Irregular negative Poisson's ratio metamaterial reverse design method based on INPR-GAN network

Abstract

The invention relates to a special-shaped negative Poisson's ratio metamaterial reverse design method based on an INPR-GAN network, and the method comprises the steps: constructing an experimental database of a mapping relation between five structural parameters and special-shaped cell Poisson's ratio, which comprise conformal geometry and material mechanics double constraints, and introducing a random forest regression model to generate a pseudo tag; a data expansion training set violating physical and geometric constraints is eliminated through a feature screening mechanism, the data acquisition cost is reduced, the generalization ability and robustness of a model are improved, a generator of the INPR-GAN network combines adversarial loss and feature matching loss, the generator is promoted to maintain physical and geometric rationality while pursuing an adversarial effect, and the robustness of the model is improved. Design parameters are automatically generated through four steps of target Poisson's ratio standardization, Gaussian noise vector generation, forward propagation of a generator network and anti-standardization parameters, the problem of reverse prediction of traditional machine learning is solved, trial and error experiments are not needed, the design period is short, universality is high, and efficient and accurate design can be achieved for a special-shaped negative Poisson's ratio structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of deep learning and metamaterial reverse design, and relates to a reverse design method for special-shaped negative Poisson's ratio metamaterials based on an INPR-GAN network. In particular, a conditional generative adversarial network framework based on INPR-GAN (Inverse Negative Poisson's Ratio GAN) is designed for reverse design of special-shaped negative Poisson's ratio metamaterials. Background Art

[0002] Negative Poisson's ratio metamaterials, due to their anomalous mechanical property of lateral expansion under axial stretching, have important applications in flexible electronics, impact protection, biomedicine, and other fields. The core performance of such materials relies on the design of their microscopic cellular structures, such as topological configurations like rhombuses and concave hexagons. However, traditional design methods rely heavily on trial-and-error experiments, requiring repeated adjustments to cellular parameters (such as rhombus side lengths, angles, and chamfers) and mechanical testing to verify performance, resulting in long design cycles and high costs. Furthermore, negative Poisson's ratio performance is affected by multi-parameter nonlinear coupling, making it difficult to accurately predict using simple theoretical models or finite element simulations. This makes the design results overly reliant on experience and lacks universal applicability. Furthermore, the design of irregularly shaped structures, such as truncated corners and curved surfaces, is even more challenging, as local stress concentration can easily lead to degradation of negative Poisson's ratio performance. Existing methods lack the ability to effectively model the mechanical response of irregularly shaped structures, further limiting the expansion of practical application scenarios.

[0003] To address these issues, deep learning technology offers new insights into metamaterial design. For example, patent publication number CN119918420A discloses a convolutional neural network-based inverse design method for metasurfaces with tunable strong circular dichroism. This method improves design efficiency by constructing a "structural parameter-optical response" mapping model. However, this approach still faces the following significant limitations in the field of negative Poisson's ratio materials:

[0004] 1. The amount of experimental data for negative Poisson's ratio materials is usually small (only a few hundred). Directly training deep learning models is prone to overfitting due to data scarcity and insufficient model generalization.

[0005] 2. Traditional forward prediction models can only achieve a one-way mapping from "parameters to performance" and cannot reversely generate parameter combinations from target performance, making it difficult to meet customized design requirements.

[0006] Existing methods for heterogeneous structures are often based on idealized assumptions of regular cells. This leads to large errors in predicting the mechanical properties of complex configurations such as truncated and asymmetric structures, making it difficult to support high-precision reverse design. Therefore, achieving high-precision reverse design of heterogeneous negative Poisson's ratio metamaterials with small sample data remains a technical challenge that technicians in this field urgently need to overcome. Summary of the Invention

[0007] In view of this, in order to solve the problem that existing metamaterial reverse design methods are mostly based on the idealized assumption of regular cells, the prediction errors of the mechanical properties of complex configurations such as truncated and asymmetric configurations are large, and it is difficult to support high-precision reverse design of negative Poisson's ratio metamaterials under small sample data, the present invention provides a reverse design method for special-shaped negative Poisson's ratio metamaterials based on the INPR-GAN network.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A reverse design method for special-shaped negative Poisson's ratio metamaterials based on an INPR-GAN network includes the following steps:

[0010] S1. Constructing an experimental database: Using SolidWorks software simulation, we obtained mapping data of five structural parameters, including rhombus side length (8-10 cm), included angle (20°-40°), chamfer radius (2-4 cm), cell thickness (fixed at 4 cm), and truncation angle (0°-30°), as well as their corresponding Poisson's ratio. The Poisson's ratio at a strain of 0.016 was used as the label for the parameter combination data. This formed a mapping database between rhombus parameters and Poisson's ratio, providing a data basis for subsequent training.

[0011] S2. Data augmentation: The original basic data obtained in step S1 is fitted with a random forest regression model. That is, the original data is sampled and pseudo labels are generated using the trained random forest model to obtain pseudo data with labels. The training set is expanded through a feature screening mechanism.

