Foaming material porous structure three-dimensional reconstruction and simulation system

Abstract

The invention relates to the technical field of three-dimensional reconstruction and simulation, and discloses a foam material porous structure three-dimensional reconstruction and simulation system, which comprises a scanning imaging module used for carrying out scanning imaging on a foam material sample to obtain pore image data; the pore boundary recognition module is used for performing pore boundary recognition based on the pore image data to obtain a pore boundary recognition result; the three-dimensional reconstruction module is used for executing three-dimensional reconstruction of bubble evolution physical constraints according to the pore boundary recognition result to obtain a three-dimensional reconstruction model; the coupling simulation module is used for performing grid division and coupling simulation on the three-dimensional reconstruction model to obtain mechanical simulation data; and the parameter solving module is used for carrying out density field optimization and parameter solving based on the mechanical simulation data to obtain optimal gap design parameters, so that seamless connection from simulation analysis to optimization design is realized, the structural design period of the foaming material is shortened, and the design precision and consistency are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of three-dimensional reconstruction and simulation, and particularly relates to a three-dimensional reconstruction and simulation system for porous structure of foamed material. BACKGROUND

[0002] The porous structure of foamed material presents typical multi-scale non-uniform characteristics, and the pore distribution is affected by multiple random factors such as bubble nucleation density, expansion rate and coalescence probability, so that a complex pore network from nanoscale to millimeter scale is formed in the material.

[0003] Traditional foamed material structure analysis methods mainly rely on single-scale imaging technology and simplified geometric models, and it is difficult to capture both microscopic pore details and macroscopic connectivity characteristics. Existing three-dimensional reconstruction techniques often ignore the physical evolution mechanism in the foaming process, and the reconstruction results lack physical rationality; and traditional mechanical simulation methods mostly use single-scale analysis, which cannot accurately reflect the cross-scale mechanical behavior of foamed material, and thus the existing structure optimization methods lack effective correlation with foaming process parameters. SUMMARY

[0004] The present application provides a three-dimensional reconstruction and simulation system for porous structure of foamed material, thereby realizing seamless connection from simulation analysis to optimization design, shortening the foamed material structure design cycle, and improving design accuracy and consistency.

[0005] The first aspect of the present application provides a three-dimensional reconstruction and simulation system for porous structure of foamed material, which comprises:

[0006] A scanning imaging module is configured to perform scanning imaging on a foamed material sample to obtain pore image data.

[0007] A pore boundary identification module is configured to perform pore boundary identification based on the pore image data to obtain a pore boundary identification result.

[0008] A three-dimensional reconstruction module is configured to perform three-dimensional reconstruction with bubble evolution physical constraints according to the pore boundary identification result to obtain a three-dimensional reconstruction model.

[0009] A coupled simulation module is configured to perform mesh division and coupled simulation on the three-dimensional reconstruction model to obtain mechanical simulation data.

[0010] A parameter solving module is configured to perform density field optimization and parameter solving based on the mechanical simulation data to obtain optimal void design parameters.

[0011] In combination with the first aspect, in a first implementation manner of the first aspect of the present application, the scanning imaging module further comprises:

[0012] a first scanning unit configured to perform a CT global scan on the foamed material sample to obtain the pore connectivity data;

[0013] a second scanning unit configured to scan the foamed material sample by using a scanning electron microscope to obtain local image data;

[0014] a registration unit configured to perform registration on the pore connectivity data and the local image data by establishing a spatial coordinate transformation matrix to obtain bimodal registration image data, and perform multi-scale weight fusion on the bimodal registration image data to obtain the pore image data.

[0015] With reference to the first aspect, in a second implementation manner of the first aspect of the present application, the registration unit is specifically configured to:

[0016] establish a spatial coordinate transformation matrix according to a first spatial position of the pore connectivity data and a second spatial position of the local image data;

[0017] perform coordinate transformation on the local image data based on the spatial coordinate transformation matrix to obtain transformed image data corresponding to the pore connectivity data;

[0018] perform pixel registration on the pore connectivity data and the transformed image data to obtain bimodal registration image data;

[0019] perform weight distribution and weighted fusion on the bimodal registration image data according to the foamed material pore density data to obtain the pore image data.

[0020] With reference to the first aspect, in a third implementation manner of the first aspect of the present application, the pore boundary recognition module further includes:

[0021] a deep feature extraction unit configured to input the pore image data into an encoder in a U-Net network, and extract pore deep feature data of the foamed material sample by the encoder;

[0022] a decoding recognition unit configured to input the pore deep feature data into a decoder in the U-Net network, and recognize different size pores by the decoder to obtain a pore segmentation feature map;

[0023] a boundary positioning unit configured to fit the curvature variation of a pore boundary in the pore segmentation feature map by using a boundary positioning algorithm to obtain first pore boundary data;

[0024] a verification unit configured to verify the physical reasonableness of the first pore boundary data in combination with a bubble minimum surface energy principle to ensure that the boundary recognition conforms to the foamed material bubble evolution law, to obtain second pore boundary data, and to generate a pore boundary recognition result based on the second pore boundary data.

[0025] In a fourth implementation form of the first aspect, in the fourth implementation form of the first aspect, the boundary positioning unit is specifically configured to:

[0026] identify the interface pixel points of the foamed material pores and the matrix material from the pore segmentation feature map, and calculate the gradient direction and gradient amplitude of each interface pixel point to determine the pore boundary gradient information;

[0027] fit the curvature variation of the pore boundary according to the pore boundary gradient information by using the least square method, and calculate the curvature radius and curvature center of the boundary curve at each point to obtain the curvature fitting parameters;

[0028] input the curvature fitting parameters into the boundary positioning algorithm to calculate the boundary coordinate data, and perform boundary continuity verification on the boundary coordinate data to obtain the first pore boundary data.

[0029] In a fifth implementation form of the first aspect, the three-dimensional reconstruction module further includes:

[0030] extract the boundary contour coordinates of each pore from the pore boundary identification result, and calculate the geometric feature data based on the boundary contour coordinates;

[0031] reconstruct the two-dimensional pore boundary into a three-dimensional pore volume along the Z-axis direction according to the geometric feature data, and generate a three-dimensional pore structure;

[0032] apply the pore size evolution law in the Ostwald ripening theory to physically constrain and correct the pore size in the three-dimensional pore structure to obtain physically constrained pore size data;

[0033] adjust the connectivity state of adjacent pores in the physically constrained pore size data according to the bubble coalescence probability characteristics of the foamed material to form a pore connectivity network;

[0034] parameterize the complex shape of irregular pores in the pore connectivity network by using spherical harmonics to establish a three-dimensional reconstruction model.

[0035] In a sixth implementation form of the first aspect, the coupling simulation module further includes:

[0036] a mesh division unit, configured to perform mesh division on the pore geometric boundary and the matrix region in the three-dimensional reconstruction model to generate a finite element mesh model;

[0037] a calculation domain establishment unit, configured to establish a molecular dynamics calculation domain on the pore surface region of the finite element mesh model, and calculate the surface energy and local elastic modulus of the pore-matrix interface based on the molecular dynamics calculation domain;

[0038] a homogenization calculation unit configured to select a typical pore region in the finite element mesh model and perform homogenization calculation with the surface energy and the local elastic modulus as input conditions to solve equivalent elastic constants and yield strength of the foamed material sample;

[0039] a mechanical simulation unit configured to assign the equivalent elastic constants and the yield strength to corresponding mesh elements of the finite element mesh model and apply boundary conditions and loads to output mechanical simulation data.

[0040] With reference to the first aspect, in a seventh implementation form of the first aspect of the application, the homogenization calculation unit is specifically configured to:

[0041] select a typical pore region with representative pore density, pore size range and connectivity in the finite element mesh model, and extract a corresponding target volume element from the finite element mesh model based on the typical pore region;

[0042] assign the surface energy and the local elastic modulus data to corresponding pore interfaces and matrix material regions in the target volume element to establish a mechanical calculation model;

[0043] apply periodic boundary conditions to the mechanical calculation model and perform multi-directional tensile and shear loading to solve an equivalent elastic modulus matrix and a Poisson's ratio of the foamed material through homogenization theory;

[0044] continue nonlinear loading analysis based on the equivalent elastic modulus matrix and the Poisson's ratio until the material yields to determine the equivalent elastic constants and the yield strength of the foamed material sample.

