Method and apparatus for generative reverse design of mechanical metamaterials

Abstract

This application relates to the field of computer-aided design technology, providing a generative reverse design method and apparatus for mechanical metamaterials. The method includes: generating a basic microstructure dataset based on a k-uniform tiling algorithm and a Voronoi diagram generation algorithm; expanding the microstructure dataset through seed translation, local weight variance increase, and global weight variance modification; performing full-field finite element simulation on microstructure samples in the microstructure dataset to obtain a physical field video dataset; constructing a video diffusion model, training the video diffusion model using the physical field video dataset as training data, and using the trained video diffusion model as a microstructure generator; and having the microstructure generator design and evaluate structures based on input target performance indicators, outputting the optimal microstructure. This invention, under the constraints of physical field video data, can accurately learn the correspondence between nonlinear mechanical responses and complex geometric configurations, achieving a unity of physical consistency and structural innovation.

Description

Technical Field

[0001] This application relates to the field of computer-aided design technology, and in particular to a method and apparatus for generative reverse design of mechanical metamaterials. Background Technology

[0002] Vibration and deformation response are ubiquitous in engineering structures and materials during service. While their characteristic behaviors can be utilized in certain specific scenarios, they often lead to structural fatigue, performance degradation, and stability issues in most applications. In recent years, metamaterials, as a class of composite systems with artificially periodic microstructures, have demonstrated broad application potential in vibration suppression, energy absorption, and structural weight reduction due to their programmable mechanical properties.

[0003] Currently, metamaterial design methods mainly fall into two categories: forward design and inverse design. Forward design generally relies on theoretical analysis, biomimetic principles, finite element simulation, and empirical optimization, achieving performance control through parameter scanning or heuristic adjustments. However, such methods are inefficient when the design space is large or the target is complex, and they struggle to adapt to nonlinear mechanical behavior. Inverse design methods, on the other hand, set a target response and directly search for structural solutions that meet performance requirements using optimization algorithms or topology optimization strategies. Traditional gradient-based or gradient-free topology optimization methods, procedural methods, and parametric methods have achieved a degree of automated design, but they still face problems such as low optimization efficiency and convergence difficulties in high-dimensional, multi-constraint, and nonlinear problems.

[0004] However, existing generative design methods are typically based on discrete structures with structured meshes, which limits their applicability when faced with irregular geometric boundaries and complex topological constraints. Furthermore, constrained by model simplification assumptions, existing generative design methods often focus on symmetrical or regular microstructures and typically rely on image features for generation, lacking constraint mechanisms based on physical laws and the ability to describe dynamic physical fields. Therefore, they are mainly suitable for design tasks under linear or small deformation conditions, and struggle to meet the structural optimization requirements under nonlinear mechanical responses. Summary of the Invention

[0005] Therefore, it is necessary to provide a method and apparatus for the generative reverse design of mechanical metamaterials to address the above-mentioned technical problems.

[0006] A generative reverse design method for mechanical metamaterials includes the following steps:

[0007] A basic microstructure dataset is generated based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. The basic microstructure dataset is then expanded by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking.

[0008] Full-field finite element simulation was performed on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. Hybrid meshes were used in the simulation process.

[0009] A video diffusion model based on the U-Net video architecture is constructed. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as a microstructure generator.

[0010] The microstructure generator designs and evaluates the structure based on the input target performance indicators and outputs the optimal microstructure that meets the target performance indicators.

[0011] In one embodiment, a basic microstructure dataset is generated based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. This basic microstructure dataset is then expanded through seed translation, local weight variance increase, and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations, including:

[0012] In two-dimensional Euclidean space, 1-uniform tiling, 2-uniform tiling and Voronoi structures are generated using the k-uniform tiling algorithm and the Voronoi graph generation algorithm. Using dual tiling, seeds are placed at the vertices of polygons, and tessellation of the same planar domain is performed with single-valued weights to obtain unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual tessellations, which constitute the basic microstructure dataset.

[0013] The basic microstructure dataset is expanded by processing the seed translation, increasing the local weight variance, and modifying the global weight variance to obtain the microstructure dataset.