[0012] S3. Establish an INPR-GAN network architecture: The generator network input is the concatenation of a 32-dimensional noise vector and a 1-dimensional Poisson's ratio conditional vector, which is processed by three fully connected layers to output a normalized five-dimensional structural parameter. The discriminator network input is the concatenation of the five-dimensional structural parameter and the 1-dimensional Poisson's ratio conditional vector, which is processed by three fully connected layers to output a one-dimensional structural parameter for probabilistic evaluation of data authenticity. This constructs an INPR-GAN network architecture with feature matching constraints.

[0013] S4, two-stage adversarial training: The pseudo data generated in step S2 and the original basic data in step S1 are combined and input into the model in step S3 for training. The discriminator training is used to distinguish between real and generated data; the generator training is used to integrate the adversarial loss and the mean squared error loss to build a complete INPR-GAN network architecture, realize conditional generative adversarial learning of structural parameters and Poisson's ratio, and further optimize the generator and discriminator;

[0014] S5. Inverse design method: Based on the INPR-GAN model trained in step S3, an inverse design method is constructed to automatically generate the target Poisson's ratio parameters through four steps: normalizing the target Poisson's ratio, generating a Gaussian noise vector, forward propagating the generator network, and denormalizing the parameters;

[0015] S6. 3D printing to verify the effectiveness: The structural parameters obtained by inverse deduction of the INPR-GAN model in step S5 are used to construct a special-shaped bond. The structure is 3D printed using a light-curing 3D printer and tested using a microcomputer-controlled electronic universal testing machine. The Poisson's ratio data under a strain of 0.016 in step S1 is taken out and compared with the target Poisson's ratio to verify the effectiveness.

[0016] Furthermore, in step S1, based on the negative Poisson's ratio cell of the rotated square structure, its internal angles and chamfers are adjusted to make it rhombus-shaped. After the structure is subjected to force, the rhombus-shaped hole can be rotated and expanded around the vertex, and at the same time, the side length, angle, chamfer offset and final cutting degree of the rhombus-shaped hole are continuously adjusted to obtain more special-shaped part models with different hole parameters and cutting degrees, and then construct a data set containing the mapping relationship between the five structural parameters and the Poisson's ratio of the special-shaped cell with the dual constraints of "conformal geometry and material mechanics".

[0017] Further, step S2 is specifically as follows:

[0018] S21. Input the dataset obtained in step S1 into the forward training of the random forest model (establishing a mapping from attributes to Poisson's ratio labels) to obtain pseudo labels, and merge the predicted Poisson's ratio pseudo labels with the attributes to obtain labeled pseudo data; use kernel density estimation (KDE) to fit the empirical distribution of the discrete attributes of the dataset in step S1, retaining the statistical characteristics of the original parameters; perform Latin hypercube sampling (LHS) within the measured extreme value interval for continuous attributes to ensure uniform coverage of the parameter combination space; after generating pseudo data, use MinMaxScaler (-1,1) for normalization to eliminate pseudo data that violates physical and geometric constraints (such as chamfer radius > 50% of side length, angle ratio > 3:1).

[0019] S22. Use the training set feature scaler to standardize the generation parameters, filter valid data with a Poisson's ratio between -0.15 and -0.01, merge the pseudo data with the original data to construct an enhanced training set, reduce the data acquisition cost, expand the training set size, and improve the model generalization ability.

[0020] Furthermore, in step S3, the generator network's hidden layers use the LeakyReLU activation function (slope 0.2) to enhance nonlinear expression, and BatchNorm1d (batch normalization) is applied after each layer to accelerate model convergence. The output layer uses the Tanh activation function, constraining parameters to the interval [-1, 1] to match the normalization strategy of the experimental data, ensuring a standardized distribution of the generated structural parameters. The generator network's input and hidden layers use a hierarchical design with 128 and 256 neurons, respectively. Specifically, the first hidden layer transforms the concatenated 33-dimensional vector input through a 128-dimensional fully connected layer; the second hidden layer further transforms the 128-dimensional output through a 256-dimensional fully connected layer. LeakyReLU (0.2) is used between each hidden layer, along with BatchNorm1d normalization. The output layer is a 5-dimensional fully connected layer with the Tanh activation function. The Tanh function limits the output value to the range of [-1, 1], so that the generated structural parameters have a standardized distribution.

[0021] The discriminator network uses a LeakyReLU activation function (slope 0.2) and Dropout regularization (probability 0.3) between hidden layers to prevent overfitting and enhance model generalization. A sigmoid function is used to output a probabilistic estimate of the data's authenticity. The discriminator network uses a hierarchical design with 256 and 128 neurons in the input and hidden layers, respectively. Specifically: The first hidden layer transforms the concatenated 6-dimensional input vector through a 256-dimensional fully connected layer. The second hidden layer further transforms the 256-dimensional output through a 128-dimensional fully connected layer. LeakyReLU (0.2) is used as the activation function between each hidden layer, along with Dropout (0.3) for regularization. LeakyReLU (0.2) also introduces nonlinearity, allowing negative values ​​to propagate with a small slope. Dropout (0.3) randomly drops 30% of neurons to prevent overfitting and enhance model generalization. The output layer is a 1-dimensional fully connected layer with a Sigmoid activation function. The Sigmoid function limits the output value to the range [0, 1], indicating the probability that the input data is real data.