[0045] With reference to the first aspect, in an eighth implementation form of the first aspect of the application, the parameter solving module further includes:

[0046] an optimization region identification unit configured to identify a to-be-optimized region in the foamed material sample according to the mechanical simulation data, and to establish a multi-objective optimization function with the objective of minimizing the structure weight while maximizing the stiffness and energy absorption, and to introduce process constraint conditions of bubble nucleation density and expansion rate;

[0047] a simulation optimization construction unit configured to construct a simulation-driven topology optimization model according to the to-be-optimized region, the multi-objective optimization function and the process constraint conditions;

[0048] a response gradient calculation unit configured to represent the pore distribution of the to-be-optimized region in the simulation-driven topology optimization model as a continuously changing density variable by using a density field method, and to synchronously calculate the response gradient of the multi-objective optimization function to the density change of each region;

[0049] An iterative optimization solving unit is configured to iteratively optimize and solve the density variable according to the response gradient to obtain an optimal density field distribution, and to analyze the optimal density field distribution into optimal void design parameters of the region to be optimized.

[0050] In combination with the first aspect, in a ninth implementation form of the first aspect of the application, the iterative optimization solving unit is specifically configured to:

[0051] The response gradient is used to guide the updating direction of the density variable, an adaptive step adjustment strategy is used to dynamically control the optimization step according to the convergence trend of the multi-objective optimization function, and the iterative updating of the density variable is performed;

[0052] The change amplitude of the response solution of the multi-objective optimization function in the iterative updating process is monitored, and the optimal density field distribution is determined according to the change amplitude of the response solution;

[0053] The optimal density field distribution is converted into discrete pore existing regions and matrix regions to form an optimized pore space layout;

[0054] The volume size and geometric center coordinates of each pore in the optimized pore space layout are counted, the ratio of the pore volume to the total volume in the region to be optimized and the distribution range of the pore size are calculated, and the optimal void design parameters are output.

[0055] Compared with the prior art, the application has the following beneficial effects: the multi-scale imaging fusion technology breaks through the limitations of a single imaging modality, and realizes complete coverage from nanometer to millimeter scale; the deep learning pore recognition technology of the improved U-Net network is used to realize sub-pixel level accurate segmentation, and effectively solve the problem of fuzzy boundary of foaming materials; the physical constraint three-dimensional reconstruction of Ostwald ripening theory and bubble coalescence probability model is introduced to ensure that the reconstruction result conforms to the real physical law of foaming materials; a three-level multi-scale coupling simulation system of molecular dynamics-representative volume element-macro structure is established to accurately predict the cross-scale mechanical behavior; the foaming process parameters are directly included in the simulation driven topology optimization of the optimization constraint to ensure the process realizability of the optimization result; the full-process automatic processing is realized through modular design and standardized data interface, the foaming material structure design cycle is significantly shortened, and the technical bottlenecks of low automation, difficult verification and multi-scale coupling complexity in the traditional method are solved. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0057] The structure, proportion, size, etc. shown in the drawings of the specification are only used to cooperate with the content disclosed in the specification, to be understood and read by those skilled in the art, and are not used to limit the conditions that the application can be implemented, so they do not have technical significance. Any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effect that the application can produce and the purpose that the application can achieve, should still fall within the scope of the technology disclosed by the application.

[0058] Figure 1 is a structural schematic block diagram of a foamed material porous structure three-dimensional reconstruction and simulation system provided by an embodiment of the application. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.

[0060] The flowchart shown in the drawings is only an example and does not necessarily include all contents and operations / steps, nor does it necessarily be executed in the described order. For example, some operations / steps can be decomposed, combined or partially merged, so the actual execution order can be changed according to the actual situation.

[0061] It should also be understood that the terms used in this application specification are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in the specification and the appended claims of the application, unless otherwise clear from the context, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0062] It should be further understood that the term "and / or" used in the specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. Please refer to Figure 1 One embodiment of the foamed material porous structure three-dimensional reconstruction and simulation system in the embodiments of the application includes:

[0063] The scanning imaging module is configured to scan and image the foamed material sample to obtain pore image data.

[0064] Specifically, the first scanning unit performs a CT global scanning operation on the foamed material sample at a micron level, a high-resolution micro-focus X-ray source is combined with a rotating platform to perform volume scanning, three-dimensional pore connectivity data covering the entire sample is obtained, including the position distribution of the pores, and the topological connection relationship and spatial extension structure of the pore network, the resolution is controlled within the range of 2-5 microns, and the connectivity and overall geometric morphology of the macroscopic structure are reflected. The second scanning unit performs scanning electron microscope imaging at a nanometer level resolution on the key area of the same material sample, selects multiple local representative sections, and obtains pore detail images in a surface scanning manner, the pore detail images reflect the microtexture, edge transition zone and pore wall curvature variation and other microfeatures of the pore wall. Due to the differences in the coordinate system, resolution scale and image orientation between the images collected by the micro-CT and the scanning electron microscope, the registration unit unifies the spatial data of the dual-mode images, the registration unit extracts spatial reference points with consistent features in the two types of images in the preprocessing stage by constructing a three-dimensional spatial coordinate transformation matrix, and adopts a combination of rigid transformation and non-rigid registration to complete the consistent processing of the image position, angle and scale, so that the registration error is controlled within 0.5 pixels, thereby ensuring the high-precision alignment of the two types of images in the spatial structure. On the basis of the registered image data, multi-scale weight fusion processing is performed, the fusion strategy dynamically adjusts the fusion weight of each modal image according to the scale level of the pore structure in the image, that is, the micro-CT data is preferentially retained in the pore overall morphology identification area, and the resolution characteristics of the scanning electron microscope image are strengthened in the pore boundary detail area, and pore image data is output.

[0065] A pore boundary recognition module is configured to recognize a pore boundary based on the pore image data to obtain a pore boundary recognition result.

[0066] Specifically, the depth feature extraction unit receives the registered pore image data and inputs it into the encoder of the U-Net neural network, which is customized for the structural features of foamed materials. The encoder adopts a multi-layer convolutional structure, combined with residual connections and attention mechanisms, to extract pore depth feature data containing semantic information such as edges, shapes, and textures at multiple scales. This captures geometric details at different levels and effectively suppresses feature extraction deviations caused by image noise or blurred pore edges. The decoding and recognition unit inputs the pore depth feature data into the decoder structure in the U-Net network. The decoder performs upsampling operations and skip connections to fuse with the high-resolution feature map of the encoder, enabling the network to restore image details while maintaining spatial resolution. This allows the network to identify pore regions of different sizes and shapes and generate structurally continuous and shape-accurate pore segmentation feature maps. The boundary localization unit performs boundary fitting on the pore regions extracted from the pore segmentation feature map. The unit uses a curvature tracking algorithm to identify the local normal direction and second derivative changes of edge pixels, establishing a curvature change model for the pore boundaries. A sub-pixel-level boundary fitting strategy is then employed to refine and correct blurred or overlapping boundaries, resulting in first pore boundary data with high continuity and edge integrity. The verification unit utilizes the physical mechanism of minimizing surface energy during the bubble evolution process of the foamed material as a recognition constraint. An energy verification model based on the principle of minimum surface tension is constructed to verify the physical rationality of the first pore boundary data. When the identified boundary morphology deviates from the natural evolution trend, a boundary correction process is automatically executed to form second pore boundary data under physical constraints. The output is the pore boundary recognition result generated under the dual constraints of image feature consistency and physical mechanism.