[0014] In one embodiment, a full-field finite element simulation is performed on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields, including:

[0015] Convert the microstructure samples in the microstructure dataset into three-dimensional geometric model inputs that can be recognized by finite element analysis software;

[0016] The finite element analysis software is used to perform simulation, generate microstructures, and simulate to obtain a physical field video dataset. The physical field video dataset contains physical field information under longitudinal load conditions and corresponding nonlinear mechanical response curves.

[0017] In one embodiment, a full-field finite element simulation is performed on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields, which also includes:

[0018] Pixel-scale compression is performed on the microstructure samples in the microstructure dataset to make the pixel scale 128×128;

[0019] The pixel-compressed microstructure samples are binarized, and microstructure samples that do not meet the entity connectivity constraints are filtered out using a connectivity detection algorithm.

[0020] In one embodiment, a video diffusion model based on the U-Net video architecture is constructed. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as a microstructure generator, including:

[0021] A video diffusion model based on the U-Net video architecture is constructed, and the video diffusion model is trained using the physical field video dataset as training data. During the training process, the nonlinear mechanical response curve is used as a constraint condition.

[0022] The trained video diffusion model is used as a microstructure generator.

[0023] In one embodiment, the microstructure generator performs structural design and evaluation based on the input target performance indicators, and outputs an optimal microstructure that meets the target performance indicators, including:

[0024] Input the target performance index and the number of candidate structures to be generated. The microstructure generator will automatically sample and generate a physical field evolution video that matches the target performance index and the corresponding candidate microstructure samples.

[0025] The generated physical field evolution video and corresponding candidate microstructure samples are visualized, and the microstructure samples with the best performance are selected.

[0026] The simulation response curve and physical field distribution of the microstructure sample with the best performance are obtained through finite element simulation, and the microstructure sample with the best performance is output.

[0027] In one embodiment, a video diffusion model based on the U-Net video architecture is constructed, and the video diffusion model is trained using the physical field video dataset as training data. The trained video diffusion model is then used as a microstructure generator. The method further includes:

[0028] The physical field video dataset is processed using min-max normalization to transform it to the range [-1, 1].

[0029] In one embodiment, the pixel-compressed microstructure samples are binarized, and microstructure samples that do not satisfy entity connectivity constraints are filtered out using a connectivity detection algorithm, including:

[0030] The pixel-compressed microstructure samples are binarized to distinguish between solid material areas and cavity regions, where white areas represent solid material areas and black areas represent cavity regions.

[0031] The connectivity detection algorithm is used to detect the connectivity of white regions in a binary image, count the number and area of ​​connected regions, filter out microstructure samples with isolated or broken structures, and retain effective microstructure samples with a single main connected region.

[0032] In one embodiment, the target performance indicators include equivalent stiffness, Poisson's ratio, energy absorption rate, and nonlinear stress-strain characteristics.

[0033] A mechanical metamaterial generative reverse design device includes:

[0034] The dataset generation module is used to generate a basic microstructure dataset based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm, and to expand the basic microstructure dataset by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking.

[0035] The training data generation module is used to perform full-field finite element simulation on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. Hybrid meshes are used in the simulation process.

[0036] The microstructure generator construction module is used to construct a video diffusion model based on the U-Net video architecture. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as the microstructure generator.

[0037] The microstructure generation module is used by the microstructure generator to design and evaluate structures based on the input target performance indicators, and output the optimal microstructure that meets the target performance indicators.

[0038] The aforementioned generative reverse design method and apparatus for mechanical metamaterials generates a dataset of basic microstructures consisting of disordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations. This dataset covers diverse topological configurations from periodic to aperiodic and from regular to disordered, providing comprehensive structural type coverage for ordered and disordered metamaterial microstructures. Simultaneously, by applying seed translation, local weight variance increase, and global weight variance modification perturbation strategies to the basic microstructure dataset, controllable topological variations and geometric distortions are introduced. This eliminates the symmetry and order constraints of traditional design, significantly expanding the design space of microstructures and enabling the dataset to have a wider distribution of morphological features. In the process of obtaining the physical field video dataset through simulation, a hybrid mesh is used. The discrete modeling method using unstructured meshes effectively improves the adaptability in complex geometric domains and overcomes the dependence of existing generative design methods on regular boundaries. By training a video diffusion model using a physical field video dataset containing dynamic evolution information of stress and strain fields, the mechanical response curve of metamaterials under compressive loading conditions is introduced as a physical constraint. Simultaneously, the video diffusion model employs a U-Net video architecture. The U-Net architecture samples and models the dynamic evolution of the stress-strain physical field through a spatiotemporal modeling mechanism, enabling rapid generation of mechanical metamaterial microstructures that satisfy the physical constraints, thus achieving a mapping from nonlinear mechanical properties to potential geometric configurations. Using the trained video diffusion model as a microstructure generator overcomes the limitation of traditional generation models that rely solely on static image features for structural mapping. This invention, under the constraint of physical field video data, can accurately learn the correspondence between nonlinear mechanical responses and complex geometric configurations, thereby achieving a unity of physical consistency and structural innovation. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating a generative reverse design method for mechanical metamaterials in one embodiment.