[0022] Furthermore, in step S4, the discriminator training stage uses a binary cross entropy loss function to distinguish between real and generated data, and the generator training adopts a hybrid loss function. The generator training stage integrates the adversarial loss and the feature matching loss, and jointly optimizes the adversarial loss and the feature matching loss. The feature matching loss is achieved by calculating the mean square error between the generated parameters and the real parameters. The weight coefficient is set to 0.5, which encourages the generator to maintain physical and geometric rationality while pursuing the adversarial effect.

[0023] The binary cross entropy loss function formula is:

[0024] The formula of the hybrid loss function is:

[0025] The Adam algorithm is used as the optimizer in the joint optimization of adversarial loss and feature matching loss, with a learning rate of 0.0002, a batch size of 64, and 100 training cycles. The discriminator and generator loss values ​​are output every 10 training cycles to monitor the model convergence status. When the generator loss fluctuation range is less than 0.001 and lasts for 20 cycles, the training is terminated to ensure model stability and generation effect.

[0026] Furthermore, in step S5, the target Poisson's ratio is input and normalized into a conditional vector. The generator receives N(0,1) distributed noise and the conditional vector, outputs the normalized structural parameters, and denormalizes the generated parameters to obtain the physical design parameters.

[0027] Furthermore, the simulation test and printing test of the special-shaped key structure design and stacking structure in step S6 include the following steps:

[0028] S61. Special-shaped part design: Based on the negative Poisson's ratio cell of a rotated square structure, its internal angles and chamfers are adjusted to form a diamond shape. When the structure is subjected to force, the diamond-shaped hole can rotate and expand around the vertex. At the same time, the side length, angle, chamfer offset, and final cutting degree of the diamond-shaped hole are continuously adjusted to obtain more special-shaped part models with different hole parameters and cutting degrees.

[0029] S62. Test mold design: In Cinema4D, create a new cube and delete one vertex to form a triangular prism. Adjust its parameters to wrap around the irregular-shaped part and reserve space. Extrude the bottom of the triangular prism to form a groove. Adjust the groove's inclination angle between 0 and 30 degrees to create a mold model suitable for mechanical property testing of irregular-shaped parts.

[0030] S63. Software simulation to obtain a Poisson's ratio label: Use Solidworks to construct a cell, the special-shaped part model constructed in step S61, and the test mold model constructed in step S62, and connect the test mold model constructed in step S62 with the special-shaped part model constructed in step S61; Simultaneously, simulate the compression process of the cell to obtain its Poisson's ratio value under a strain of 0.016; Assign the Poisson's ratio value of the cell to the special-shaped part, perform a compression simulation of the special-shaped part, and calculate the Poisson's ratio value of the special-shaped part under a strain of 0.016;

[0031] S64, light-curing 3D printing model production: using a light-curing 3D printer to 3D print the special-shaped part model, the cell standard part model, and the test mold model constructed in step S63;

[0032] S65. Model Poisson's ratio and force-displacement data testing: Use a microcomputer-controlled electronic universal testing machine to test the models printed in step S64, and use the computer software Origin to draw the transverse strain-longitudinal strain diagram of each model, calculate the Poisson's ratio of each model at a strain of 0.016, and export the report generated by the software.

[0033] The beneficial effects of the present invention are:

[0034] 1. The reverse design method of the special-shaped negative Poisson's ratio metamaterial disclosed in the present invention shows significant advantages in multiple aspects and provides innovative solutions for the fields of materials science and structural engineering. By constructing a hollow three-variable chamfered rhombus structure that satisfies the adjustable nonlinear relationship between the "Poisson's ratio and strain" of the cell, a data set containing the mapping relationship between the five structural parameters and the Poisson's ratio of the special-shaped cell with the dual constraints of "conformal geometry and material mechanics" is obtained, and the random forest algorithm is introduced for data enhancement, which effectively expands the scale of training data while retaining the statistical characteristics of the original parameters. On this basis, the INPR-GAN network can deeply learn the complex nonlinear relationship between parameters and Poisson's ratio, and realize the automatic generation of structural parameters under the target Poisson's ratio conditions. This process significantly reduces the links in traditional design that rely on manual trial and error and empirical judgment, and greatly improves design efficiency and parameter accuracy. By limiting the five parameters of the chamfered diamond structure, the reliability, consistency and success rate of subsequent machine learning reverse design can be guaranteed, as well as the success rate of 3D printing. The use of a two-stage training strategy further optimizes the performance balance between the generator and the discriminator, ensuring that the generated structural parameters not only meet the mathematical adversarial conditions but are also closer to actual physical constraints, thereby improving the reliability and rationality of the design results, and providing an efficient, intelligent and precise approach for the design of special-shaped negative Poisson's ratio structures.

