amplitude curve (Amp-1) that grows linearly with time, and displacement boundary conditions are applied to the reference points of the upper and lower pressure plates in the analysis step to achieve compression loading on the sample;

[0169] The compression ratio is set to 0.7, and the specimen height is determined by the matrix height. The upper pressure plate moves along the negative Z-axis, and the lower pressure plate moves along the positive Z-axis, so that the specimen achieves a total compression deformation of 0.7 between the upper and lower pressure plates. The lateral translational and rotational degrees of freedom of the upper and lower pressure plates are constrained, and compression loading is only allowed through Z-axis displacement.

[0170] The displacement of the upper pressure plate is determined by the following formula:

[0171]

[0172] In the formula, U3_top is the displacement of the upper pressure plate reference point along the Z direction, h is the sample height, and k is the compression ratio;

[0173] The displacement of the lower pressure plate is determined by the following formula:

[0174]

[0175] In the formula, U3_bottom is the displacement of the lower platen reference point along the Z direction, h is the sample height, and k is the compression ratio;

[0176] The compression ratio is represented by the script parameter (k), and the specimen height is represented by the script parameter (h or specimen_height); the amplitude curve data is set to increase from 0 at time 0 to 1 at the end of the analysis; the constraint degrees of freedom of the upper and lower pressure plates include lateral translational degrees of freedom and rotational degrees of freedom (u1, u2, ur1, ur2, and ur3); in S14, S15, and S17, the script can be used to adapt to a large number of matrix models of different sizes and realize batch execution. The above steps can be performed manually in Abaqus.

[0177] S18, Mesh Generation

[0178] In the finite element software, the porous matrix obtained in step S11, the hollow spherical shell obtained in step S12, and the pressure plate obtained in step S14 are meshed.

[0179] This step is implemented using script programming via the Abaqus secondary development interface; the pressure plate is divided into coarse grids, the porous substrate is divided into free tetrahedral grids, and the hollow spherical shell is divided into partitioned solid grids. Figure 4 This is a mesh diagram and cross-sectional view of a compressed assembly structure; each coordinate system in the diagram represents a hollow sphere.

[0180] In this embodiment, the pressure plate component uses a 10.0 μm mesh size for seeding and mesh generation; the porous matrix component uses a 4.0 μm mesh size for seeding and is set as a free tetrahedral mesh to accommodate complex pore boundaries; the hollow spherical shell component uses a 2.0 μm mesh size for seeding. To improve the mesh quality and analysis stability of the spherical shell structure, before meshing the spherical shell, the script first establishes a local coordinate system (Ball-i-CSYS) for the sphere and partitions the spherical shell through three orthogonal planes, subsequently generating a high-quality hexahedral mesh. The script can be used to partition and cut a large number of hollow spheres; the above steps can be performed manually in Abaqus.

[0181] This embodiment uses the Abaqus secondary development interface for programming, but it can also be done manually in the Abaqus graphical window;

[0182] This embodiment generates a spherical reinforced porous composite material finite element model suitable for finite element solution based on a CT recognition parameter table. This model is then used for solution submission and post-processing, as well as other applications, including:

[0183] Import the finite element model, submit it to the finite element solver for solution and post-processing;

[0184] After completing material definition, section assignment, assembly, contact, analysis steps, boundary conditions, mesh generation, and output settings, submit the explicit finite element solver (Abaqus / Explicit) for solving; when submitting the solution, the script creates an analysis job and sets the computational resources according to the model size;

[0185] After the solution is completed, the output database file (ODB file) is read, and the vertical displacement and vertical reaction force of the upper pressure plate reference point are extracted to obtain the compression displacement-reaction force curve. Combined with the initial cross-sectional area and initial height of the sample, the engineering stress-engineering strain curve is further calculated. At the same time, the stress, strain, damage variables and element deletion states in the porous matrix and hollow spherical shell are extracted to analyze the stress concentration around the pores, shell failure, plastic deformation of the matrix and changes in the overall bearing capacity during the compression process.

[0186] The surface displacement field, strain field, and local deformation zone obtained by finite element simulation are compared with relevant experimental results. Under the same compressive strain level, the surface principal strain distribution obtained by the experiment is compared with the logarithmic strain or equivalent plastic strain distribution output by the finite element to determine the influence of the hollow microsphere position, pore distribution, and boundary truncation characteristics on the local deformation mode in the model.

[0187] Furthermore, the pore geometry parameters, CSV parameter tables, load-displacement curves, stress-strain curves, damage evolution results, and corresponding experimental results are integrated into a structure-performance dataset for subsequent performance prediction model training. This dataset includes structural input features and performance output labels. The structural input features include the number of pores, pore size distribution, sphere center coordinates, volume fraction, sphericity, spatial enclosing range, matrix size, shell wall thickness or inner-outer diameter ratio, material parameters, and mesh parameters. The performance output labels include peak stress, plateau stress, energy absorption capacity, failure strain, and local strain concentration.