[0040] Figure 2 This is a schematic diagram of the basic microstructure dataset in one embodiment;

[0041] Figure 3 This is a schematic diagram illustrating the effects of seed translation, local weight variance increase, and global weight variance modification in one embodiment. Figure 3 (a) is a schematic diagram illustrating the effect of global weight variance modification. Figure 3 (b) is a schematic diagram illustrating the effect of increasing the local weight variance. Figure 3 (c) is a schematic diagram of the effect of seed translation;

[0042] Figure 4 This is a schematic diagram illustrating the process of full-field finite element simulation of a microstructure sample in one embodiment, wherein, Figure 4(a) is a schematic diagram of the full-field finite element simulation process for the microstructure sample. Figure 4 (b) is a schematic diagram of strain-stress response;

[0043] Figure 5 This is a schematic diagram illustrating the principle of a video diffusion model in one embodiment;

[0044] Figure 6 This is a schematic diagram of the U-Net video architecture in one embodiment;

[0045] Figure 7 This is a schematic diagram of the sampling and evaluation process in one embodiment;

[0046] Figure 8 This is a structural block diagram of a mechanical metamaterial generative reverse design device in one embodiment. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0048] In one embodiment, such as Figure 1 As shown, a generative reverse design method for mechanical metamaterials is provided, including the following steps:

[0049] Step 201: Generate a basic microstructure dataset based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. Expand the basic microstructure dataset by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking.

[0050] Step 202: Perform full-field finite element simulation on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. A hybrid mesh is used in the simulation process.

[0051] Step 203: Construct a video diffusion model based on the U-Net video architecture. Train the video diffusion model using the physical field video dataset as training data, and use the trained video diffusion model as a microstructure generator.

[0052] Step 204: The microstructure generator performs structural design and evaluation based on the input target performance indicators, and outputs the optimal microstructure that meets the target performance indicators.

[0053] The aforementioned generative inverse design method for mechanical metamaterials generates a dataset of basic microstructures consisting of disordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations. This dataset covers diverse topological configurations from periodic to aperiodic and from regular to disordered, providing comprehensive structural type coverage for ordered and disordered metamaterial microstructures. Simultaneously, by applying seed translation, local weight variance increase, and global weight variance modification perturbation strategies to the basic microstructure dataset, controllable topological variations and geometric distortions are introduced. This eliminates the symmetry and order constraints of traditional design, significantly expanding the design space of microstructures and giving the dataset a wide range of morphological features. Hybrid meshes are used in the simulation to obtain the physical field video dataset. Through the discrete modeling of unstructured meshes, the adaptability in complex geometric domains is effectively improved, overcoming the dependence of existing generative design methods on regular boundaries. By training a video diffusion model using a physical field video dataset containing dynamic evolution information of stress and strain fields, the mechanical response curve of metamaterials under compressive loading conditions is introduced as a physical constraint. Simultaneously, the video diffusion model employs a U-Net video architecture. The U-Net architecture samples and models the dynamic evolution of the stress-strain physical field through a spatiotemporal modeling mechanism, enabling rapid generation of mechanical metamaterial microstructures that satisfy the physical constraints, thus achieving a mapping from nonlinear mechanical properties to potential geometric configurations. Using the trained video diffusion model as a microstructure generator overcomes the limitation of traditional generation models that rely solely on static image features for structural mapping. This invention, under the constraint of physical field video data, can accurately learn the correspondence between nonlinear mechanical responses and complex geometric configurations, thereby achieving a unity of physical consistency and structural innovation.