[0035] 2. The reverse design method for special-shaped negative Poisson's ratio metamaterials disclosed in the present invention has built a complete closed-loop verification system in the design verification link to ensure the validity and accuracy of the design results. Solidworks is used to simulate and analyze cells and special-shaped parts, providing key data support for design optimization. By designing special-shaped parts and special test molds, combining software simulation with 3D printing technology, the connection from virtual design to physical testing is achieved. The physical object of the complex structure is obtained through light-curing 3D printing technology, and finally the mechanical properties of the physical model are tested using a universal testing machine to obtain the actual Poisson's ratio data and compare and analyze it with the design goals. This series of verification steps proves the feasibility and accuracy of the proposed reverse design method.

[0036] 3. The reverse design method for special-shaped negative Poisson's ratio metamaterials disclosed in the present invention demonstrates unique value in terms of innovation, practicality and operability. Its innovation is reflected in the deep integration of advanced machine learning technology and material structure design, which has opened up a new path for reverse design; its practicality lies in providing a complete tool chain from design to verification, which can be directly applied to the research and development and structural optimization process of new materials; and its operability is due to the combination of detailed and clear step-by-step guidance and mature software and hardware technology, making the complex design and verification process clear and easy. In addition, the present invention solves the problem of deep learning training difficulties under small samples by constructing an experimental database and establishing pseudo-labels; by optimizing the conditions to generate adversarial network architecture and training strategies, it solves the problem of traditional machine learning being difficult to reverse predict; and without relying on trial and error experiments, it solves the problems of long design cycles and lack of universality of traditional methods, providing a new approach to the design and application of negative Poisson's ratio materials.

[0037] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0039] Figure 1 Schematic diagram of the process of the reverse design method of special-shaped negative Poisson's ratio metamaterial based on INPR-GAN network of the present invention;

[0040] Figure 2 For the present invention Figure 1 INPR-GAN network structure diagram;

[0041] Figure 3 Three views of the cube 2 according to the embodiment of the present invention, from left to right, are the main view, side view and top view;

[0042] Figure 4 Schematic diagram of a sheet with diamond-shaped holes in an embodiment of the present invention;

[0043] Figure 5 Reproduced for this invention Figure 3 Schematic diagram of a cube 4 formed by rotating the X, Y, and Z coordinates of the five flakes;

[0044] Figure 6A schematic diagram of a cube 8 obtained by performing a Boolean operation on cubes 6 and 7 in an embodiment of the present invention;

[0045] Figure 7 This is a schematic diagram of performing a "Boolean" operation on cube 8 and cube 9 to obtain the final special-shaped part in an embodiment of the present invention;

[0046] Figure 8 Schematic diagram of a mold model for testing the mechanical properties of special-shaped parts in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0048] like Figure 1 The following is a reverse design method for shaped negative Poisson's ratio structures based on an INPR-GAN network. Its main purpose is to achieve high-precision reverse design of shaped negative Poisson's ratio metamaterials with small sample data. The design method mainly includes: 1) constructing an experimental database containing the mapping relationship between diamond parameters and Poisson's ratio; 2) generating a pseudo-data augmented training set through random forest; 3) establishing an INPR-GAN network architecture with feature matching constraints; 4) using a two-stage training strategy to optimize the generator and discriminator; 5) constructing an inverse design function to achieve the target Poisson's ratio parameter generation; 6) verifying the design effectiveness through 3D printing. The specific steps are as follows:

[0049] S1. Construct a database mapping rhombus parameters to Poisson's ratio: Five design variables were determined: rhombus side length (8-10 cm), included angle (20°-40°), chamfer radius (2-4 cm), cell thickness (fixed at 4 cm), and truncation angle (0°-30°). The experimental design generated 189 parameter combinations. Cells and special-shaped parts were constructed using SolidWorks, and simulations were conducted within the software. The Poisson's ratio of the cell at a strain of 0.016 was used as the label for the parameter combination data. This database, mapping rhombus parameters to Poisson's ratio, provided a data foundation for subsequent design and covered the multi-parameter combination space.

[0050] S2. Random Forest Pseudo-Data Augmentation: Using the basic data obtained in step S1, a random forest regression model is trained to establish a positive prediction relationship from "parameter → Poisson's ratio", that is, a mapping from attribute to Poisson's ratio label. Furthermore, based on the parameter distribution characteristics of the original data, five cell attributes, such as the rhombus side length and angle, are sampled appropriately. For discrete attributes, kernel density estimation (KDE) is used to fit the empirical distribution, preserving the statistical characteristics of the original parameters. For continuous attributes, Latin hypercube sampling (LHS) is performed within the measured extreme value interval to ensure uniform coverage of the parameter combination space.

