A design method for lattice metamaterials based on Kelvin structure

Abstract

The present invention discloses a method for designing lattice metamaterials based on Kelvin structures. The method comprises: firstly, generating a group of initial sample configurations based on the reference space coordinates of the equidistant Kelvin structure, and constructing an initial training data set based on the group of initial sample configurations; then, taking the representative elastic constant components of each group of elastic constant components as prediction values, training and obtaining multiple basic prediction functions corresponding to each representative elastic constant component; then, updating the training data set and training the multiple basic prediction functions corresponding to each representative elastic constant component for multiple times; after updating and iterating for several times, determining the optimal basic prediction function corresponding to each representative elastic constant component and constructing a prediction network model, and using the prediction network model to iteratively optimize the sample configuration corresponding to the target elastic constant matrix, obtaining the optimal sample configuration, and then completing the design of the lattice metamaterial. The method proposed by the present invention greatly reduces the time consumption and computational complexity of data set generation and network model training.

Description

Technical Field

[0001] The invention belongs to the field of mechanical properties of metamaterials and relates to a lattice metamaterial design method, in particular to a lattice metamaterial design method based on a Kelvin structure. Background Art

[0002] Lattice metamaterial is a typical mechanical metamaterial, which is composed of periodic arrangement and combination of structural materials (such as trusses). With the artificially set specific microstructure, it can obtain extraordinary mechanical properties that natural materials do not have. Changing the cell configuration of the lattice metamaterial will make the lattice metamaterial exhibit different mechanical properties. Lattice metamaterials can also achieve a combination of extraordinary material properties and functions. Therefore, there is a huge design space for the cell configuration of lattice metamaterials. For example, lattice metamaterials for acoustic wave guidance and vibration control, lightweight materials with high specific stiffness and specific strength, etc. Based on these characteristics, lattice metamaterials have great application prospects in aerospace, civil engineering, biomaterials and other fields.

[0003] The Kelvin structure is a typical lattice structure with Kelvin cells as the unit cells, which is an ideal model for open-cell foam materials. The structural characteristics of the Kelvin structure give it good energy absorption properties and have good application prospects in the fields of vibration reduction and protection. At the same time, its porous properties are conducive to maintaining permeability and thus maintaining the supply of nutrients to surrounding tissues when used as a biological implant material. One of the better applications is artificial bone implants. The premise for these applications to achieve good results is that the mechanical properties of the material must meet the design expectations. For example, when used as a vibration reduction material, the propagation of elastic waves is directly related to the elastic constant of the material; when used as an artificial bone implant, its stiffness matching with the surrounding tissue is an important influencing factor in the bone reconstruction process, because osteoblasts and osteoclasts control bone growth or absorption by sensing mechanical stimuli.

[0004] The mechanical properties of materials are directly affected by their elastic constants. Although the Kelvin structure can achieve the purpose of changing the elastic constants by changing its structural features, the complexity and diversity of its structural features lead to certain difficulties in reverse designing its geometric configuration for the target elastic constant matrix. Existing studies on reverse design of elastic constants based on Kelvin structures mainly focus on the category of orthogonal anisotropy, and the mapping relationship from structural features to elastic constants is constructed by mapping all components. Although this method is direct, it is not efficient enough and often requires a lot of computing resources and computing time. Secondly, beam units are used when constructing the mapping relationship, which affects the accuracy of the mapping relationship. This effect will be further amplified when the structural features are designed for the target elastic constant matrix in the future. Moreover, the conventional methods of changing the diameter of the rod, stretching and mixing the cells, etc., can only achieve a limited range of anisotropic elastic properties. Therefore, based on the Kelvin structure, how to efficiently and accurately construct the mapping relationship from structural features to elastic constants, and how to design structural features with the target elastic constant matrix through this mapping relationship, is still a problem that needs to be solved. Summary of the invention

[0005] The problems in existing lattice metamaterial design methods are:

[0006] 1) The traditional neural network-based prediction of "structure" to "elastic constant" often uses the method of training all components of the target elastic constant matrix, which consumes a huge amount of computing resources and computing time;

[0007] 2) Traditional training data sets for neural network training all come from direct finite element method calculation results, which consumes huge amounts of computing resources and time;

[0008] 3) The traditional neural network-based prediction of "structure" to "elastic constant" is limited to the range of orthogonal anisotropy, which makes it difficult to extend the reverse design of metamaterial elastic properties to the full anisotropy range;

[0009] 4) Traditional truss-type lattice metamaterials often use beam units in calculations, which reduces the accuracy of the calculated results and further affects the accuracy when optimizing the structural features of the elastic constants in the subsequent process.