[0054] In one embodiment, step 201 involves generating a basic microstructure dataset based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. This basic microstructure dataset is then expanded through seed translation, local weight variance increase, and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations, including:

[0055] In two-dimensional Euclidean space, 1-uniform tiling, 2-uniform tiling, and Voronoi structures are generated using the k-uniform tiling algorithm and the Voronoi graph generation algorithm. Using dual tiling, seeds are placed at the vertices of polygons, and tessellation is performed on the same planar domain using single-valued weights to obtain unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations, which constitute the basic microstructure dataset.

[0056] The basic microstructure dataset is expanded by processing the seed translation, increasing the local weight variance, and modifying the global weight variance to obtain the microstructure dataset.

[0057] Understandably, the k-uniform tiling algorithm is used to systematically generate ordered periodic microstructures such as 1-uniform tiling and 2-uniform tiling in two-dimensional Euclidean space. Simultaneously, the Voronoi generation algorithm is used to generate unordered Voronoi structures by inputting randomly distributed seed points. Utilizing the duality of the structures, the vertices of the generated k-uniform tiling polygons are extracted as seed points, and tessellations are performed on the same planar domain using single-valued weights, thereby generating Voronoi tessellations that are topologically dual to the original k-uniform tiling. Furthermore, it is understandable that the k-uniform tiling algorithm and the Voronoi generation algorithm are two parallel generation algorithms.

[0058] Specifically, in one embodiment, a planar domain of finite size is defined in two-dimensional Euclidean space. D Divided into n Unit set Each seed Corresponding to a unit, the position is The convex region occupied by each unit is defined as follows:

[0059] ;

[0060] in, For Laguerre distance; These are the sample points to be clustered; For the first j One seed; To be assigned to the i The weights of each seed are determined. By controlling the position of the seed and its corresponding weight, dual tiling is used. Seeds are placed at the vertices of a polygon, and then tessellation of the same planar domain is performed using single-valued weights to generate a basic microstructure dataset, such as... Figure 2 As shown, the basic microstructure dataset generated in this embodiment contains 11 types of 1-uniform tiling (three regular types are marked in purple, and eight semi-regular types are marked in green), 20 types of 2-uniform tiling (marked in orange), one disordered Voronoi structure (marked in black), and their corresponding dual tessellations (marked in blue).

[0061] In this embodiment, the basic microstructure dataset containing 64 structures is expanded into a microstructure dataset containing 1646 structures by processing the basic microstructure dataset through seed translation, local weight variance increase and global weight variance modification.

[0062] Specifically, refer to Figure 3 Global weight variance refers to the macroscopic distribution of seed weights relative to their mean, using global weight coefficients. Each seed According to the following formula Assign new weights, where This represents the average of the seed weights. It should be noted that the global weight variance modification is only meaningful for designs generated from power maps with non-uniform weights, i.e., semi-regular and 2-uniform tiling. Local weight variance describes the fluctuation of the seed weights from their original values ​​in the basic mosaic. (The last part, "with weights," appears to be incomplete and unrelated to the preceding text.) Each seed is given a weight The new seed replacement, in which Follow the local weight coefficients Scaled normal distribution. It should be noted that the increase in local weight variance applies to all microstructures included in the basic microstructure dataset. Seed translation refers to changing the seed position from its corresponding value in the initial basic design. For each seed... Seed location Along random direction Radial distance modified This leads to an updated seed location. for Two uniform random variables and Generate independently within their respective scopes, among which , .coefficient Applied to the maximum relative change in position, while This represents the minimum distance between adjacent seeds. Seed translation is only applied to regular microstructures in basic sets, namely 1-uniform tiling and 2-uniform tiling and their dual structures, because this operation has little effect on the microstructural features of disordered Voronoi mosaics.

[0063] In one embodiment, step 202 involves performing a full-field finite element simulation on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of the stress and strain fields. The simulation uses a hybrid mesh, including:

[0064] The microstructure samples in the microstructure dataset are converted into three-dimensional geometric models that can be recognized by finite element analysis software.