[0051] After generating pseudo data, we normalized it using MinMaxScaler(-1,1) and removed pseudo data that violated physical and geometric constraints (e.g., chamfer radius > 50% of edge length, angle ratio > 3:1). This data was then fed into a trained random forest model to forward-predict the corresponding Poisson's ratio labels. The predicted values ​​were then reverse-normalized to match the original data range, filtering out valid samples with Poisson's ratios in the range [-0.15, -0.01]. The predicted Poisson's ratio pseudo labels were then merged with the sampled attributes to generate labeled pseudo data. This reduced data acquisition costs, expanded the training set, and improved model generalization.

[0052] S3. Establish the INPR-GAN network architecture: The pseudo data generated in step S2 is combined with the original baseline data in step S1 as input to the model. The generator network receives a concatenated input consisting of a 32-dimensional Gaussian noise vector and a 1-dimensional Poisson's ratio conditional vector. The input and hidden layers of the generator network use a hierarchical design with 128 and 256 neurons, respectively. Specifically, the first hidden layer transforms the concatenated 33-dimensional input vector through a 128-dimensional fully connected layer. The second hidden layer further transforms the 128-dimensional output through a 256-dimensional fully connected layer. LeakyReLU (0.2) is used as the activation function between each hidden layer, and BatchNorm1d is used for normalization. The output layer is a 5-dimensional fully connected layer with the Tanh activation function. The Tanh function constrains the output values ​​to the range [-1, 1], ensuring that the generated structural parameters have a standardized distribution.

[0053] The input to the discriminator network is a concatenation of five-dimensional structural parameters and a one-dimensional Poisson's ratio conditional vector. The input and hidden layers of the discriminator network use a hierarchical design with 256 and 128 neurons, respectively. Specifically: The first hidden layer transforms the concatenated six-dimensional vector input through a 256-dimensional fully-connected layer. The second hidden layer further transforms the 256-dimensional output through a 128-dimensional fully-connected layer. LeakyReLU (0.2) is used as the activation function between each hidden layer, and Dropout (0.3) is used for regularization. LeakyReLU (0.2) is also used to introduce nonlinearity, allowing negative values ​​to propagate with a small slope. Dropout (0.3) randomly drops 30% of neurons to prevent overfitting and enhance the model's generalization ability. The output layer is a one-dimensional structural parameter, which ultimately outputs a probability assessment of the data's authenticity through a Sigmoid function, effectively preventing overfitting.

[0054] S4. Training strategy: For the model constructed in step S3, a two-stage adversarial optimization strategy is adopted. The discriminator distinguishes real data from generated data through the binary cross entropy loss function, and the generator jointly optimizes the adversarial loss and feature matching loss. The feature matching loss is achieved by calculating the mean square error between the generated parameters and the real parameters. The weight coefficient is set to 0.5, forcing the generator to maintain physical and geometric rationality while pursuing the adversarial effect. The optimizer uses the Adam algorithm, the initial learning rate is set to 0.0002, the batch size is fixed to 64, and the training cycle is 100 rounds. After completing 10 training cycles, the loss values ​​of the discriminator and the generator are output to monitor the convergence status of the model. The training termination condition is set to the generator loss fluctuation range being less than 0.001 and lasting for 20 cycles to ensure model stability. The discriminator training uses binary cross entropy loss: , the generator training adopts a mixed loss function, the formula is: The CGAN network architecture is as follows. Figure 2 shown.

[0055] S5. Inverse Design Method: Based on the model in step S3, an inverse design function is constructed. This design function automatically generates design parameters through four steps: normalizing the target Poisson's ratio, generating a Gaussian noise vector, forward-propagating the generator network, and denormalizing the parameters. Using a target Poisson's ratio of -0.08 as an example, the function first generates 100 candidate design parameter sets. The Poisson's ratio value of each parameter is predicted using a random forest model. The 10 candidate solutions with the smallest prediction error are selected for 3D printing verification, improving design efficiency and accuracy.

[0056] S6. 3D printing verification: Use a light-curing 3D printer to 3D print the test structure. Use a microcomputer-controlled electronic universal testing machine to test the cell structure properties obtained by inverse deduction of the above model. Export the original force-displacement data of the experiment, and use a vernier caliper to measure the lateral width of the model at this time. Each compression degree is measured three times and the average value is taken. Repeat the above compression operation until the longitudinal compression distance is 3mm, and export the report generated by the software. Take out the Poisson's ratio data under 0.016 strain and compare it with the target Poisson's ratio. The test results are as follows Figure 8 shown.

[0057] Specifically, the simulation test and printing test of the special-shaped key structure design and stacking structure in step S6 include the following steps:

[0058] S61. Design of special-shaped parts: Based on the negative Poisson's ratio cell of the rotated square structure, its internal angles and chamfers are adjusted to make it diamond-shaped. When the structure is subjected to force, the diamond-shaped hole can be rotated around the vertex and expanded. Therefore, the diamond-shaped hole negative Poisson's ratio structure has good performance in both tension and compression during deformation.