[0188] Example 2:

[0189] In this embodiment, without a parameter table, a three-dimensional structural model and a finite element model of a hollow microsphere-reinforced metal matrix porous composite material are automatically generated in the finite element software by pre-setting matrix size parameters, sphere size distribution parameters, and spatial random point layout rules; this embodiment uses the randomly distributed sphere size and sphere center coordinates as input to complete the automatic establishment of the porous matrix and hollow spherical shell structure;

[0190] The method for generating the randomly generated near-spherical reinforced porous composite material finite element model in this embodiment is performed according to the following steps:

[0191] S1. Random Modeling Parameter Settings

[0192] In the finite element software, set the basic parameters required for the randomly generated model; the basic parameters required for the model include matrix shape parameters, distribution pattern parameters, distribution type parameters, sphere distribution parameters, matrix half-width, matrix height, total number of spheres, total analysis time, maximum time increment, compression ratio, number of history output points, pressure plate mesh size, matrix mesh size, and hollow spherical shell mesh size;

[0193] This step utilizes the Abaqus secondary development interface for script programming. In this embodiment, the substrate is a cuboid with a half-width of 150.0 μm and a height of 450.0 μm. The total number of spheres is set to 210. The total analysis time is set to 1, the maximum time increment to 0.0001, the compression ratio to 0.7, and the number of history output points to 1000. The pressure plate mesh size is set to 5.0 μm, the substrate mesh size to 10.0 μm, and the hollow spherical shell mesh size to 2.0 μm. The script internally converts all length inputs from micrometers to millimeters and uses a unit conversion function (um_to_mm) to achieve the length unit conversion. The input parameter unit is micrometers, while the internal modeling unit is millimeters.

[0194] The matrix shape parameter (container_type) controls the matrix geometry, the sphere distribution mode parameter (distribution_mode) controls whether to use sphere diameter distribution, and the distribution type parameter (distribution_type) controls the sphere diameter distribution function. Scripts can be used to generate models with different parameters in batches. The above steps can be performed manually in Excel or Abaqus.

[0195] S2, Sphere size is randomly generated.

[0196] Import the sphere distribution parameters set in step S1 to randomly generate sphere sizes and form a sphere size list; the sphere size list includes a list of sphere outer diameters, a list of sphere inner diameters, outer diameter grouping results, and inner diameter grouping results;

[0197] This step utilizes the Abaqus secondary development interface for script programming. This embodiment uses a normal distribution to generate the outer diameter of the spheres. The mean of the outer diameter is set to 40.0 μm, the standard deviation to 5.0 μm, the minimum diameter to 30.0 μm, and the maximum diameter to 60.0 μm. The script generates candidate outer diameters one by one, retaining only those within the minimum and maximum diameter ranges until the total number of spheres is met. The generated outer diameters are converted to millimeters and used in modeling, forming a list of outer diameters (d1_values) according to the set decimal places. Subsequently, the script counts all different outer diameter values ​​and their corresponding quantities, forming an outer diameter grouping result (d1_grouped). Based on the preset inner-outer diameter ratio, the script continues to calculate the inner diameter of each hollow spherical shell, forming a list of inner diameters (d2_values) and an inner diameter grouping result (d2_grouped).

[0198] In this embodiment, the inner diameter of the hollow spherical shell is determined according to the following formula:

[0199]

[0200] In the formula, D2 is the inner diameter of the hollow spherical shell, D1 is the outer diameter of the hollow spherical shell, and Diameter_Ratio is the ratio of the inner and outer diameters of the hollow spherical shell.

[0201] If a fixed wall thickness model is adopted, the inner diameter of the hollow spherical shell is determined according to the following formula:

[0202]

[0203] In the formula, D2 is the inner diameter of the hollow spherical shell, D1 is the outer diameter of the hollow spherical shell, and t is the wall thickness of the hollow spherical shell.

[0204] The outer diameter of the sphere is generated using a random function (random.normalvariate function) in the normal distribution mode; the inner-outer diameter ratio is set to 0.9, which is implemented by the script parameter (Diameter_Ratio); the fixed wall thickness mode is set by the wall thickness parameter (wall_thickness or t_um); the normal distribution parameter is set by the parameter dictionary (normal_dist_um);

[0205] S3, Random placement of sphere centers and overlap check

[0206] The list of sphere outer diameters obtained in step S2 is used to randomly place the sphere centers and perform overlap checks. When randomly placing the sphere centers, candidate sphere center positions are generated based on the half-width of the base, the height of the base, and the current radius of the sphere. When checking for overlap, it is determined whether the sphere corresponding to the candidate sphere center position overlaps with the spheres already placed in the base space. If there is no overlap, the candidate sphere center position is accepted. If there is an overlap, the candidate sphere center positions are regenerated until all spheres are placed, and finally a list of sphere placement points is generated. The list of sphere placement points includes the sphere center coordinates and outer diameter.