[0067] The three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the physical constraints of bubble evolution based on the pore boundary identification results, and obtain a three-dimensional reconstruction model;

[0068] Specifically, based on the pore boundary recognition results, the boundary contour coordinate information of each pore region is extracted. The boundary contour is composed of the spatial position of edge pixels. After boundary sorting, denoising and smoothing, a closed boundary path is formed. On this basis, the geometric feature data of the pores are extracted by curve fitting and tangent normal calculation, including various descriptive parameters such as contour area, edge curvature, principal axis direction, equivalent circle diameter and pore spacing. Based on these two-dimensional boundary features, the pore contours of each slice are vertically stacked and interpolated along the Z-axis, thereby constructing a voxel mesh or parametric surface in the vertical direction, realizing the reconstruction operation of two-dimensional pore contours into three-dimensional pore volume. In this process, the spatial boundary closure algorithm and volume preservation constraint are used to ensure that the reconstructed three-dimensional pore structure is both geometrically continuous and structurally complete. To ensure the physical credibility of the constructed pore structure, the pore size evolution mechanism from Ostwald ripening theory is introduced. Based on the dynamic equations describing the mass migration of bubbles due to surface energy differences in Ostwald ripening theory, a time evolution model for size correction is constructed. The ripening rate parameter in the model is mapped to parameters such as the expansion time constant and bubble wall thickness of the foamed material, ensuring that the equivalent radius or equivalent volume of each three-dimensional pore conforms to the actual bubble evolution law, forming pore size data under physical constraints. Furthermore, a statistical probability model of bubble coalescence in the foamed material is combined. The coalescence probability of adjacent pores is derived based on pore spacing, contact area, and boundary indentation degree. The connectivity state is determined based on the coalescence probability threshold, and the connectivity of local structures is adjusted to repair isolated pores or merge overlapping areas, forming a pore connectivity network describing the actual pore topology of the foamed material. Since the pores themselves have complex shapes and irregular geometric boundaries, each pore volume in the pore network is parametrically modeled by using spherical harmonic functions. Any irregular three-dimensional shape is projected onto a unit sphere, and its morphological characteristics are represented by multi-order spherical basis function expansion. The optimal order is truncated to compress the description dimension, so as to reduce redundant information while retaining the main geometric features, and establish a three-dimensional reconstruction model that includes structural morphology, topological relationships and physical constraints.

[0069] The coupled simulation module is used to perform mesh generation and coupled simulation on the three-dimensional reconstructed model to obtain mechanical simulation data.

[0070] Specifically, the mesh generation unit receives the 3D reconstructed model and incorporates porous regions with complex boundary morphologies and solid matrix regions into the mesh processing scope. An adaptive mesh generation algorithm is employed to refine the meshing of local regions based on the curvature variations and density distribution of the pore geometric boundaries. High-density tetrahedral or hexahedral elements are used in regions with abrupt boundary changes, pore intersections, or high stress concentrations, while coarse mesh elements are used in uniform regions. This reduces the overall number of elements while maintaining geometric accuracy, generating a finite element mesh model. The computational domain establishment unit identifies representative pore wall regions at the pore-matrix interface of the finite element mesh model and extracts these regions as molecular dynamics computational domains. By constructing atomic arrangement structures, defining boundary particle types and interaction potential functions, molecular dynamics simulations are performed in the molecular dynamics computational domain to obtain surface energy values ​​at the pore interface and local elastic modulus response data at the atomic level, revealing the direct influence mechanism of material structure on mechanical properties at the microscale. The homogenization unit selects representative pore regions from the entire finite element mesh model. Combining this with the obtained pore surface energy and local elastic modulus, these are used as input conditions in the multi-scale homogenization analysis process. Through periodic boundary condition constraints and mean-field theory, the equivalent strain and stress of the typical pore regions under external loading are calculated at the mesoscale. Then, volume integration is used to solve for the equivalent elastic constants and yield strength of the entire sample in each principal direction, achieving a quantitative transfer of mechanical properties from the microscopic to the macroscopic level. The mechanical simulation unit receives the homogenization results and assigns the obtained equivalent elastic constants and yield strengths to the corresponding element properties in the finite element mesh model according to the region assignment rules. Simultaneously, boundary conditions and external loads consistent with the application scenario are applied to the model boundaries, including fixed constraints, compression, tension, or shear conditions. Static or dynamic finite element solutions are then performed on the entire model, yielding output results such as stress distribution diagrams, deformation fields, and load response curves, constituting the mechanical simulation data.

[0071] The parameter solving module is used to optimize the density field and solve the parameters based on the mechanical simulation data to obtain the optimal void design parameters.

[0072] Specifically, the optimization region identification unit analyzes and processes the mechanical simulation data. By quantitatively screening stress concentration areas, deformation abrupt change areas, and areas with low energy dissipation efficiency, it identifies the regions to be optimized in the foamed material sample. Based on this, the optimization region identification unit constructs a multi-objective optimization function with the goals of minimizing the overall structural weight, maximizing local stiffness, and improving energy absorption capacity. Constraint variables related to the foamed material manufacturing process are introduced into this function construction, including upper and lower limits on bubble nucleation density, the process-feasible range of bubble expansion rate, pore connectivity, and minimum pore size conditions. The simulation optimization construction unit uses the regions to be optimized, the multi-objective optimization function, and process constraints as joint inputs to construct a simulation-driven topology optimization model. This model is driven by physical simulation, aims at structural performance, and establishes a mapping relationship between topological distribution and performance indicators. The response gradient calculation unit introduces the density field method into the simulation-driven topology optimization model, expressing the distribution of pores within the optimization region using continuously varying density variables. Specifically, the distribution of density values ​​between 0 and 1 represents different pore filling degrees. Based on the partial derivative relationship between the finite element response function and the objective function, the response gradient of each density variable to the multi-objective optimization function is calculated, serving as the optimization direction criterion. The iterative optimization solution unit performs iterative updates on the density variables based on the response gradient, employing a variable step-size strategy and an adaptive convergence control algorithm. The search amplitude of each iteration is dynamically adjusted according to the descent rate of the objective function. A convergence criterion is set, automatically terminating the iteration when the improvement amplitude of the objective function falls below a preset threshold for several consecutive iterations. The obtained spatial distribution of density variables is then analyzed into explicit pore structure design parameters, including local porosity, pore size distribution, pore connectivity paths, and morphological parameters.

[0073] In one specific embodiment, the scanning imaging module further includes:

[0074] The first scanning unit is used to perform a full-area CT scan on the foamed material sample to obtain pore connectivity data.

[0075] The second scanning unit is used to scan the foamed material sample using a scanning electron microscope to acquire local image data;

[0076] The registration unit is used to register the pore connectivity data with the local image data by establishing a spatial coordinate transformation matrix to obtain dual-modal registered image data, and to perform multi-scale weighted fusion on the dual-modal registered image data to obtain pore image data.

[0077] Specifically, the first scanning unit performs microfocus X-ray computed tomography on the target foamed material sample. By continuously acquiring multi-angle X-ray projection images on a rotating platform and performing volume reconstruction, three-dimensional pore structure image data covering the entire sample area is obtained. The three-dimensional pore structure image data is recorded in voxel form, with micron-level spatial resolution, which can reflect the shape, spatial distribution, and connectivity information of pores. The contrast of pore boundaries and the clarity of pore size recognition are improved through image enhancement algorithms, thereby extracting pore connectivity data of the foamed material sample at the macro scale. At the same time, the exposure voltage, scanning step size, and image reconstruction parameters are adjusted during the scanning process to ensure that the acquired data balances imaging accuracy and scanning speed. The second scanning unit selectively performs scanning electron microscopy (SEM) imaging at representative locations in the sample. Using a field emission scanning electron microscope (FET), the local pore walls are imaged at nanoscale resolution through beam spot scanning combined with a signal acquisition mechanism. This allows for the acquisition of microstructural details, including thin-wall cracks, roughness of the pore inner walls, distribution of microcracks, and pore wall thickness fluctuations, while ensuring the accuracy of sample pretreatment. Since the SEM image is a two-dimensional grayscale image, its physical spatial position is marked during the acquisition process using a coordinate calibration device, and its positioning reference point in the overall coordinate system of the sample is recorded simultaneously. After the first and second scanning units acquire data, the registration unit imports the two types of image data into a unified image processing framework. Initial registration point pairs are established using geometric feature points, boundary contours, or internal reference structures in each image. A three-dimensional spatial coordinate transformation matrix is ​​constructed through affine transformation, rigid transformation, or elastic registration. In the spatial domain, the scanning electron microscope (SEM) image data is nested and mapped to the corresponding region in the CT volume data. The accuracy of the spatial transformation is evaluated in real time using an error correction function, ensuring that the registration error converges to the sub-pixel level and is controlled within 0.5 pixels. A multi-scale weighted fusion operation is performed on the two types of images using an image fusion algorithm. During the fusion process, fusion weights are assigned based on regional scale characteristics, image sharpness, and edge gradient information. Specifically, connectivity information from the CT image is preferentially used in structural backbone areas to preserve their volumetric continuity, while the local proportion of the SEM image is increased in detailed texture areas to enhance image sharpness. Simultaneously, an image gradient smoothing function is designed to reconstruct edges in transition areas. During the fusion process, image noise suppression and boundary sharpening modules are used to compensate for artifacts, interference stripes, or tomographic seams in the images. The dual-modal registered image data is fused and output as porosity image data.