[0010] The purpose of the present invention is to solve the above technical problems in the prior art and provide a lattice metamaterial design method based on Kelvin structure;

[0011] The specific technical solutions adopted by the present invention are as follows:

[0012] 1. A design method for lattice metamaterials based on Kelvin structure

[0013] S1: Determine the cell size corresponding to a single equidistant Kelvin structure, thereby determining its reference space coordinate vector P; then generate a set of initial sample configurations based on the reference space coordinate vector P of the equidistant Kelvin structure, and construct an initial training data set based on the set of initial sample configurations;

[0014] S2: Taking the representative elastic constant component of each group of elastic constant components as the prediction value, using the current training data set to train a neural network-based machine learning model under different initial conditions, and obtaining several basic prediction functions corresponding to the representative elastic constant component; after traversing and processing all representative elastic constant components, obtaining several basic prediction functions corresponding to each representative elastic constant component;

[0015] S3: updating the training data set, and combining the updated training data set, training a number of basic prediction functions corresponding to each representative elastic constant component for multiple times, and finally determining the optimal basic prediction function corresponding to each representative elastic constant component;

[0016] S4: Construct a prediction network model based on the optimal basic prediction function corresponding to each representative elastic constant component, and use the prediction network model to iteratively optimize the sample configuration X' corresponding to the target elastic constant matrix to obtain the optimal sample configuration, and complete the design of the lattice metamaterial based on the optimal sample configuration.

[0017] In S1, a set of initial sample configurations is generated based on the reference space coordinate vector P of the equidistant Kelvin structure, specifically:

[0018] Within the movable range of the independent vertices of the equidistant Kelvin structure, a set of spatial displacement vectors for all independent vertices is randomly generated, and the i-th spatial displacement vector W i After being applied to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained. i , satisfying X i =P+W i , after traversing and processing all spatial displacement vectors, a set of initial sample configurations are obtained.

[0019] In S1, an initial training data set is constructed based on the group of initial sample configurations, specifically:

[0020] The elastic constant matrix C corresponding to each initial sample configuration is obtained by finite element method simulation calculation. After traversing and processing each initial sample configuration in the group of initial sample configurations, the elastic constant matrix C corresponding to all initial sample configurations is obtained, thereby obtaining the original training data set. After data enhancement of the original training data set using the geometric rotation enhancement method, a data enhanced data set is obtained. The initial training data set is composed of the original training data set and the data enhanced data set.

[0021] The S2 is specifically:

[0022] S2.1: According to the physical meaning of the elastic constant components, the elastic constant components in the elastic constant matrix C are divided into several groups, and one component is selected from each group of elastic constant components as a representative elastic constant component;

[0023] S2.2: Taking the representative elastic constant component of each group of elastic constant components as the prediction value, using the current training data set to train a neural network-based machine learning model under different initial conditions, and obtaining several basic prediction functions corresponding to the representative elastic constant component of the group of elastic constant components;

[0024] S2.3: Taking the representative elastic constant components of other groups of elastic constant components as prediction values, repeat S2.2 to obtain several basic prediction functions corresponding to the representative elastic constant components of other groups of elastic constant components.

[0025] The S3 is specifically:

[0026] S3.1: Within the movable range of the independent vertices of the equidistant Kelvin structure, a set of spatial displacement vectors for all independent vertices is randomly generated, and the i-th spatial displacement vector W i 'After applying to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained i ', satisfying X i =P+W i ', after traversing and processing all spatial displacement vectors, a set of new sample configurations are obtained;

[0027] S3.2: For each sample configuration in the current group of new sample configurations, use several basic prediction functions corresponding to each representative elastic constant component to predict the representative elastic constant component corresponding to each sample configuration, and then use several basic prediction functions corresponding to the remaining representative elastic constant components to traverse and predict other representative elastic constant components corresponding to the current sample configuration, and determine its matching degree according to the predicted representative elastic constant components of the current sample configuration; traverse and process other sample configurations in the current group of new sample configurations to determine the matching degree of other sample configurations; construct a new supplementary data set according to the sample configurations with poor matching degree;

[0028] S3.3: adding the new supplementary data set to the existing training data set, using the new training data set to train several basic prediction functions corresponding to each representative elastic constant component and update the corresponding basic prediction functions;

[0029] S3.4: Repeat S3.1- S3.3 several times to complete the construction of a new training data set and the training of the basic prediction function, obtain several final basic prediction functions corresponding to each representative elastic constant component, and select the corresponding optimal basic prediction function from the several final basic prediction functions corresponding to the representative elastic constant component.

[0030] In S3.2, the matching degree of the sample configuration is the variance of the predicted representative elastic constant components. When the variances of all representative elastic constant components are less than or equal to the preset variance, the matching degree of the sample configuration is good, otherwise the matching degree of the sample configuration is not good. After traversing and judging the matching degrees of all sample configurations, the preset variance is calculated and updated.

[0031] In S3.3, a new supplementary data set is constructed based on the sample configurations with poor matching, specifically:

[0032] The elastic constant matrix C corresponding to each sample configuration with a poor matching degree is obtained by simulation calculation using the finite element method. After traversing and processing all sample configurations with a poor matching degree, the elastic constant matrix C corresponding to all sample configurations with a poor matching degree is obtained, thereby obtaining the first data set. After data enhancement of the first data set using the geometric rotation enhancement method, the second data set is obtained, and the first data set and the second data set form a new supplementary data set.