[0207] This step utilizes the Abaqus secondary development interface for script programming; in this embodiment, the candidate point generation function (generate_candidate) is used to generate the coordinates of the candidate sphere centers, and the overlap check function (is_sphere_valid) is used to determine whether there is overlap between spheres; the maximum number of attempts is set to 10000×m;

[0208] For a cuboid base, the current candidate sphere center coordinates satisfy the following range:

[0209]

[0210]

[0211]

[0212] In the formula, x, y, z are the coordinates of the current candidate sphere center, R is the half width of the cuboid base, h is the base height, and current_r is the radius of the current sphere;

[0213] The determination of sphere overlap is performed according to the following formula:

[0214]

[0215] In the formula, dx, dy, and dz are the coordinate differences between the center of the candidate sphere and the center of the placed sphere in the base space, respectively; r_i is the radius of the candidate sphere, and r_j is the radius of the placed sphere; when the above formula holds, it is determined that the two spheres overlap.

[0216] After filtering, all valid sphere center positions and their corresponding outer diameters are stored together in the sphere layout list (selected_nodes); each element in the sphere layout list includes the sphere center coordinates and the corresponding outer diameter information;

[0217] S4. Generation of Sphere Size and Center Parameters

[0218] Import the sphere size list obtained in step S2 and the sphere point list obtained in step S3 into the finite element software to form the sphere size and sphere center parameters required for subsequent finite element modeling; the sphere size and sphere center parameters include the outer diameter of the sphere, the inner diameter of the sphere, the coordinates of the sphere center, the grouping results of the outer diameter, and the grouping results of the inner diameter;

[0219] This step utilizes the Abaqus secondary development interface for script programming. In this embodiment, the sphere size and center parameters are generated by a random algorithm. In Embodiment 1, the sphere size and center parameters are generated by reading from a CSV parameter table. Apart from this, the subsequent finite element preprocessing steps are the same for both. The list of sphere outer diameters is denoted as d1_values, the list of sphere inner diameters is denoted as d2_values, the outer diameter grouping result is denoted as d1_grouped, the inner diameter grouping result is denoted as d2_grouped, and the list of sphere placement points is denoted as selected_nodes.

[0220] S5, Matrix Establishment

[0221] Import the base shape parameters, base half-width and base height set in step S1, and establish the base geometric model in the finite element software by sketch extrusion;

[0222] This step utilizes the Abaqus secondary development interface for script programming; this embodiment uses a cuboid base; the script establishes the cuboid base based on the base's half-width and height; specifically, the script draws a rectangular outline in the sketch and extrudes it along the height direction to form a three-dimensional cuboid base;

[0223] In this embodiment, the half-width of the base is 150.0 μm and the height is 450.0 μm, therefore the dimensions of the created cuboid base are 0.30 mm × 0.30 mm × 0.45 mm; the base shape parameter (container_type) is used to control the geometry of the base; when container_type is 0, the script creates a cuboid base; when container_type is 1, the script creates a cylindrical base; the solid extrusion uses the BaseSolidExtrude command, and the three-dimensional cuboid base component is named Part-1;

[0224] S6, Establishment of Sphere Component Reuse

[0225] Import the outer diameter grouping results and inner diameter grouping results obtained in step S4, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, first count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with that diameter already exists, reuse that component directly; if a spherical component with that diameter does not yet exist, create a new corresponding spherical component. This step is implemented using script programming via the Abaqus secondary development interface.

[0226] In this embodiment, during the reuse of the sphere component, the script first constructs a cross-section in the sketch using a semicircular arc with a radius equal to half the diameter and a rotation axis. Then, it uses the BaseSolidRevolve command to rotate the sphere 360° around the axis to generate a three-dimensional solid sphere. The script creates an outer sphere component (D1-Sphere_xxx) and an inner sphere component (D2-Sphere_xxx) respectively. When multiple holes have the same diameter, the same sphere component is instantiated and called only subsequently. The script converts the diameter value to a component name suffix using the diameter name conversion function (diameter_to_name_str) and automatically determines whether a sphere component with the same diameter already exists using the sphere creation function (create_sphere_part). If the sphere component with the same diameter already exists, it is reused directly; if the sphere component with the same diameter does not yet exist, a new sphere component is created.

[0227] S7, Outer sphere assembly and substrate hole cutting

[0228] Import the sphere center coordinates obtained in step S4 and the outer sphere component obtained in step S6, and complete the outer sphere assembly and base hole cutting in the assembly environment;

[0229] The method for assembling the outer sphere and cutting holes in the substrate is as follows: Create an outer sphere instance for each sphere sequentially and translate the outer sphere instance to the corresponding center coordinate position; after all outer sphere instances are arranged, use the substrate instance (Container_1) as the object to be cut and all outer sphere instances as the cutting objects, and execute the Boolean cut operation (InstanceFromBooleanCut command) sequentially to finally obtain a new porous substrate entity (Perforated_Container); this step is implemented using script programming via the Abaqus secondary development interface.

[0230] S8, Hollow spherical shell formation

[0231] Import the inner sphere component obtained in step S6 and the outer sphere assembly result obtained in step S7, and generate a hollow spherical shell in the finite element software;

[0232] The method for generating a hollow spherical shell is as follows: For each sphere, a corresponding inner sphere instance is created, and the inner sphere instance and the corresponding outer sphere instance have the same center coordinates. Then, using the newly instantiated outer sphere as the object to be cut and the corresponding inner sphere as the cutting object, a Boolean difference operation (InstanceFromBooleanCut) is performed to obtain the hollow spherical shell entity (Hollow_Sphere_i). This step is implemented using script programming via the Abaqus secondary development interface.