[0078] In one specific embodiment, the registration unit is specifically used for:

[0079] A spatial coordinate transformation matrix is ​​established based on the first spatial position of the pore connectivity data and the second spatial position of the local image data;

[0080] Based on the spatial coordinate transformation matrix, the local image data is transformed to obtain the transformed image data corresponding to the porosity data;

[0081] Pixel registration is performed between the pore connectivity data and the transformed image data to obtain dual-modal registered image data;

[0082] The dual-modal registration image data is weighted and fused based on the pore density data of the foamed material to obtain pore image data.

[0083] Specifically, a first spatial location identifier for pore connectivity data is extracted from the known full-domain CT scan data of the foamed material sample. This first spatial location identifier is composed of three-dimensional coordinate information, orientation angle, sampling density, and reference datum from the CT reconstructed voxel data, and is standardized by combining the internal geometric calibration parameters provided by the scanning equipment. Simultaneously, a corresponding second spatial location identifier is extracted from the local image data acquired by the scanning electron microscope (SEM). This second spatial location identifier includes parameters such as the absolute position of the scanned area in the sample coordinate system, image acquisition tilt angle, objective lens focal length, and resolution. Based on the spatial mapping rules of the sample's physical structure, the two-dimensional SEM image is mapped to the sample's three-dimensional structural coordinate system. A spatial coordinate transformation matrix is ​​established based on the first and second spatial positions. This matrix is ​​a set of data transformation functions that align local image data from its original space to the global CT space. Specifically, it uses homogeneous coordinates and sets translation vectors, rotation matrices, and scale factors through initial matching point pairs. During the fine registration stage, rigid registration or affine registration algorithms are introduced, and an elastic registration model is used for deformed regions. This ensures that the coordinate transformation matrix satisfies global structural alignment and adapts to local detail changes, mathematically constructing a mapping function from local image space to global image space. The local image data is input into the transformation process. Based on the established spatial coordinate transformation matrix, coordinate remapping is performed on the local image data. During this process, the original image pixels are resampled using bilinear interpolation or cubic B-spline interpolation, and an anti-aliasing mechanism is introduced to suppress image distortion caused by scale transformation. The output is a set of new image data with spatial consistency in the CT coordinate system—the transformed image data. Image alignment is performed by analyzing the gray-level gradient distribution, edge contour, and feature point density of the same region in the transformed image and the original CT image. Multi-scale evaluation functions such as mutual information matching, normalized cross-correlation, and structural similarity index are used as optimization objective functions. The local sliding window method is used to fine-tune the pixel-level of minor misalignments, achieving high-precision alignment in terms of structural continuity and pixel consistency, and outputting dual-modal registration image data.The dual-modal registration image data is weighted based on the pore density distribution information of the foamed material. The pore density data is calculated from the pore volume fraction per unit volume in the CT 3D data voxels and mapped to the region corresponding to each pixel in the image as a fusion weight reference factor. In areas with higher density, the contribution of the scanning electron microscope image is prioritized to highlight the detail boundaries, while in areas with lower density or simple structure, the proportion of the CT image is increased to maintain structural connectivity. The dual-modal registration image data is fused using a weighted fusion algorithm. Algorithms such as spatial weighted averaging, image pyramid fusion, or multi-resolution interpolation are used to weight and superimpose the pixel values ​​at corresponding positions. At the same time, image sharpening and edge enhancement mechanisms are introduced in the fusion boundary region to repair the blurred or gradient discontinuous regions generated by fusion, ensuring a natural transition of the dual-modal registration image data in terms of gray level, edge features, and morphological contours, and outputting pore image data.

[0084] In one specific embodiment, the pore boundary identification module further includes:

[0085] A depth feature extraction unit is used to input the pore image data into the encoder in the U-Net network and extract the pore depth feature data of the foamed material sample through the encoder.

[0086] The decoding and recognition unit is used to input the pore depth feature data into the decoder in the U-Net network, and to identify pores of different sizes through the decoding to obtain a pore segmentation feature map;

[0087] A boundary positioning unit is used to fit the curvature change of the pore boundary in the pore segmentation feature map using a boundary positioning algorithm to obtain the first pore boundary data.

[0088] The verification unit is used to verify the physical rationality of the first pore boundary data by combining the principle of minimum surface energy of bubbles, to ensure that the boundary recognition conforms to the bubble evolution law of foamed materials, to obtain the second pore boundary data, and to generate the pore boundary recognition result based on the second pore boundary data.

[0089] Specifically, in the deep feature extraction stage, the encoder part of the U-Net network structure performs layer-by-layer convolution, normalization, and activation processing on the pore image data. Through multi-scale downsampling operations, it continuously extracts multi-dimensional semantic information such as edges, textures, and morphology, obtaining a set of high-dimensional feature vectors representing the pore morphology inside the foamed material sample, i.e., pore depth feature data. The encoder embeds residual connections and channel attention mechanisms to enhance high-level morphology perception capabilities while maintaining low-level boundary features, thereby improving the recognition effect on complex pore structures. The pore depth feature data is then input into the decoder structure of the U-Net network. The decoder recovers the spatial resolution layer by layer through upsampling operations and performs skip connections between the feature maps of each decoding layer and the corresponding encoding layer, fusing low-level edge information and high-level semantic features to output a pore segmentation feature map with spatial semantic consistency and size recognition capabilities. The boundary localization unit performs edge pixel contour extraction for each pore region identified in the pore segmentation feature map. It refines the coarse edges using a sub-pixel-level gradient interpolation method and mathematically models the boundary change trend using a curvature fitting algorithm. The curvature fitting algorithm uses the curvature change rate of the boundary point sequence as the core feature and combines multinomial regression and smoothing factor control to construct a boundary curve function. This extracts the irregular boundary into a continuous, differentiable, and reproducible contour path and outputs it as the first pore boundary data. The first pore boundary data has high curvature resolution and high edge continuity, describing the edge inhomogeneity and shrinkage distortion characteristics caused by wall tension disturbance during the pore expansion process. The verification unit uses the principle of minimum surface energy of bubbles to judge the mechanical rationality of the boundary morphology. This principle is based on the energy minimization trend during the nucleation and expansion of foamed materials, assuming that pore boundaries tend to form smooth, closed contours under tension equilibrium in all directions. The verification unit constructs an evaluation model with surface energy density as the objective function, performs regional integral analysis on the first pore boundary data, and uses local energy shift indicators to determine whether there are abnormal abrupt changes in the boundary that do not conform to the evolutionary law, such as sharp corners, depressions, or non-physically closed shapes. If such problems exist, an automatic correction process is triggered, using a physically stable convergence strategy to smooth the boundary through convergence deformation, obtaining the second pore boundary data after physical constraint verification. Using the second pore boundary data as a basis, combined with the original image spatial location and the recognition label map, the pore boundary recognition result is generated.