[0065] The finite element analysis software was used to perform simulation, generate microstructures and simulate physical field video datasets. Hybrid meshes were used in the simulation process. The physical field video datasets contain physical field information under longitudinal load conditions and corresponding nonlinear mechanical response curves.

[0066] Specifically, in one embodiment, microstructure samples (image data) from a microstructure dataset are imported into commercial Rhino software and converted into a three-dimensional geometric model input that can be recognized by finite element analysis software. Then, simulation is performed using ABAQUS / Explicit software, such as... Figure 4 As shown in (a), to obtain the stress-strain response under compressive loading, a metamaterial microstructure was placed between two rigid plates with periodic boundary conditions in the horizontal direction and subjected to compressive strain up to 20%. The corresponding stress and displacement fields in the microstructure were calculated using finite element simulation, and the overall effective stress-strain response was obtained. (Represented by red dots) are extracted from nodal reaction forces. Figure 4 (b) The rightmost part shows a schematic diagram of the nonlinear physical behavior, i.e., strain-stress response, of the mechanical metamaterial designed by the finite element method under compressive loading. During the simulation, the three-node plane strain element (CPE3) was comprehensively utilized: quadrilateral elements were preferentially generated in geometrically regular regions to improve computational accuracy; triangular elements were automatically added in local curved surfaces or complex boundary regions to ensure mesh continuity and convergence. After the simulation, the stress field, strain field, and displacement field information at different time steps were extracted through post-processing of the output database (ODB) file, and the overall stress-strain response curve was calculated. The results not only reflect the mechanical evolution characteristics of the metamaterial in the nonlinear deformation stage but also provide a sequence of physical field data for the subsequent training of the video diffusion model, achieving a physical consistency mapping from finite element simulation to the deep generative model.

[0067] In one embodiment, step 202 involves performing full-field finite element simulation on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields, and further includes:

[0068] The microstructure samples in the microstructure dataset are pixel-scale compressed to a pixel scale of 128×128.

[0069] The pixel-compressed microstructure samples are binarized, and microstructure samples that do not meet the entity connectivity constraints are filtered out using a connectivity detection algorithm.

[0070] In this embodiment, the pixel scale of the microstructure samples in the microstructure dataset is compressed to 128×128 to establish a reasonable balance between computational complexity and structural feature fidelity. This ensures that the training and generation processes can run stably under acceptable time and hardware conditions, while effectively identifying and processing microstructure features. Furthermore, after binarizing the microstructure samples, a connectivity detection algorithm is used to filter out microstructure samples that do not satisfy entity connectivity constraints, thereby guaranteeing the structural integrity and manufacturability of the generated metamaterial.

[0071] In one embodiment, the pixel-compressed microstructure samples are binarized, and microstructure samples that do not satisfy entity connectivity constraints are filtered out using a connectivity detection algorithm, including:

[0072] The pixel-compressed microstructure samples are binarized to distinguish between solid material areas and cavity regions, where white areas represent solid material areas and black areas represent cavity regions.

[0073] The connectivity detection algorithm is used to detect the connectivity of white regions in a binary image, count the number and area of ​​connected regions, filter out microstructure samples with isolated or broken structures, and retain effective microstructure samples with a single main connected region.

[0074] Specifically, in one embodiment, the OTSU adaptive thresholding algorithm is used to binarize the pixel-compressed microstructure samples to distinguish between material entities and cavity regions. The OpenCV function cv2.connectedComponentsWithStats() is used to perform connectivity detection on the white regions in the binary image, count the number and area of ​​connected regions, filter out microstructure samples with isolated or broken structures, and retain valid microstructure samples with a single main connected region.

[0075] In one embodiment, step 203 involves constructing a video diffusion model based on the U-Net video architecture, training the video diffusion model using a physical field video dataset as training data, and using the trained video diffusion model as a microstructure generator, including:

[0076] A video diffusion model based on the U-Net video architecture is constructed. The model is trained using a physical field video dataset, with nonlinear mechanical response curves used as constraints during the training process.

[0077] The trained video diffusion model is used as a microstructure generator.

[0078] In this embodiment, a physical field video dataset is used as training data to train the video diffusion model, and a nonlinear mechanical response curve is used as a constraint during the training process, so that the video diffusion model learns the mapping relationship between the nonlinear mechanical response and the video of the geometric structure evolution.