[0233] After the hollow spherical shell is built, the script assigns display colors to spherical shells of different diameters based on their outer diameter (color assignment is achieved through the colorsys.hsv_to_rgb function) to distinguish different particle size groups during visualization inspection; then, the temporary outer sphere instance, inner sphere instance, and initial matrix instance are deleted to preserve the final porous matrix and hollow spherical shell assembly structure; at this point, the automatic creation of the randomly generated geometric model under the condition of no parameter table is completed;

[0234] S9. Material Definition and Section Assignment

[0235] In the finite element software, the material definition and section assignment are performed on the porous matrix obtained by cutting holes in the matrix in step S7 and the hollow spherical shell obtained in step S8 to obtain the material model.

[0236] The method for defining materials and assigning sections is as follows: The matrix material adopts the Johnson-Cook hardening and damage constitutive model of 6061 aluminum alloy (the matrix material model is named Material-jc); the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material are imported; the hollow spherical shell material adopts the JH-2 brittle material constitutive model (the spherical shell material model is named abq_jh2_sio2); then, homogeneous solid sections of the matrix and the spherical shell are established respectively, and the matrix section is assigned to the porous matrix component, and the spherical shell section is assigned to all hollow spherical shell components one by one; this step is implemented by script programming using the Abaqus secondary development interface.

[0237] In this embodiment, the matrix material parameters include density, elastic modulus, Poisson's ratio, Johnson-Cook plastic hardening parameters, Johnson-Cook strain rate parameters, damage initiation parameters, and damage evolution displacement parameters; the density is 2.7e-09; the elastic modulus is 70000.0; the Poisson's ratio is 0.33; the plastic hardening parameters are 275.96, 288.39, 0.59, 1.0, 893.0, and 293.0; the strain rate parameters are 0.0064 and 0.001; the damage initiation parameters are 0.362, -4.57e-06, 17.434, 0.0112, 0.0, 893.0, 293.0, and 0.001; and the damage evolution displacement is 0.02.

[0238] S10, Pressure Plate Establishment and Compression Assembly

[0239] Based on the material model obtained in step S9, a pressure plate is built in the finite element software, and the compression assembly of the pressure plate and the material model is completed to obtain the compression assembly structure.

[0240] The method for establishing the pressure plate and completing the compression assembly is as follows: The pressure plate adopts a discrete rigid body form, and the geometry of the pressure plate is formed by extruded circular sketches and defined as a rigid loading component through reference points and rigid body constraints; First, draw the circular outline, and then extrude it along the thickness direction to form the pressure plate component (Part-6); Then, remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface (DISCRETE_RIGID_SURFACE), and establish a reference point (ReferencePoint) in the middle of the pressure plate; In the assembly environment, create an upper pressure plate instance (Part-6-1) and a lower pressure plate instance (Part-6-2) respectively; The upper pressure plate is translated to the outer side of the top of the sample, and the lower pressure plate is translated to the outer side of the bottom of the sample to form a compression assembly structure; Further establish rigid body constraints (Rigid-Top and Rigid-Bottom) so that the pressure plate surface area is controlled by the corresponding reference point; This step is implemented using script programming through the Abaqus secondary development interface.

[0241] In this embodiment, the outer diameter of the pressure plate is determined based on the transverse dimension of the sample and the outer expansion distance of the pressure plate; the outer expansion distance of the pressure plate is set to 100.0 μm, and the thickness of the pressure plate is set to 20.0 μm; the rigid body constraint corresponds to the finite element keyword (*RIGID BODY).

[0242] S11. Analysis Step and Output Settings

[0243] In the finite element software, an explicit dynamics analysis step and output settings are established for the compression assembly structure obtained in step S10; an explicit dynamics analysis step (ExplicitDynamicsStep) is established, and the total analysis time and maximum time increment are set; the total analysis time t is set to 1, and the maximum time increment is set to 0.0001; this analysis step is used to simulate the dynamic explicit response during the compression of the specimen by the pressure plate; this step is implemented using script programming through the Abaqus secondary development interface;

[0244] The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. The field output interval is set to 2000. History output includes the vertical displacement and vertical reaction force (U3 and RF3) of the upper pressure plate reference point, used to output the compression displacement-reaction force curve. The number of history output points is set to 1000.

[0245] S12, Contact Relationships and Interaction Settings

[0246] Establish the contact properties and global contact relationships of the compression assembly structure obtained in step S10 in the finite element software;

[0247] This step utilizes the Abaqus secondary development interface for script programming. In this embodiment, the script establishes contact properties for the interaction between the pressure plate and the sample, and assigns these properties to global contact or corresponding contact pairs. The contact properties include tangential friction behavior and normal hard contact behavior. Tangential contact uses a penalty friction model with a friction coefficient set to 0.5. Normal contact uses hard contact, allowing contact surface separation. Subsequently, the script establishes explicit universal contact (ContactExp or Int-1), incorporating all external surface contacts into global contact, and assigns contact properties to global self-contact relationships. The first contact property is named IntProp-1, with a maximum elastic slip ratio set to 0.005. The second contact property is named IntProp-2, with a friction coefficient set to 0.2, for use with other specific contact pairs.