[0090] In one specific embodiment, the boundary positioning unit is specifically used for:

[0091] Identify the boundary pixels between the foam material pores and the matrix material from the pore segmentation feature map, and calculate the gradient direction and gradient magnitude of each boundary pixel to determine the pore boundary gradient information;

[0092] Based on the pore boundary gradient information, the least squares method is used to fit the curvature change of the pore boundary and calculate the radius of curvature and center of curvature of the boundary curve at each point to obtain the curvature fitting parameters.

[0093] The curvature fitting parameters are input into the boundary positioning algorithm to calculate the boundary coordinates, and the boundary coordinate data is then verified to obtain the first pore boundary data.

[0094] Specifically, the boundary transition zone between the pore region and the matrix material in the target foamed material is extracted from the pore segmentation feature map. The pore segmentation feature map originates from the U-Net decoding and recognition stage, where each pixel has been labeled as either a pore region or a non-pore region. The boundary pixels whose labeling categories change are detected by the local binary difference algorithm, obtaining a set of all pixels located at the boundary between the pores and the matrix. Local gray-level gradient analysis is performed on the boundary pixels. A local 3×3 or 5×5 window is established around each boundary pixel using the Sobel operator, Prewitt operator, or Canny edge detection kernel function. The change of the first derivative of the pixel gray value within the window in the horizontal and vertical directions is calculated, and the gradient direction of each pixel is obtained by combining it with the arctangent function. At the same time, the gradient magnitude function is used to calculate the gradient magnitude of the pixel, forming a set of pore boundary gradient information data, which describes the direction and intensity variation characteristics of the boundary contour at each pixel. The pore boundary gradient information is input into the least squares fitting module. Data samples are organized according to the boundary point sequence, with each group of several consecutive boundary pixels forming a fitting interval. A polynomial boundary curve fitting operation is performed, fitting a quadratic or cubic curve function to the boundary point coordinates. By minimizing the squared error between the actual boundary point coordinates and the predicted coordinates of the fitted curve function, the coefficient matrix of the fitted function is solved and its derivative is taken to obtain the tangent direction and curvature function. Furthermore, the radius of curvature is calculated at each point, which is the reciprocal of the rate of change of the derivative of the boundary curvature function at that point. Simultaneously, the coordinates of the curvature center are calculated based on the curvature function, thus obtaining curvature fitting parameters that include curvature direction, curvature intensity, and the trend of boundary movement. The curvature fitting parameters are processed by a boundary localization algorithm. This algorithm uses the fitted curvature center and radius of curvature as basic information to reconstruct a continuous boundary trajectory. The boundary coordinates are transformed into boundary path coordinate data in polar coordinates or a three-dimensional spatial coordinate system through parameterization. The boundary path coordinate data is represented as a continuous sequence of boundary points. The boundary continuity is verified using the boundary coordinate data. Three indicators—the rate of change of tangent direction, the angle between normals, and the consistency of the neighborhood direction—are extracted from the boundary coordinate sequence to determine whether there are abrupt changes, breaks, or irregular jumps between any two adjacent boundary points. A sliding window convolution is used to check the stability of the linear or curvilinear extension trend of the boundary trajectory. If discontinuities, drastic fluctuations, or directional contradictions are found in the local boundary, the boundary correction module is triggered to perform boundary smoothing reconstruction. Cubic spline interpolation or Gaussian filtering is used to adjust the curvature of abnormal boundary segments until the continuity evaluation indicators of the boundary meet the preset threshold requirements. After completing the continuity verification of the boundary coordinate data, the boundary coordinate data is output as the first pore boundary data.

[0095] In one specific embodiment, the three-dimensional reconstruction module further includes:

[0096] Extract the boundary contour coordinates of each pore from the pore boundary identification results, and calculate geometric feature data based on the boundary contour coordinates;

[0097] Based on the geometric feature data along the Z-axis, the two-dimensional pore boundary is reconstructed into a three-dimensional pore volume, generating a three-dimensional pore structure;

[0098] The pore size in the three-dimensional pore structure is physically constrained and corrected by applying the pore size evolution law in Ostwald ripening theory to obtain physically constrained pore size data.

[0099] By adjusting the connectivity of adjacent pores in the pore size data after physical constraints based on the probability characteristics of bubble coalescence in foamed materials, a pore connectivity network is formed.

[0100] The complex shape of irregular pores in the pore network is parametrically characterized using spherical harmonic functions, and a three-dimensional reconstruction model is established.

[0101] Specifically, in the pore boundary recognition results, the closed contour of the boundary corresponding to each pore is identified. A contour index structure is established based on connectivity rules in the image space using a boundary extraction algorithm. By sequentially traversing the boundary pixel coordinate sequence, the geometric distribution position of each pore contour on the two-dimensional plane is recorded. Geometric feature calculations are performed on the boundary contour coordinates, and morphological feature analysis methods are used to extract data sets for each pore, including perimeter, area, principal axis direction, mean boundary curvature, maximum and minimum boundary curvature radii, shape compactness, equivalent diameter, and ellipse fitting parameters, thus establishing a structural attribute description for each two-dimensional pore. Based on geometric feature data, the pore volume reconstruction operation along the Z-axis is performed by vertically registering and matching two-dimensional boundary contours on multiple different Z-axis layers. An interpolation algorithm is used to establish three-dimensional connection channels between the layer contours. Methods include contour stretching, central axis tracking, or cross-section stacking reconstruction. The evolution trend of pores along the Z-axis is inferred based on the contour area change law. A closed curved surface mesh structure is constructed by combining the spatial interpolation of boundary coordinate points. In this way, the two-dimensional boundary information is reconstructed into a three-dimensional pore structure model with volume attributes, closed shape, and connected boundaries. Based on a three-dimensional structural model, Ostwald ripening theory is introduced to establish a physical constraint mechanism. Ostwald ripening theory is based on the mass transfer mechanism of bubble size evolution over time, pointing out that small pores tend to transfer gas mass to large pores due to higher internal pressure, resulting in an evolutionary process where small pores become smaller and large pores become larger. Therefore, based on the pore size evolution differential model, a size evolution equation is constructed. The size data in the current three-dimensional pore structure are substituted into the size evolution equation, and the physical reasonable size parameters corresponding to each pore are solved through numerical integration or optimization iteration. This allows for physical constraint correction of the original geometric reconstruction results, eliminating excessively large or small size distortions that do not conform to the evolution law, and generating a set of physically constrained pore size data that conforms to the ripening equilibrium state. Based on the bubble aggregation behavior of foamed materials, a connectivity adjustment mechanism is introduced. A statistical model based on the probability of bubbles approaching each other is established. The statistical model comprehensively considers factors such as the center distance between pores, boundary overlap, volume ratio, and connectivity direction angle to construct a pore aggregation probability function. A probability threshold is set as a connectivity criterion. If the aggregation probability of a pair of pores exceeds the probability threshold, a topological connectivity update operation is performed. Virtual channels or topological boundary transition surfaces are inserted into the spatial structure to realize the structural connectivity of physically disconnected pores. A multi-node connectivity graph structure containing the connection relationships between pores is established to form a pore connectivity network that truly reflects the connectivity of material bubbles.Based on the pore connectivity network, spherical harmonic functions are called to perform morphological parameterization operations. Spherical harmonic functions can map any closed three-dimensional surface to a unit sphere. The morphological features of the pore surface are expressed through a set of rational basis functions. Spherical harmonic decomposition is performed on each irregular pore unit, and its complex shape is represented as a combination of multiple low-order spherical harmonic coefficients. The shape information of the main frequency is preserved while high-frequency disturbances are filtered out, thereby realizing the compressed description and controllable expression of the three-dimensional morphology. All parameterization results are combined into a unified data structure and output as a three-dimensional reconstruction model.

[0102] In one specific embodiment, the coupled simulation module further includes:

[0103] Mesh generation unit is used to perform mesh generation on the pore geometric boundaries and matrix region in the three-dimensional reconstruction model to generate a finite element mesh model;

[0104] The computational domain establishment unit is used to establish a molecular dynamics computational domain in the pore surface region of the finite element mesh model, and to calculate the surface energy and local elastic modulus of the pore-matrix interface based on the molecular dynamics computational domain.