[0059] The initial cube parameters are length × width × height = 24.495cm × 24.495cm × 4.000cm, the length a of the diamond hole is designed to be 8-10cm, and the small angle of the diamond hole is Designed to be 20°-40° (for the convenience of model design, half angles are often used in subsequent drawings ), the chamfer radius b of the diamond-shaped hole is designed to be 2-4 cm, and the target special-shaped parts are cut at 0°-30° to obtain the target special-shaped parts.

[0060] Use computer software Cinema4D to draw the model file, create a new cube 1, adjust its parameters to length × width × height = 24.495cm × 24.495cm × 4cm, create a new cube 2 (such as Figure 3 ), adjust its parameters to length × width × height = 10cm × 10cm × 5cm, rotate the Z axis 45°, enable the axis, change the axis Z axis to 0°, enable point mode, and adjust the coordinates of all points of cube 2 to the formula and The calculation results of

[0061] Furthermore, chamfer the four sides of the rhombus, adjust the chamfer subdivision to 10, and the chamfer offset is the b value. Duplicate the 8 rhombuses created, and adjust the coordinates and angles of each rhombus so that its center point is located on the four corners and four sides of cube 1. Perform a "Boolean" operation on cube 1 and each rhombus to generate a rhombus-shaped hole cube 3 from cube 1. Scale the Y coordinate of cube 3 to 24.744cm, clone cube 3, clone 5 at a distance of 24.744cm in the Y direction, and clone 7 at a distance of 24.495cm in the X direction, so that it becomes a sheet with a rhombus-shaped hole (such as Figure 4 ), copy 5 of these sheets and rotate their X, Y, and Z coordinates to form a cube 4 (such as Figure 5 Create a new cube 5, adjust its parameters to length × width × height = 122.475cm × 122.475cm × 122.475cm, perform a "Boolean" operation on cube 5 and cube 4, adjust the Boolean type to "A, B intersection", and get cube 6. Create a new cube 7, adjust its parameters to length × width × height = 200cm × 200cm × 200cm, adjust the coordinates to X = 70.711cm, Y = 0cm, Z = 70.711cm, rotate the Z axis 45°, perform a "Boolean" operation on cube 6 and cube 7, and get cube 8 (as shown in the figure). Figure 6 ), create a new cube 9, adjust its parameters to length × width × height = 500cm × 500cm × 500cm, according to the spherical coordinate formula: , fill in its X, Y, and Z coordinates, where is the degree of cutting of cube 8, which is designed to be 0-30°; 122.475 is the side length of cube 6 after the "Boolean" operation. The "Boolean" operation is performed on cubes 8 and 9 to obtain the final special-shaped piece (such as Figure 7 Repeat the above steps to adjust the side length, angle, chamfer offset of the diamond-shaped hole and the degree of final cutting of the special-shaped part to obtain more C4D models of special-shaped parts with different hole parameters and cutting degrees. Scale all models by 10mm and export them as STL files.

[0062] S62. Design of test mold

[0063] Use the computer software Cinema4D to create a cube 10, delete one of its vertices to turn it into a triangular prism, adjust the parameters of the triangular prism so that it can wrap the special-shaped part of the housing design, and reserve enough space. Extrude the bottom of the triangular prism inward to form a groove that can wrap the special-shaped part, adjust the inclination angle of the internal groove to 0°-30°, and obtain a mold model (such as Figure 8 ), and scaled by 10mm to export as an STL file.

[0064] S63, software simulation to obtain Poisson's ratio label

[0065] Use Solidworks to construct the cell, the special-shaped part model constructed in step S61, and the test mold model constructed in step S62. The special-shaped part is designed using a plane without holes. The test mold model constructed in step S62 is added and connected to the special-shaped part model constructed in step S61. The simulation process first simulates the compression process of the cell to obtain the Poisson's ratio value of the cell under a strain of 0.016. After assigning the Poisson's ratio value of the cell to the special-shaped part, the compression process of the special-shaped part is simulated. The right side points of the two intersection surfaces on the left side of the special-shaped part are taken to obtain the coordinate change data of the point in the radial direction. The coordinate change data of the structure vertex in the axial direction are also obtained. The above data are used to calculate the Poisson's ratio of the special-shaped part, and the Poisson's ratio value of the special-shaped part under a strain of 0.016 can be obtained.