[0248] S13, Boundary Conditions and Compressive Loading

[0249] Boundary conditions and compressive loading are applied to the compressed assembly structure obtained in step S10 in the finite element software.

[0250] The compression ratio of the compression loading is set to 0.7, and the compression loading is completed by Z-axis displacement;

[0251] This step is implemented using script programming via the Abaqus secondary development interface; in this embodiment, the script is used to establish an amplitude curve (Amp-1) that grows linearly with time, and displacement boundary conditions are applied to the reference points of the upper and lower pressure plates in the analysis step to achieve compression loading on the sample;

[0252] The compression ratio is set to 0.7, and the specimen height is determined by the matrix height. The upper pressure plate moves along the negative Z-axis, and the lower pressure plate moves along the positive Z-axis, so that the specimen achieves a total compression deformation of 0.7 between the upper and lower pressure plates. The lateral translational and rotational degrees of freedom of the upper and lower pressure plates are constrained, and compression loading is only allowed through Z-axis displacement.

[0253] The displacement of the upper pressure plate is determined by the following formula:

[0254]

[0255] In the formula, U3_top is the displacement of the upper pressure plate reference point along the Z direction, h is the sample height, and k is the compression ratio;

[0256] The displacement of the lower pressure plate is determined by the following formula:

[0257]

[0258] In the formula, U3_bottom is the displacement of the lower platen reference point along the Z direction, h is the sample height, and k is the compression ratio;

[0259] The compression ratio is represented by the script parameter (k), and the specimen height is represented by the script parameter (h or specimen_height); the amplitude curve data is set to increase from 0 at time 0 to 1 at the end of the analysis; the constraint degrees of freedom of the upper and lower pressure plates include lateral translational degrees of freedom and rotational degrees of freedom (u1, u2, ur1, ur2 and ur3).

[0260] S14, Mesh Generation

[0261] In the finite element software, the porous matrix and hollow spherical shell obtained in step S9 and the pressure plate obtained in step S10 are meshed; the pressure plate is meshed with a coarse mesh, the porous matrix is ​​meshed with a free tetrahedral mesh, and the hollow spherical shell is meshed with a partitioned solid mesh. Figure 5 The left image shows the mesh generation diagram of the compressed assembly structure in Example 2, and the right image shows its cross-section. The cross-section on the right shows the random distribution of positions and the normal distribution of dimensions. This step was implemented using script programming via the Abaqus secondary development interface.

[0262] In this embodiment, the pressure plate component is seeded and meshed using a 5.0 μm mesh size; the porous matrix component is seeded using a 10.0 μm mesh size and set as a free tetrahedral mesh to adapt to complex pore boundaries; the hollow spherical shell component is seeded using a 2.0 μm mesh size. To improve the mesh quality and analysis stability of the spherical shell structure, before meshing the spherical shell, the script first establishes a local coordinate system (Ball-i-CSYS) for the sphere and partitions the spherical shell using three orthogonal planes, and then generates the mesh.

[0263] This embodiment uses the Abaqus secondary development interface for programming, but it can also be done manually in the Abaqus graphical window;

[0264] This embodiment is suitable for generating a finite element model of a spherical reinforced porous composite material for finite element solution, followed by solution submission and post-processing, as well as other uses, including:

[0265] Import the finite element model, submit it to the finite element solver for solution and post-processing; after completing material definition, section assignment, assembly, contact, analysis step, boundary conditions, mesh generation and output settings, the script generates a finite element model database and submits it to the explicit finite element solver (Abaqus / Explicit) for solution; when submitting the solution, the script creates an analysis job and sets the computing resources according to the model size;

[0266] After the solution is completed, the script reads the output database file (ODB file), extracts the vertical displacement and vertical reaction force of the upper pressure plate reference point, and obtains the compression displacement-reaction force curve; combined with the initial cross-sectional area and initial height of the sample, it further calculates the engineering stress-engineering strain curve; at the same time, it extracts the stress, strain, damage variables and element deletion state in the porous matrix and hollow spherical shell, and analyzes the stress concentration around the pores, shell failure, plastic deformation of the matrix and changes in the overall bearing capacity during the compression process;

[0267] The surface displacement field, strain field, and local deformation zone obtained by finite element simulation are compared with relevant experimental results. Under the same compressive strain level, the surface principal strain distribution obtained by the experiment is compared with the logarithmic strain or equivalent plastic strain distribution output by the finite element to determine the influence of the hollow microsphere position, pore distribution, and boundary truncation characteristics on the local deformation mode in the model.