[0079] The video diffusion model works by continuously adding Gaussian noise to destroy the training data (forward noise addition), then reversing this noise process to learn how to recover the data. After training (reverse denoising process), randomly sampled noise is passed to the learned denoising process, allowing the trained model to generate data. Figure 5As shown, given a stress frame under different strain conditions during continuous deformation as input, the video diffusion model iteratively destroys the video frame with Gaussian noise at a series of time steps, eventually leaving pure Gaussian noise. Then, the video diffusion model works in reverse, learning how to remove noise at each time step and undo the previously occurred destruction process. After training, starting from randomly sampled pure Gaussian noise, the model gradually denoises under the constraints of physical behavior, i.e., the stress-strain curve, to generate a video of the physical field (stress contour map) changes under mechanical metamaterial compressive loading conditions.

[0080] A video diffusion model based on the U-Net video architecture, where the U-Net video architecture is as follows: Figure 6 As shown, the U-Net video architecture relies on the construction of spatiotemporal residual blocks. In these blocks, the stress images of all frames are fused with the features of the temporal embedding module along with the diffusion step size t. This fusion is then combined with a vector formed by a 3D spatial convolution module and a token embedding module (the conditional response, i.e., the stress points of each frame), which serves as the input to the spatiotemporal attention module, generating the input image for the next denoising step. By using the stress cloud map of each frame during the deformation process of porous materials and the corresponding stress points as conditions, the video diffusion model captures the mechanical consistency of the deformation process under load on porous materials. Throughout the diffusion process, four feature map resolutions are used (128×128→64×64→32×32→16×16), and the latent dimension is expanded (64→128→256→512) to enable the model to capture and process the stress cloud map information of each frame more meticulously, enriching the model's latent expressive power. Each attention block consists of eight attention heads, each with a dimension of 32.

[0081] It should be noted that, Figure 5 , Figure 6 In the middle, X t The feature map represents time step t, where C, F, H, and W represent the number of channels, number of frames, height, and width of the feature map, respectively. C0 is the initial number of channels.

[0082] In one embodiment, step 203, constructing a video diffusion model based on the U-Net video architecture, training the video diffusion model using a physical field video dataset as training data, and using the trained video diffusion model as a microstructure generator, further includes:

[0083] The physical field video dataset is processed using min-max normalization to transform it to the range [-1, 1].

[0084] In this embodiment, min-max normalization is used to process the physical field video dataset, transforming it to the range of [-1,1], thereby avoiding the performance degradation of the neural network due to the difference in the dimensions of features of different dimensions.

[0085] Specifically, all input data x (i.e., stress and displacement distribution) and conditions (stress-strain curves) are processed using min-max normalization and transformed to [ Within the range of 1,1], that is:

[0086] ;

[0087] The minimum and maximum value operations are performed on all corresponding data points. For stress and displacement fields, all corresponding pixel values ​​for all strain steps in the entire training dataset are considered. For stress-strain response, the minimum and maximum values ​​of the recorded stress response for all strain steps in the entire training dataset are considered.

[0088] In one embodiment, the target performance indicators include equivalent stiffness, Poisson's ratio, energy absorption rate, and nonlinear stress-strain characteristics.

[0089] In one embodiment, step 204 involves the microstructure generator performing structural design and evaluation based on the input target performance indicators, and outputting an optimal microstructure that meets the target performance indicators, including:

[0090] Input the target performance index and the number of candidate structures to be generated. The microstructure generator will automatically sample and generate a physical field evolution video that matches the target performance index, as well as corresponding candidate microstructure samples.

[0091] The generated physical field evolution video and corresponding candidate microstructure samples are visualized, and the microstructure samples with the best performance are selected.

[0092] The simulation response curve and physical field distribution of the microstructure sample with the best performance are obtained through finite element simulation, and the microstructure sample with the best performance is output.