[0066] S64, light-curing 3D printing model making

[0067] Use a light-curing 3D printer to 3D print the special-shaped part model, cell standard part model, and test mold model constructed in step S63. Import the model file in step S62 into the model pre-processing software ShapeWare, automatically repair the model, and then scale it by 50%. Move the model to the center of the platform, rotate the model so that its bottom is parallel to the platform, adjust the model's z-axis displacement to 0, and make the bottom of the model fit the platform. Some models cannot fit. In this case, use the "Polygon Cut" tool to cut the excess lines at the bottom of the model and delete the cut lines. At this time, the bottom of the model can be successfully fit to the platform. Adjust the slice thickness to 0.01mm, slice the model and save it as an RS print file. Transfer the file to the light-curing 3D printer, pour an appropriate amount of high-resolution photosensitive resin into the resin tank, and click the target file on the display to print. After the printing time is over, use a plastic spatula to clean the resin on the platform, use a metal shovel to remove the model, and use anhydrous ethanol to wash off the residual resin on the model. After the ethanol evaporates, use a gel pen to record the diamond hole side length, hole angle, and chamfer radius of the model on the back.

[0068] S65, Model Poisson's ratio and force-displacement data test

[0069] Use a microcomputer-controlled electronic universal testing machine to test the model printed out in step S64. Open the computer testing software SANS--PowerTest of the testing machine, select the 5KN sensor, turn on the instrument, click "Online", create a new experimental plan, adjust the compression direction to pressure, the deformation sensor to displacement, the material type to plate, and the control mode to program control. Add a new program control mode: inlet force 0.5N, compression speed 2mm / min, end value 0.5mm, set the output data to force-displacement, and save the experimental plan. Assemble and fix the upper and lower compression platforms of the universal mechanical tester, place the model to be tested and the test mold, move the upper platform of the instrument down until it just contacts the model, use a vernier caliper to measure the initial longitudinal height and transverse width of the model, then clear the force, displacement and strain values ​​in the software, click to start the test, pause the compression after every 0.5mm compression, export the original force-displacement data of the experiment, and use a vernier caliper to measure the transverse width of the model at this time. Measure each compression degree three times and take the average value. Repeat the above compression operation until the longitudinal compression distance is 3mm. Use the formula Calculate its lateral strain under different compression levels and longitudinal strain .in is the difference between the compressed distance and the initial distance of the model, is the initial distance of the model. The computer software Origin is used to draw the transverse strain-longitudinal strain diagram of each model. According to the formula Calculate the Poisson's ratio for each model at a strain of 0.016 and export the report generated by the software.

[0070] Finally, the target Poisson's ratio was compared with the actual measured Poisson's ratio (a structure constructed from the parameters derived from the model inversion process) to determine the error. The model achieved an average percentage error of only 8.0375% (Table 1), significantly outperforming traditional machine learning models (Table 2). In this comparative experiment, the machine learning model first fitted the data from step S1 and then used the optuna optimization algorithm to infer the attributes.

[0071] Table 1

[0072]

[0073] The table above compares the target Poisson's ratio with the actual measured Poisson's ratio (the structure formed by the parameters obtained by inverse deduction of the model). A cut angle of 0 indicates a standard part.

[0074] Table 2

[0075]

[0076] The above table compares the percentage errors of the model proposed by the present invention and other models.

[0077] This reverse design method for shaped negative Poisson's ratio metamaterials addresses the difficulty of deep learning training with small sample sizes by building an experimental database and establishing pseudo-labels. By optimizing network architecture and training strategies, it also addresses the difficulty of reverse prediction in traditional machine learning. This approach eliminates the need for trial-and-error experiments, addressing the long design cycles and lack of universal applicability of traditional methods. It achieves efficient and accurate design of shaped negative Poisson's ratio structures and verifies their effectiveness.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A reverse design method for special-shaped negative Poisson's ratio metamaterials based on INPR-GAN network, characterized by: The following steps are involved: S1. Constructing an experimental database: For irregular structures whose surfaces can be decomposed into rectangular isosceles triangles, a two-variable truncated half-face-centered cubic framework is used as the stacking cell. The coincident projection of the half-face-centered cubic framework and the rectangular isosceles triangle is utilized to meet the conformal design requirements of the array cells to the irregular units. The three-variable chamfered diamond hollowing of the framework ensures that the nonlinear "Poisson's ratio-strain" relationship of the cells is adjustable. A dataset is constructed that includes the mapping relationship between five structural parameters and the Poisson's ratio of the irregular cells, which contains the dual constraints of "conformal geometry and material mechanics". This provides basic data for model training. S2. Data augmentation: The original basic data obtained in step S1 is fitted with a random forest regression model. That is, the original data is sampled and pseudo labels are generated using the trained random forest model to obtain pseudo data with labels. The training set is expanded through a feature screening mechanism. S3. Establish an INPR-GAN network architecture: The generator network input is the concatenation of a 32-dimensional noise vector and a 1-dimensional Poisson's ratio conditional vector, which is processed by three fully connected layers to output a normalized five-dimensional structural parameter. The discriminator network input is the concatenation of the five-dimensional structural parameter and the 1-dimensional Poisson's ratio conditional vector, which is processed by three fully connected layers to output a one-dimensional structural parameter for probabilistic evaluation of data authenticity. This constructs an INPR-GAN network architecture with feature matching constraints. S4, two-stage adversarial training: The pseudo data generated in step S2 and the original basic data in step S1 are combined and input into the model in step S3 for training. The discriminator is trained to distinguish between real and generated data. Generator training is used to integrate adversarial loss and mean squared error loss to build a complete INPR-GAN network architecture, realize conditional generative adversarial learning of structural parameters and Poisson's ratio, and further optimize the generator and discriminator; S5. Inverse design method: Based on the INPR-GAN model trained in step S3, an inverse design method is constructed to automatically generate the target Poisson's ratio parameters through four steps: normalizing the target Poisson's ratio, generating a Gaussian noise vector, forward propagating the generator network, and denormalizing the parameters; S6. 3D printing to verify the effectiveness: The structural parameters obtained by inverse deduction of the INPR-GAN model in step S5 are used to construct a special-shaped bond. The structure is 3D printed using a light-curing 3D printer and tested using a microcomputer-controlled electronic universal testing machine. The Poisson's ratio data under a strain of 0.016 in step S1 is taken out and compared with the target Poisson's ratio to verify the effectiveness.

2. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 1, wherein: In step S1, a mapping data set containing five structural parameters including rhombus side length, included angle, chamfer, model height, and truncation angle and their corresponding Poisson's ratio is obtained through Solidworks software simulation. The Poisson's ratio at a strain of 0.016 is used as the label of the parameter combination data to form a mapping database between rhombus parameters and Poisson's ratio.

3. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 2, wherein: In step S1, the internal angles and chamfers of the rotated square structure negative Poisson's ratio cell are adjusted to make it diamond-shaped. After the structure is subjected to force, the diamond-shaped hole can be rotated and expanded around the vertex. At the same time, the side length, angle, chamfer offset and final cutting degree of the diamond-shaped hole are continuously adjusted to obtain more special-shaped part models with different hole parameters and cutting degrees. Then, a data set containing the mapping relationship between the five structural parameters and the Poisson's ratio of the special-shaped cell with the dual constraints of "conformal geometry and material mechanics" is constructed.

4. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 1, wherein: Step S2 is specifically as follows: S21, input the data set obtained in step S1 into the random forest model for forward training to obtain pseudo labels, and merge the predicted Poisson's ratio pseudo labels with the attributes to obtain labeled pseudo data; S22. Use the training set feature scaler to standardize the generation parameters, filter valid data with a Poisson's ratio between -0.15 and -0.01, and merge the pseudo data with the original data to construct an enhanced training set.

5. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 4, characterized in that: In step S21, kernel density estimation (KDE) is used to fit the empirical distribution of the discrete attributes of the data set in step S1, and Latin hypercube sampling (LHS) is performed on the continuous attributes within the measured extreme value interval to ensure uniform coverage of the parameter combination space. After generating pseudo data, MinMaxScaler (-1, 1) is used for normalization to eliminate pseudo data that violates physical and geometric constraints.

6. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 1, wherein: In step S3, the generator network hidden layer is equipped with the LeakyReLU activation function (slope 0.2) to enhance the nonlinear expression, and each layer is followed by the BatchNorm1d (batch normalization) operation to accelerate the convergence of the model; the output layer uses the Tanh activation function to constrain the parameters in the range [-1, 1], matching the normalization strategy of the experimental data, so that the generated structural parameters have a standardized distribution; the discriminator network hidden layers are equipped with the LeakyReLU activation function (slope 0.2) and Dropout regularization (probability 0.3) to prevent overfitting and enhance the generalization ability of the model. Finally, the probability evaluation of the authenticity of the output data is performed through the Sigmoid function.

7. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to any one of claims 1 to 6, characterized in that: In step S4, the discriminator training stage uses a binary cross entropy loss function to distinguish between real and generated data, and the generator training uses a hybrid loss function. The generator training stage integrates the adversarial loss and the feature matching loss, and jointly optimizes the adversarial loss and the feature matching loss. The feature matching loss is achieved by calculating the mean square error between the generated parameters and the real parameters. The weight coefficient is set to 0.5, which encourages the generator to maintain physical and geometric rationality while pursuing the adversarial effect. The binary cross entropy loss function formula is: The formula of the hybrid loss function is: The Adam algorithm is used as the optimizer in the joint optimization of adversarial loss and feature matching loss, with a learning rate of 0.0002, a batch size of 64, and 100 training cycles. The discriminator and generator loss values ​​are output every 10 training cycles to monitor the model convergence status. When the generator loss fluctuation range is less than 0.001 and lasts for 20 cycles, the training is terminated to ensure model stability and generation effect.

8. The reverse design method for a special-shaped negative Poisson's ratio metamaterial according to claim 7, characterized in that: In step S5, the target Poisson's ratio is input and normalized into a conditional vector. The generator receives N(0,1) distributed noise and the conditional vector, outputs the normalized structural parameters, and denormalizes the generated parameters to obtain the physical design parameters.

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