[0268] Furthermore, the geometric parameters of the pores, load-displacement curves, stress-strain curves, damage evolution results, and corresponding experimental results are integrated into a structure-performance dataset for subsequent performance prediction model training. This dataset includes structural input features and performance output labels. The structural input features include the number of pores, pore size distribution, sphere center coordinates, volume fraction, spatial enclosing range, matrix size, shell wall thickness or inner-outer diameter ratio, material parameters, and mesh parameters. The performance output labels include peak stress, plateau stress, energy absorption capacity, failure strain, and local strain concentration.

Claims

1. A method for generating finite element models of near-spherical reinforced porous composite materials based on CT recognition, characterized in that: The method for generating finite element models of porous composite materials with near-spherical reinforcements based on CT identification follows these steps: S1, CT Data Acquisition Two-dimensional cross-sectional images of the interior of the hollow microsphere-reinforced metal matrix porous composite material sample were obtained by scanning the sample with a CT scanning device. S2. Three-dimensional volume data establishment and voxel size calibration Import the sliced ​​image obtained in step S1 into the 3D image visualization and analysis software. During the import, a 3D volume data object is created, and the voxel size parameter is set in the object properties. Finally, the 3D volume data of the sliced ​​image is obtained. S3, Volume Data Preprocessing The three-dimensional volume data obtained in step S2 are sequentially subjected to three-dimensional nonlocal mean filtering, local contrast enhancement or gamma adjustment to obtain preprocessed volume data that balances smoothing image noise and maintaining edge sharpness. S4. Local Region Extraction and Binary Segmentation of Holes The preprocessed volume data obtained in step S3 is subjected to local region truncation, and the truncated region is subjected to hole binary segmentation; then, the obtained hole binary volume is subjected to morphological cleaning and local boundary smoothing repair; the morphological cleaning includes opening operation, closing operation and small connected component deletion; S5, Separation of Adhesion and Cavities The binary pore obtained in step S4 is separated into multiple independent pores. S6. Hole Connectivity Labeling and Geometric Parameter Statistics Connectivity labeling is performed on the separated hole data obtained in step S5, and a unique label is automatically assigned to each independent hole to form a hole label body. After the label body is generated, the statistical analysis module is called to perform statistical analysis on the hole structure parameters. The statistical analysis includes the hole center coordinates, hole volume, hole equivalent sphere diameter, hole spatial enclosing range, and hole sphericity. The connected component labeling is implemented using the Connected Components module in the 3D image visualization and analysis software; Steps S2-S6 are all performed in 3D image visualization and analysis software, such as Avizo, Dragonfly, or VGSTUDIO MAX. S7, CSV parameter table export The statistical analysis results obtained in step S6 are exported as a CSV parameter table. The CSV parameter table includes the center coordinates of the hole and the equivalent sphere diameter of the hole. The center coordinates of the hole are used to determine the position of the sphere's center, and the equivalent sphere diameter of the hole is used to determine the inner or outer diameter of the sphere. S8. Generation of Sphere Size and Center Parameters Import the CSV parameter table obtained in step S7 into the finite element software to generate the sphere size and center parameters; the sphere size and center parameters include the center coordinates, the list of outer diameters of the sphere, the list of inner diameters of the sphere, the grouping results of the outer diameters, and the grouping results of the inner diameters; S9, Matrix Establishment Import the sphere center parameters obtained in step S8 and establish the matrix geometric model in the finite element software; S10, Establishment of Sphere Component Reuse Import the outer diameter grouping results and inner diameter grouping results obtained in step S8, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, first count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with that diameter already exists, reuse that component directly. If a spherical component with that diameter does not yet exist, create a new corresponding spherical component. Continue until a spherical component is created for each different diameter value. S11, Outer sphere assembly and substrate hole cutting Import the sphere center coordinates obtained in step S8 and the outer sphere component obtained in step S10, and complete the outer sphere assembly and base hole cutting in the assembly environment; the sphere center coordinates are the modeling coordinates after local region origin subtraction, unit conversion and container boundary repositioning. S12, Hollow spherical shell formation The inner sphere component obtained in step S10 is sequentially imported into the outer sphere assembly result obtained in step S11. A hollow sphere shell and an assembly structure of a porous substrate and a hollow sphere shell are generated in the finite element software. S13, Material Definition and Section Assignment In the finite element software, the porous matrix obtained by cutting holes in the matrix in step S11 and the hollow spherical shell obtained in step S12 are material-defined and cross-section-assigned to obtain the material-assigned model. S14, Pressure Plate Establishment and Compression Assembly A pressure plate is created in the finite element software, and a compression assembly is completed with the porous matrix and hollow spherical shell assembly structure obtained in step S12 to obtain a compression assembly structure. The method for establishing the pressure plate and completing the compression assembly is as follows: the pressure plate adopts a discrete rigid body form, and the geometry of the pressure plate is formed by extruded circular sketches and defined as a rigid loading component through reference points and rigid body constraints; first, draw the circular outline, and then extrude it along the thickness direction to form the pressure plate component; then, remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface, and establish a reference point in the middle of the pressure plate; in the assembly environment, create an upper pressure plate instance and a lower pressure plate instance respectively; translate the upper pressure plate to the outer side of the top of the sample, and translate the lower pressure plate to the outer side of the bottom of the sample to form a compression assembly structure; and further establish rigid body constraints so that the pressure plate surface area is controlled by the corresponding reference point; S15, Analysis Step and Output Settings Import the compressed assembly structure obtained in step S14, and establish explicit dynamic analysis steps and output settings in the finite element software; The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. History output includes the vertical displacement and vertical reaction force of the upper pressure plate reference point, used to output the compression displacement-reaction force curve. S16. Contact Relationships and Interaction Settings Establish the contact properties and global contact relationships of the compression assembly structure obtained in step S14 in the finite element software; S17, Boundary Conditions and Compression Loading Boundary conditions and compression loading are applied to the compressed assembly structure obtained in step S14 in the finite element software. S18, Mesh Generation In the finite element software, the porous substrate obtained in step S11, the hollow spherical shell obtained in step S12, and the pressure plate obtained in step S14 are meshed; the pressure plate is meshed with a coarse mesh, the porous substrate is meshed with a free tetrahedral mesh, and the hollow spherical shell is meshed with a partitioned solid mesh.