[0105] The homogenization calculation unit is used to select typical pore regions in the finite element mesh model and use the surface energy and the local elastic modulus as input conditions to perform homogenization calculations, and solve for the equivalent elastic constants and yield strength of the foamed material sample.

[0106] The mechanical simulation unit is used to assign the equivalent elastic constant and the yield strength to the corresponding mesh elements of the finite element mesh model, apply boundary conditions and loads, and output mechanical simulation data.

[0107] Specifically, based on the 3D reconstructed model, the mesh generation unit identifies the complex pore geometric boundaries and continuous matrix solid regions. An adaptive mesh generation algorithm is used to automatically adjust the mesh density according to the degree of local morphological changes. In regions with abrupt boundary changes, large curvature changes, or small pore spacing, high-density tetrahedral or hexahedral elements are preferentially used to construct a fine mesh structure. In regions with smooth morphology and uniform structure, coarse-grained meshing is used to control the overall number of elements, forming a finite element mesh model. During the generation process, a mesh quality control function is introduced to constrain indicators such as mesh shape, element twist rate, volume ratio, and boundary fitting error, ensuring that the mesh generation result has the high-quality topological structure required for physical simulation. The computational domain establishment unit identifies key interface regions at the pore-matrix contact interface of the finite element mesh model. It extracts the set of pore surface nodes through geometric screening and surface search algorithms, and establishes an atomic-scale molecular dynamics computational domain around it. The molecular dynamics computational domain uses periodic boundary conditions and potential energy functions to describe interatomic interactions, including Lennard-Jones potential, Tersoff potential, or EAM potential, to simulate the arrangement changes of material atoms under external perturbations at the microscale. By gradually loading displacement perturbations or temperature perturbations, it tracks the energy change process of the interface structure at the atomic level in real time, calculates the interface surface energy value per unit area, and the stress-strain response curves of the pore wall in different loading directions, thereby obtaining local elastic modulus data. The homogenization computational unit selects representative typical pore regions from the entire finite element mesh model. These regions have periodic topological structures, typical pore morphologies, and representative loading paths, which can reflect the stress distribution characteristics of the material at the microscale. The obtained local elastic modulus and interface surface energy are used as input variables. The multi-scale homogenization theoretical framework is introduced, and a microscopic analysis model is constructed through representative volume elements (RVEs). The local response field is solved under given boundary conditions. The equivalent stress and equivalent strain relationship corresponding to the representative volume elements are calculated by the volume integral averaging method. The equivalent elastic constant matrix of the foamed material as a whole is further derived, and the yield strength parameter is solved by the yield stress distribution function under the ultimate loading path. The mechanical simulation unit couples the aforementioned homogenization parameters with the mesh model, maps the equivalent elastic constants and yield strength to the corresponding mesh elements in the finite element mesh model, and uses the domain assignment method or continuous field interpolation method to embed local mechanical properties into the model attribute table element by element. It sets boundary conditions and external loads according to the preset simulation scheme, including typical working conditions such as uniaxial compression, biaxial tension, shear loading, and torsional disturbance. It performs global response analysis through explicit or implicit finite element solvers and outputs key mechanical simulation data such as nodal displacement field, stress-strain distribution diagram, equivalent stiffness response curve, and load-displacement curve in real time.

[0108] In one specific embodiment, the homogenization calculation unit is specifically used for:

[0109] Typical pore regions with representative pore density, pore size range, and connectivity are selected from the finite element mesh model, and corresponding target volume elements are extracted from the finite element mesh model based on the typical pore regions.

[0110] The surface energy and local elastic modulus data are assigned to the corresponding pore interface and matrix material region in the target volume element to establish a mechanical calculation model.

[0111] Periodic boundary conditions are applied to the mechanical calculation model and multi-directional tensile and shear loading is performed. The equivalent elastic modulus matrix and Poisson's ratio of the foamed material are solved by homogenization theory.

[0112] Based on the equivalent elastic modulus matrix and the Poisson's ratio, nonlinear loading analysis is performed until the material yields, thereby determining the equivalent elastic constant and yield strength of the foamed material sample.

[0113] Specifically, in the finite element mesh model, pore density, pore size range, and connectivity parameters are classified in multiple dimensions based on the statistical characteristics of pore distribution. Typical pore regions that meet statistical representativeness requirements are extracted through global scanning and structural clustering, ensuring that the selected regions effectively reflect the structural homogeneity, morphological complexity, and evolutionary regularity of the foamed material at the microscopic level. Within the finite element model corresponding to the typical pore regions, a set of spatially topologically continuous target volumetric elements is extracted. During the volumetric element extraction process, a minimum envelope box algorithm and a voxel skeleton constraint mechanism are introduced to ensure that the target region has a closed, connected, and non-simplified complete structural representation. Mechanical properties are assigned to different material regions within the target volumetric elements based on microscopic surface energy values ​​and local elastic modulus data. The spatial position of the element's central node is used to determine its affiliation. Nodes and elements near the pore boundaries are assigned interface attribute data, including anisotropic surface tension coefficients and shear modulus reduction factors, while nodes and elements located in the main matrix region are assigned bulk elastic modulus and Poisson's ratio data, forming a multiphase composite material calculation model with spatially partitioned material property differences. Periodic boundary conditions are applied to the mechanical calculation model. These conditions establish nodal coupling between the six faces of the model to ensure that rigid motion or unreasonable stress concentration does not occur at the model boundaries under external loading, and to ensure the continuity and integrability of the microscopic response at the macroscopic scale. Unit tensile or shear loading is applied in the three principal directions (X, Y, Z) and the three shear directions (XY, YZ, ZX). The strain tensor response and stress tensor distribution of the model under each loading condition are recorded using a finite element solver. Based on the equivalent constitutive relation defined by homogenization theory, the stress and strain data are averaged to construct the equivalent elastic modulus matrix derived from the microstructure of the foamed material. The equivalent elastic modulus matrix is ​​a sixth-order symmetric tensor containing the elastic modulus of the three principal directions, three Poisson's ratios, and three shear moduli. The equivalent elastic modulus matrix describes the response stiffness of the material under force in each direction, and the Poisson's ratio values ​​in the principal axis directions are extracted to evaluate the lateral deformation characteristics of the material.To obtain the yield behavior of foamed materials, a nonlinear loading model is constructed based on the equivalent elastic modulus matrix and Poisson's ratio. The amplitude of external tensile or shear load is continuously increased through incremental loading. Steady-state finite element calculations are performed after each loading step. In each iteration, the maximum equivalent stress value and equivalent plastic strain distribution within the model are extracted. The model is monitored to see if yield criteria are met, such as the von Mises yield criterion, the Drucker-Prager criterion, or the Hill anisotropy criterion. When the number of nodes or elements that meet the yield criteria for the first time exceeds a certain percentage threshold (e.g., 5%) of the entire model, the material is determined to have entered the yield state. At this critical loading point, the principal value of the corresponding stress tensor is extracted as the yield strength output of the foamed material. At the same time, the equivalent stress tensor at this point and the equivalent elastic modulus matrix output in the previous elastic stage are recorded together as the final result, forming a multi-scale physical response dataset.

[0114] In one specific embodiment, the parameter solving module further includes:

[0115] An optimization region identification unit is used to identify the region to be optimized in the foamed material sample based on the mechanical simulation data. At the same time, a multi-objective optimization function is established with the goal of minimizing structural weight while maximizing stiffness and energy absorption, and process constraints such as bubble nucleation density and expansion rate are introduced.

[0116] The simulation optimization construction unit is used to construct a simulation-driven topology optimization model based on the region to be optimized, the multi-objective optimization function, and the process constraints.

[0117] The response gradient calculation unit is used to represent the pore distribution of the region to be optimized in the simulation-driven topology optimization model as a continuously changing density variable using the density field method, and to simultaneously calculate the response gradient of the multi-objective optimization function to the density changes in each region.