[0093] Reference Figure 7 The microstructure generator designs and evaluates the structure based on the input target performance indicators. When evaluating the global physical behavior throughout the deformation process, it uses the Normalized Root Mean Square Error (NRMSE). This index measures the overall deviation between the predicted effective stress evolution and the actual result over a series of strain increments. The definition of NRMSE is as follows:

[0094] ;

[0095] in, Indicates in N The global effective stress-strain response over discrete strain frames, where pred represents the prediction and true represents the actual result; This represents the Euclidean norm. A lower NRMSE value indicates a higher consistency between the predicted curve and the actual stress evolution curve, meaning the model performs better in terms of global prediction accuracy. A value of 0 indicates a perfect match. NRMSE provides a holistic assessment of the model's ability to generate stress curves during strain evolution, effectively capturing the discrepancy between predictions and actual physical behavior.

[0096] To evaluate the prediction accuracy at the local fine-grained level, a pixel-by-pixel relative... Error, a metric used to measure the spatial consistency between the predicted stress field and the stress field obtained from the finite element simulation at each strain frame, is defined as follows:

[0097] ;

[0098] in, Indicates that the size is The vertical stress components on the discrete grid, where pred represents the prediction and true represents the actual result; This represents the Frobenius norm. Smaller... The value corresponds to better pixel-by-pixel alignment between the predicted and actual stress fields, indicating higher fidelity in capturing local stress concentrations and spatial distribution patterns. A value of 0 indicates that the stress field is fully reconstructed at the pixel level. This metric is crucial for verifying whether the model can accurately reproduce the complex stress concentration effects and spatial non-uniformities within the material.

[0099] In this embodiment, by combining NRMSE for global evaluation with relative NRMSE for local stress field evaluation... To address the error, a balanced model generation performance evaluation system was constructed. This dual-index evaluation strategy can comprehensively analyze the model's strengths and limitations, thereby ensuring its robust conditional generation capability in nonlinear mechanical metamaterial inverse design tasks.

[0100] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0101] In one embodiment, such as Figure 8 As shown, a mechanical metamaterial generative reverse design device is provided, comprising:

[0102] The dataset generation module 901 is used to generate a basic microstructure dataset based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. The basic microstructure dataset is expanded by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking.

[0103] The training data generation module 902 is used to perform full-field finite element simulation on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress field and strain field. A hybrid mesh is used in the simulation process.

[0104] The microstructure generator building module 903 is used to build a video diffusion model based on the U-Net video architecture. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as the microstructure generator.

[0105] The microstructure generation module 904 is used by the microstructure generator to perform structural design and evaluation based on the input target performance indicators, and output the optimal microstructure that meets the target performance indicators.

[0106] Specific limitations regarding the generative reverse design device for mechanical metamaterials can be found in the limitations of the generative reverse design method for mechanical metamaterials described above, and will not be repeated here. Each module in the aforementioned generative reverse design device for mechanical metamaterials can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0107] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0108] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A generative reverse design method for mechanical metamaterials, characterized in that, Includes the following steps: A basic microstructure dataset is generated based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. The basic microstructure dataset is then expanded by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking. Full-field finite element simulation was performed on the microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. Hybrid meshes were used in the simulation process. A video diffusion model based on the U-Net video architecture is constructed. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as a microstructure generator. The microstructure generator designs and evaluates structures based on input target performance indicators, and outputs the optimal microstructure that meets the target performance indicators, including: Input the target performance index and the number of candidate structures to be generated. The microstructure generator will automatically sample and generate a physical field evolution video that matches the target performance index and the corresponding candidate microstructure samples. The generated physical field evolution video and corresponding candidate microstructure samples are visualized, and the microstructure samples with the best performance are selected. The simulation response curve and physical field distribution of the microstructure sample with the best performance are obtained through finite element simulation, and the microstructure sample with the best performance is output.

2. The mechanical metamaterial generative reverse design method according to claim 1, characterized in that, A basic microstructure dataset is generated based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm. This dataset is then expanded through seed shifting, increasing local weight variance, and modifying global weight variance to obtain a microstructure dataset. This basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling, and corresponding dual tessellations, including: In two-dimensional Euclidean space, 1-uniform tiling, 2-uniform tiling and Voronoi structures are generated using the k-uniform tiling algorithm and the Voronoi graph generation algorithm. Using dual tiling, seeds are placed at the vertices of polygons, and tessellation of the same planar domain is performed with single-valued weights to obtain unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual tessellations, which constitute the basic microstructure dataset. The basic microstructure dataset is expanded by processing the seed translation, increasing the local weight variance, and modifying the global weight variance to obtain the microstructure dataset.