2. The method for generating a finite element model of a near-spherical reinforced porous composite material based on CT recognition according to claim 1, characterized in that: The method for separating holes in step S5 is as follows: First, the Distance Map module is used to perform distance transformation on the binary volume of holes, and the distance value from each hole voxel to the nearest boundary is calculated to form a three-dimensional distance field; then, seed points are generated based on the local peaks in the distance field, and the Watershed module is used to perform three-dimensional watershed segmentation, thereby separating the mutually adhered holes into multiple independent holes.

3. The method for generating a finite element model of a near-spherical reinforced porous composite material based on CT recognition according to claim 1, characterized in that: The method for assembling the outer sphere and cutting holes in the substrate in step S11 is as follows: In the assembly environment, create an outer sphere instance for each sphere in sequence and translate the outer sphere instance to the corresponding center coordinate position; after all the outer sphere instances are arranged, take the substrate instance as the object to be cut and all the outer sphere instances as the cutting objects, and perform Boolean cut operation in sequence to finally generate a new porous substrate entity; for the outer sphere instances located at the boundary, after Boolean cut, retain their real intersection relationship with the substrate to reflect the boundary truncation characteristics.

4. The method for generating a finite element model of a near-spherical reinforced porous composite material based on CT recognition according to claim 1, characterized in that: Step S12 generates the hollow spherical shell by: creating a corresponding inner sphere instance for each sphere, and ensuring that the inner sphere instance has the same center coordinates as the corresponding outer sphere instance in the assembly environment; then, performing a Boolean difference operation with the re-instantiated outer sphere as the cutting object and the corresponding inner sphere as the cutting object to obtain the hollow spherical shell entity.

5. The method for generating a finite element model of a near-spherical reinforced porous composite material based on CT recognition according to claim 1, characterized in that: The method for defining materials and assigning cross sections in step S13 is as follows: import the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material; adopt the constitutive model of brittle materials for hollow spherical shell materials; then establish the homogeneous solid cross section of the matrix and the homogeneous solid cross section of the spherical shell respectively, and assign the matrix cross section to the porous matrix component, and assign the spherical shell cross section to all hollow spherical shell components one by one.