[0118] The iterative optimization solution unit is used to iteratively optimize the density variable based on the response gradient to obtain the optimal density field distribution, and to resolve the optimal density field distribution as the optimal void design parameters of the region to be optimized.

[0119] Specifically, response parameters of foamed material samples under various loading conditions are extracted from mechanical simulation data. By analyzing stress concentration regions, plastic deformation boundaries, compressive stiffness gradients, and energy dissipation density distributions, a multi-scale structural performance distribution map is constructed. Based on this, spatial regions with significant structural responses, prominent local performance bottlenecks, or low material utilization efficiency are selected as optimization regions using statistical distribution functions and sensitivity threshold screening methods. The optimization region identification unit establishes a joint performance-driven multi-objective optimization function within the optimization region. This function aims to minimize structural weight as the material utilization rate objective, maximize macroscopic equivalent stiffness as the load-bearing capacity objective, and maximize energy absorption efficiency per unit volume as the energy absorption function objective. These objectives are integrated into a unified optimization function expression through a multi-objective normalization function. During the optimization function construction process, the optimization region identification unit introduces a constraint model of key process parameters in the manufacturing process of the foamed material. Specifically, the bubble nucleation density is set as the boundary condition between the minimum pore size and the maximum number of voids. The bubble expansion rate is mapped to the void connectivity trend, the rate of change of pore wall thickness, and the minimum safe distance constraint between adjacent pores, ensuring that the final topology optimization scheme does not produce microstructure configurations that exceed process limits or manufacturing error tolerance. The simulation optimization building unit constructs a simulation-driven topology optimization model based on the region to be optimized, the multi-objective optimization function, and the process constraints. This model uses finite element method (FEM) as its core feedback mechanism, iteratively analyzing the structural response parameters under each density field distribution. The optimization function and constraints are embedded into the objective function expression using Lagrange multipliers or penalty functions, achieving coupled modeling of process parameters and mechanical properties during the optimization process. The response gradient calculation unit describes the pore distribution as a continuous variable based on the density field method. It transforms the material filling state of each finite element in the region to be optimized in the simulation-driven topology optimization model into a density variable varying between 0 and 1. The continuous density values ​​are converted into equivalent stiffness parameters using a density-stiffness mapping function (such as the SIMP function). Then, based on the topology optimization theoretical framework, the first-order partial derivative of the objective function with respect to the density variable is calculated for each density variable. This first-order partial derivative is recorded as the response gradient in the response gradient tensor field. Boundary condition sensitivity, node coordination adjustment terms, and manufacturing feasibility penalty terms are introduced to form a complete gradient expression model integrating mechanical response, process constraints, and structural continuity control.The iterative optimization solution unit updates all density variables step by step based on the response gradient. It adopts an optimization path control algorithm based on gradient descent, combined with mainstream optimizers such as steepest descent, quasi-Newton method, or moving asymptote method. In each iteration, it evaluates the magnitude of the objective function descent, the degree of constraint violation, and the intensity of local structural disturbance. It automatically adjusts the step size according to the convergence criterion, dynamically selects active variable regions, and performs density field projection operations in a timely manner. Gradient weighted suppression is implemented for regions with blurred boundaries to avoid excessive topological jitter. When the magnitude of the objective function descent falls below a set threshold for several consecutive iterations, or when the constraint error converges to a preset tolerance range, the optimization process is terminated. The final density variable distribution is analyzed into quantifiable structural topological features, including porosity gradient distribution, void shape factor, local connectivity path graph, and structural stiffness partitioning graph. The density field is then binarized by combining the original geometric information of the optimization region, and high-density regions are extracted as retained materials and low-density regions are extracted as design void regions, thus forming the optimal void design parameters.

[0120] In one specific embodiment, the iterative optimization solution unit is specifically used for:

[0121] The response gradient is used to guide the update direction of the density variable, and an adaptive step size adjustment strategy is adopted to dynamically control the optimization step size according to the convergence trend of the multi-objective optimization function, and to perform iterative update of the density variable.

[0122] Monitor the magnitude of the change in the response solution of the multi-objective optimization function during the iterative update process, and determine the optimal density field distribution based on the magnitude of the change in the response solution;

[0123] The optimal density field distribution is converted into discrete pore existence regions and matrix regions to form an optimized pore space layout.

[0124] The volume and geometric center coordinates of each pore in the optimized pore space layout are statistically analyzed. The ratio of pore volume to total volume and the distribution range of pore size in the region to be optimized are calculated, and the optimal pore design parameters are output.

[0125] Specifically, the response gradient tensor field consists of the first-order partial derivatives of the multi-objective optimization function with respect to each density variable, representing the direction and intensity of each region's contribution to the objective function under the current structural distribution. The density variable is a continuous variable in the topology optimization model used to represent the material filling state, with a value range between 0 and 1. Values ​​close to 1 indicate solid material regions, and values ​​close to 0 indicate void regions. Therefore, the response gradient is used to guide the update direction of the density variable, and the negative gradient direction drives the spatial redistribution of the material. An adaptive step size adjustment strategy is introduced during the update process. The step size is dynamically determined based on the convergence trend of the multi-objective optimization function in each optimization iteration. If the objective function's descent rate is stable and continuous, the step size is increased to improve convergence efficiency. If the objective function oscillates violently or the convergence speed slows down sharply, the step size is decreased to prevent the optimization path from deviating or getting trapped in a local optimum. The adaptive step size adjustment strategy obtains the current optimal movement range by constructing the slope function of the iteration history curve, second-order response residual analysis, and momentum weighted average calculation. During the iterative update of density variables, the change in the response solution of the multi-objective optimization function is continuously monitored. The response solution includes the output results of the objective function, such as the total structural weight, local and global stiffness, and energy absorption integral value. After each round of density field update, the relative change ratio between the current objective function value and the previous round's objective function value is calculated to determine whether the response solution is continuously improving and stabilizing. If the change in the response solution is less than a set threshold for several consecutive rounds, for example, within 0.1%, the current density variable configuration is considered to be close to convergence, and the current density variable distribution is marked as the optimal density field distribution. The optimal density field distribution is discretized. By setting a density threshold (e.g., 0.5), regions with density values ​​higher than the density threshold are classified as matrix material regions, and regions with density values ​​lower than the density threshold are classified as porosity regions, forming an optimized porosity space layout composed of porosity regions and matrix regions. The geometric statistical analysis module quantitatively describes the pore structure in the pore spatial layout. Volume integration is performed on each discrete pore region to calculate its three-dimensional volume, and all pore volume data are extracted to form a statistical sample set. The geometric center coordinates of each pore are then calculated using a spatial centroid function, thereby establishing a spatial distribution map and size distribution matrix of the pores within the optimization region. Simultaneously, the summation of all pore volumes is compared with the total volume of the optimization region to obtain the overall porosity index. The overall porosity index reflects the optimal level of material removal efficiency while maintaining stiffness and energy absorption capacity. Range, standard deviation, and distribution density analyses are performed on the volume of all pores, outputting the minimum, maximum, average, and distribution range of pore sizes, forming a set of pore structure features describing the optimal topological configuration, which constitutes the optimal pore design parameters.

[0126] The scanning imaging module in this invention integrates micro-CT full-domain scanning and scanning electron microscopy local scanning to achieve complete coverage from nanometer to millimeter scales, solving the technical problem of the mutual constraint between imaging resolution and scanning range in traditional methods. The pore boundary recognition module adopts an improved U-Net network structure, combined with residual connections and attention mechanisms, specifically optimized for the blurred features of the pore-matrix interface in foamed materials, achieving sub-pixel-level accurate segmentation and effectively solving the technical limitations of traditional image processing methods in dealing with the blurred boundary problem of foamed materials. The 3D reconstruction module introduces Ostwald ripening theory and bubble coalescence probability model, integrating the physical evolution mechanism of the foaming process into the reconstruction algorithm to ensure that the reconstruction results conform to the real physical laws of foamed materials, overcoming the deficiency of traditional geometric reconstruction methods that lack physical basis. The coupled simulation module establishes a three-level simulation system of molecular dynamics-representative volume unit-macrostructure, realizing cross-scale information transfer through scale bridging functions, accurately reflecting the mechanical response characteristics of foamed materials from micro to macro, and solving the problem that single-scale simulation cannot accurately predict the overall performance of materials. The parameter solving module directly incorporates foaming process parameters (bubble nucleation density and expansion rate) into the optimization constraints. This invention realizes fully automated processing from raw imaging data to optimal design parameters, eliminating a large number of manual intervention steps in traditional methods, significantly shortening the design cycle of foamed material structures, and improving design accuracy and consistency.