3. The mechanical metamaterial generative reverse design method according to claim 1, characterized in that, Full-field finite element simulations were performed on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. Hybrid meshes were used in the simulation, including: Convert the microstructure samples in the microstructure dataset into three-dimensional geometric model inputs that can be recognized by finite element analysis software; The finite element analysis software was used to perform simulation, generate microstructures and simulate physical field video datasets. Hybrid meshes were used in the simulation process. The physical field video datasets contain physical field information under longitudinal load conditions and corresponding nonlinear mechanical response curves.

4. The mechanical metamaterial generative reverse design method according to claim 3, characterized in that, Full-field finite element simulations were performed on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields, which also includes: Pixel-scale compression is performed on the microstructure samples in the microstructure dataset to make the pixel scale 128×128; The pixel-compressed microstructure samples are binarized, and microstructure samples that do not meet the entity connectivity constraints are filtered out using a connectivity detection algorithm.

5. The mechanical metamaterial generative reverse design method according to claim 3, characterized in that, A video diffusion model based on the U-Net video architecture is constructed. The physical field video dataset is used as training data to train the video diffusion model. The trained video diffusion model is then used as a microstructure generator, including: A video diffusion model based on the U-Net video architecture is constructed, and the video diffusion model is trained using the physical field video dataset as training data. During the training process, the nonlinear mechanical response curve is used as a constraint condition. The trained video diffusion model is used as a microstructure generator.

6. The mechanical metamaterial generative reverse design method according to claim 5, characterized in that, Constructing a video diffusion model based on the U-Net video architecture, training the video diffusion model using the aforementioned physical field video dataset as training data, and using the trained video diffusion model as a microstructure generator, further includes: The physical field video dataset is processed using min-max normalization to transform it to the range [-1, 1].

7. The mechanical metamaterial generative reverse design method according to claim 4, characterized in that, The pixel-compressed microstructure samples are binarized, and microstructure samples that do not satisfy entity connectivity constraints are filtered out using a connectivity detection algorithm, including: The pixel-compressed microstructure samples are binarized to distinguish between solid material areas and cavity regions, where white areas represent solid material areas and black areas represent cavity regions. The connectivity detection algorithm is used to detect the connectivity of white regions in a binary image, count the number and area of ​​connected regions, filter out microstructure samples with isolated or broken structures, and retain effective microstructure samples with a single main connected region.

8. The mechanical metamaterial generative reverse design method according to claim 1, characterized in that, The target performance indicators include equivalent stiffness, Poisson's ratio, energy absorption rate, and nonlinear stress-strain characteristics.

9. A mechanical metamaterial generative reverse design device, characterized in that, include: The dataset generation module is used to generate a basic microstructure dataset based on the k-uniform tiling algorithm and the Voronoi diagram generation algorithm, and to expand the basic microstructure dataset by seed translation, local weight variance increase and global weight variance modification to obtain a microstructure dataset. The basic microstructure dataset consists of unordered Voronoi structures, 1-uniform tiling, 2-uniform tiling and corresponding dual mosaicking. The training data generation module is used to perform full-field finite element simulation on microstructure samples in the microstructure dataset to obtain a physical field video dataset containing dynamic evolution information of stress and strain fields. Hybrid meshes are used in the simulation process. The microstructure generator construction module is used to construct a video diffusion model based on the U-Net video architecture. The video diffusion model is trained using the physical field video dataset as training data, and the trained video diffusion model is used as the microstructure generator. The microstructure generation module is used by the microstructure generator to design and evaluate structures based on input target performance indicators, and output the optimal microstructure that meets the target performance indicators, including: Input the target performance index and the number of candidate structures to be generated. The microstructure generator will automatically sample and generate a physical field evolution video that matches the target performance index and the corresponding candidate microstructure samples. The generated physical field evolution video and corresponding candidate microstructure samples are visualized, and the microstructure samples with the best performance are selected. The simulation response curve and physical field distribution of the microstructure sample with the best performance are obtained through finite element simulation, and the microstructure sample with the best performance is output.

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