6. A method for generating a finite element model of a randomly generated near-spherical reinforced porous composite material, characterized in that: The method for generating randomly generated finite element models of porous composite materials with near-spherical reinforcements follows these steps: S1. Random Modeling Parameter Settings In the finite element software, set the basic parameters required for the randomly generated model; the basic parameters required for the model include matrix shape parameters, distribution pattern parameters, distribution type parameters, sphere distribution parameters, matrix half-width, matrix height, total number of spheres, total analysis time, maximum time increment, compression ratio, number of history output points, pressure plate mesh size, matrix mesh size, and hollow spherical shell mesh size; S2, Sphere size is randomly generated. Import the sphere distribution parameters set in step S1 to randomly generate sphere sizes and form a sphere size list; the sphere size list includes a list of sphere outer diameters, a list of sphere inner diameters, outer diameter grouping results, and inner diameter grouping results; S3, Random placement of sphere centers and overlap check The list of sphere outer diameters obtained in step S2 is used to randomly place the sphere centers and perform overlap checks. When randomly placing the sphere centers, candidate sphere center positions are generated based on the half-width of the base, the height of the base, and the current radius of the sphere. When checking for overlap, it is determined whether the sphere corresponding to the candidate sphere center position overlaps with the spheres already placed in the base space. If there is no overlap, the candidate sphere center position is accepted. If there is an overlap, the candidate sphere center positions are regenerated until all spheres are placed, and finally a list of sphere placement points is generated. The list of sphere placement points includes the sphere center coordinates and outer diameter. S4. Generation of Sphere Size and Center Parameters Import the sphere size list obtained in step S2 and the sphere point list obtained in step S3 into the finite element software to form the sphere size and sphere center parameters required for subsequent finite element modeling; the sphere size and sphere center parameters include the outer diameter of the sphere, the inner diameter of the sphere, the coordinates of the sphere center, the grouping results of the outer diameter, and the grouping results of the inner diameter; S5, Matrix Establishment Import the base shape parameters, base half-width and base height set in step S1, and establish the base geometric model in the finite element software by sketch extrusion; S6, Establishment of Sphere Component Reuse Import the outer diameter grouping results and inner diameter grouping results obtained in step S4, and create a reused spherical component in the finite element software. The reused spherical component includes an inner spherical component and an outer spherical component. During the creation of the reused spherical component, count all different outer diameter values ​​and inner diameter values, and then determine whether a spherical component with the same diameter already exists. If a spherical component with the same diameter already exists, reuse the component directly. If a spherical component with the same diameter does not yet exist, create a new corresponding spherical component. S7, Outer sphere assembly and substrate hole cutting Import the sphere center coordinates obtained in step S4 and the outer sphere component obtained in step S6, and complete the outer sphere assembly and base hole cutting in the assembly environment; S8, Hollow spherical shell formation Import the inner sphere component obtained in step S6 and the outer sphere assembly result obtained in step S7, and generate a hollow spherical shell in the finite element software; S9. Material Definition and Section Assignment In the finite element software, the material definition and section assignment are performed on the porous matrix obtained by cutting holes in the matrix in step S7 and the hollow spherical shell obtained in step S8 to obtain the material model. S10, Pressure Plate Establishment and Compression Assembly Based on the material model obtained in step S9, a pressure plate is built in the finite element software, and the pressure plate and the material model are compressed and assembled to obtain a compressed assembly structure. S11. Analysis Step and Output Settings In the finite element software, establish the explicit dynamic analysis step and output settings for the compression assembly structure obtained in step S10; The output settings include field output and history output. Field output includes stress, average stress, plastic strain, equivalent plastic strain, logarithmic strain, displacement, velocity, acceleration, reaction force, contact stress, element volume fraction, state variables, and element states. History output includes the vertical displacement and vertical reaction force (U3 and RF3) of the upper pressure plate reference point, used to output the compression displacement-reaction force curve. S12, Contact Relationships and Interaction Settings Establish the contact properties and global contact relationships of the compression assembly structure obtained in step S10 in the finite element software; S13, Boundary Conditions and Compressive Loading Boundary conditions and compressive loading are applied to the compressed assembly structure obtained in step S10 in the finite element software. S14, Mesh Generation In the finite element software, the porous matrix and hollow spherical shell obtained in step S9 and the pressure plate obtained in step S10 are meshed.

7. The method for generating a randomly generated finite element model of a near-spherical reinforced porous composite material according to claim 6, characterized in that: The method for assembling the outer sphere and cutting holes in the substrate in step S7 is as follows: create an outer sphere instance for each sphere in sequence and translate the outer sphere instance to the corresponding center coordinate position; after all the outer sphere instances are arranged, take the substrate instance as the object to be cut and all the outer sphere instances as the cutting objects, and perform Boolean cut operation in sequence to finally obtain a new porous substrate entity.

8. The method for generating a randomly generated finite element model of a near-spherical reinforced porous composite material according to claim 6, characterized in that: The method for generating a hollow spherical shell in step S8 is as follows: a corresponding inner sphere instance is created for each sphere, and the inner sphere instance and the corresponding outer sphere instance have the same center coordinates; then, Boolean difference operation is performed with the newly instantiated outer sphere as the cutting object and the corresponding inner sphere as the cutting object, thereby obtaining the hollow spherical shell entity.

9. The method for generating a finite element model of a randomly generated near-spherical reinforced porous composite material according to claim 6, characterized in that: The method for defining materials and assigning cross sections in step S9 is as follows: import the density, elastic parameters, plastic hardening parameters, strain rate parameters, damage initiation parameters, and damage evolution parameters of the matrix material; then establish the homogeneous solid cross section of the matrix and the homogeneous solid cross section of the spherical shell respectively, and assign the matrix cross section to the porous matrix component, and assign the spherical shell cross section to all hollow spherical shell components one by one.

10. The method for generating a finite element model of a randomly generated near-spherical reinforced porous composite material according to claim 6, characterized in that: The method for establishing the pressure plate and completing the compression assembly in step S10 is as follows: The pressure plate adopts a discrete rigid body form, and the geometry of the pressure plate is formed by extruded circular sketches and defined as a rigid loading component through reference points and rigid body constraints; First, draw a circular outline, and then extrude it along the thickness direction to form the pressure plate component; Then, remove the volume region corresponding to the solid element, convert the pressure plate into a discrete rigid body surface, and establish a reference point in the middle of the pressure plate; In the assembly environment, create an upper pressure plate instance and a lower pressure plate instance respectively; The upper pressure plate is translated to the outer side of the top of the sample, and the lower pressure plate is translated to the outer side of the bottom of the sample to form a compression assembly structure; Further establish rigid body constraints so that the pressure plate surface area is controlled by the corresponding reference point.

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