[0127] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing system embodiments, and will not be repeated here.

[0128] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the system described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0129] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A three-dimensional reconstruction and simulation system for porous structures of foamed materials, characterized in that, include: The scanning imaging module is used to scan and image foam material samples to obtain pore image data; A pore boundary recognition module is used to recognize pore boundaries based on the pore image data and obtain pore boundary recognition results. The three-dimensional reconstruction module is used to perform three-dimensional reconstruction of the physical constraints of bubble evolution based on the pore boundary identification results, and obtain a three-dimensional reconstruction model; The coupled simulation module is used to perform mesh generation and coupled simulation on the three-dimensional reconstructed model to obtain mechanical simulation data. The parameter solving module is used to optimize the density field and solve the parameters based on the mechanical simulation data to obtain the optimal void design parameters.

2. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 1, characterized in that, The scanning imaging module also includes: The first scanning unit is used to perform a full-area CT scan on the foamed material sample to obtain pore connectivity data. The second scanning unit is used to scan the foamed material sample using a scanning electron microscope to acquire local image data; The registration unit is used to register the pore connectivity data with the local image data by establishing a spatial coordinate transformation matrix to obtain dual-modal registered image data, and to perform multi-scale weighted fusion on the dual-modal registered image data to obtain pore image data.

3. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 2, characterized in that, The registration unit is specifically used for: A spatial coordinate transformation matrix is ​​established based on the first spatial position of the pore connectivity data and the second spatial position of the local image data; Based on the spatial coordinate transformation matrix, the local image data is transformed to obtain the transformed image data corresponding to the porosity data; Pixel registration is performed between the pore connectivity data and the transformed image data to obtain dual-modal registered image data; The dual-modal registration image data is weighted and fused based on the pore density data of the foamed material to obtain pore image data.

4. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 1, characterized in that, The pore boundary identification module further includes: A depth feature extraction unit is used to input the pore image data into the encoder in the U-Net network and extract the pore depth feature data of the foamed material sample through the encoder. The decoding and recognition unit is used to input the pore depth feature data into the decoder in the U-Net network, and to identify pores of different sizes through the decoding to obtain a pore segmentation feature map; A boundary positioning unit is used to fit the curvature change of the pore boundary in the pore segmentation feature map using a boundary positioning algorithm to obtain the first pore boundary data. The verification unit is used to verify the physical rationality of the first pore boundary data by combining the principle of minimum surface energy of bubbles, to ensure that the boundary recognition conforms to the bubble evolution law of foamed materials, to obtain the second pore boundary data, and to generate the pore boundary recognition result based on the second pore boundary data.

5. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 4, characterized in that, The boundary positioning unit is specifically used for: Identify the boundary pixels between the foam material pores and the matrix material from the pore segmentation feature map, and calculate the gradient direction and gradient magnitude of each boundary pixel to determine the pore boundary gradient information; Based on the pore boundary gradient information, the least squares method is used to fit the curvature change of the pore boundary and calculate the radius of curvature and center of curvature of the boundary curve at each point to obtain the curvature fitting parameters. The curvature fitting parameters are input into the boundary positioning algorithm to calculate the boundary coordinates, and the boundary coordinate data is then verified to obtain the first pore boundary data.

6. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 1, characterized in that, The three-dimensional reconstruction module also includes: Extract the boundary contour coordinates of each pore from the pore boundary identification results, and calculate geometric feature data based on the boundary contour coordinates; Based on the geometric feature data along the Z-axis, the two-dimensional pore boundary is reconstructed into a three-dimensional pore volume, generating a three-dimensional pore structure; The pore size in the three-dimensional pore structure is physically constrained and corrected by applying the pore size evolution law in Ostwald ripening theory to obtain physically constrained pore size data. By adjusting the connectivity of adjacent pores in the pore size data after physical constraints based on the probability characteristics of bubble coalescence in foamed materials, a pore connectivity network is formed. The complex shape of irregular pores in the pore network is parametrically characterized using spherical harmonic functions, and a three-dimensional reconstruction model is established.

7. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 6, characterized in that, The coupled simulation module also includes: Mesh generation unit, used to perform mesh generation on the pore geometric boundaries and matrix region in the three-dimensional reconstruction model to generate a finite element mesh model; The computational domain establishment unit is used to establish a molecular dynamics computational domain in the pore surface region of the finite element mesh model, and to calculate the surface energy and local elastic modulus of the pore-matrix interface based on the molecular dynamics computational domain. The homogenization calculation unit is used to select typical pore regions in the finite element mesh model and use the surface energy and the local elastic modulus as input conditions to perform homogenization calculations, and solve for the equivalent elastic constants and yield strength of the foamed material sample. The mechanical simulation unit is used to assign the equivalent elastic constant and the yield strength to the corresponding mesh elements of the finite element mesh model, apply boundary conditions and loads, and output mechanical simulation data.

8. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 7, characterized in that, The homogenization calculation unit is specifically used for: Typical pore regions with representative pore density, pore size range, and connectivity are selected from the finite element mesh model, and corresponding target volume elements are extracted from the finite element mesh model based on the typical pore regions. The surface energy and local elastic modulus data are assigned to the corresponding pore interface and matrix material region in the target volume element to establish a mechanical calculation model. Periodic boundary conditions are applied to the mechanical calculation model and multi-directional tensile and shear loading is performed. The equivalent elastic modulus matrix and Poisson's ratio of the foamed material are solved by homogenization theory. Based on the equivalent elastic modulus matrix and the Poisson's ratio, nonlinear loading analysis is performed until the material yields, thereby determining the equivalent elastic constant and yield strength of the foamed material sample.

9. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 8, characterized in that, The parameter solving module also includes: An optimization region identification unit is used to identify the region to be optimized in the foamed material sample based on the mechanical simulation data. At the same time, a multi-objective optimization function is established with the goal of minimizing structural weight while maximizing stiffness and energy absorption, and process constraints such as bubble nucleation density and expansion rate are introduced. The simulation optimization construction unit is used to construct a simulation-driven topology optimization model based on the region to be optimized, the multi-objective optimization function, and the process constraints. The response gradient calculation unit is used to represent the pore distribution of the region to be optimized in the simulation-driven topology optimization model as a continuously changing density variable using the density field method, and to simultaneously calculate the response gradient of the multi-objective optimization function to the density changes in each region. The iterative optimization solution unit is used to iteratively optimize the density variable according to the response gradient to obtain the optimal density field distribution, and to resolve the optimal density field distribution as the optimal void design parameters of the region to be optimized.

10. The three-dimensional reconstruction and simulation system for porous structures of foamed materials according to claim 9, characterized in that, The iterative optimization solution unit is specifically used for: The response gradient is used to guide the update direction of the density variable, and an adaptive step size adjustment strategy is adopted to dynamically control the optimization step size according to the convergence trend of the multi-objective optimization function, and to perform iterative update of the density variable. Monitor the magnitude of the change in the response solution of the multi-objective optimization function during the iterative update process, and determine the optimal density field distribution based on the magnitude of the change in the response solution; The optimal density field distribution is converted into discrete pore existence regions and matrix regions to form an optimized pore space layout. The volume and geometric center coordinates of each pore in the optimized pore space layout are statistically analyzed. The ratio of pore volume to total volume and the distribution range of pore size in the region to be optimized are calculated, and the optimal pore design parameters are output.

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