[0033] In S4, a prediction network model is constructed according to the optimal basic prediction function corresponding to each representative elastic constant component, specifically:

[0034] For the elastic constant components other than the representative elastic constant component in each group of elastic constant components, a rotation transformation function between the representative elastic constant component and each elastic constant component is added before the optimal basic prediction function corresponding to the current representative elastic constant component, and the basic prediction function of the elastic constant component is composed of the rotation transformation function corresponding to each elastic constant component and the optimal basic prediction function corresponding to the representative elastic constant component. The remaining elastic constant components of the current group of elastic constant components are traversed to obtain the basic prediction functions corresponding to all elastic constant components in the current group of elastic constant components; then all groups of elastic constant components are traversed to obtain the basic prediction functions corresponding to all elastic constant components in different groups of elastic constant components, and the basic prediction functions corresponding to all elastic constant components are set in parallel to form a prediction network model.

[0035] In S4, the sample configuration X' corresponding to the target elastic constant matrix is ​​iteratively optimized using the prediction network model to obtain the optimal sample configuration, which is specifically:

[0036] Based on the target elastic constant matrix C target , construct the objective function f(N(X'), Ctarget ), N(X') is the prediction network model, and the optimization algorithm is used to optimize the sample configuration X' at the local minimum and take it as the optimal sample configuration.

[0037] 2. A computer device

[0038] The device includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the Kelvin structure-based lattice metamaterial design method when executing the computer program.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1) Compared with the traditional method of training all elastic constant components through neural networks, the present invention adopts a rotation enhancement method based on neural networks, which greatly reduces the computing resources and computing time of machine learning model training.

[0041] 1) Compared with the traditional training data sets that are all directly generated by the finite element method, the present invention adopts a geometric rotation enhancement method, which greatly reduces the computing resources and computing time required to generate the training data set.

[0042] 3) Compared with the traditional elastic performance design which is limited to orthogonal anisotropy, the present invention has excellent forward prediction from "structure" to "elastic performance" and reverse design performance from "elastic performance" to "structure" for the fully anisotropic Kelvin structure.

[0043] 4) Compared with the traditional training data set for truss-type lattice metamaterials, which uses beam units for calculation in the finite element calculation method, the present invention uses finite element solid units to improve the accuracy of the training data set. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the Kelvin structure.

[0045] Figure 2 Schematic diagram of elastic constant components in the elastic constant matrix, where (a) is a schematic diagram of the elastic constant matrix and (b) is a schematic diagram of specific grouping of elastic constant components.

[0046] Figure 3 Schematic diagram of a neural network-based machine learning model.

[0047] Figure 4 Schematic diagram of the prediction effect for representative elastic constant components, where (a) is the first representative elastic constant component C 11 ' is a schematic diagram of the predicted effect, (b) is the second representative elastic constant component C 44' is a schematic diagram of the predicted effect, (c) is the third representative elastic constant component C 12 ' is a schematic diagram of the predicted effect, (d) is the fourth representative elastic constant component C 14 ' is a schematic diagram of the predicted effect, (e) is the fifth representative elastic constant component C 16 ' is a schematic diagram of the predicted effect, (f) is the sixth representative elastic constant component C 45 'Schematic diagram of the prediction effect.

[0048] Figure 5 Schematic diagram of the conjugate gradient method with bounded constraints.

[0049] Figure 6 is the result of the inverse design of the fully anisotropic elastic constant components of the Kelvin structure, where (a) is the R of the elastic constant matrix predicted by the machine learning model based on the neural network 2 , (b) is the elastic constant matrix R calculated by the finite element method 2 .

[0050] Figure 7 The results of the reverse design of the Kelvin structure for bovine femur, where (a) is the target elastic constant matrix and (b) is the elastic constant obtained by the reverse design of the present invention.

[0051] Figure 8 The present invention is a flow chart of the method. DETAILED DESCRIPTION

[0052] The present invention will be further described and illustrated below in conjunction with the accompanying drawings and specific implementation methods.

[0053] The present invention proposes a design method of lattice metamaterial based on Kelvin structure, such as Figure 8 As shown, the method comprises the following steps:

[0054] S1: Determine the rod unit diameter and the corresponding cell size a in a single equidistant Kelvin structure, a=3mm, the rod unit diameter is a / 12, that is, the rod unit diameter is 0.25mm; the constituent material of the Kelvin structure is selected as 3D printing resin, whose Young's modulus E=563 Mpa and Poisson's ratio v=0.3; the independent vertices are Figure 1 The vertices in the structure are numbered 2-12. The spatial positions of all independent vertices in a single equidistant Kelvin structure form a reference space coordinate vector P; a set of initial sample configurations is generated based on the reference space coordinate vector P of the equidistant Kelvin structure, and an initial training data set is constructed based on the set of initial sample configurations;

[0055] The cell corresponding to the Kelvin structure in this embodiment is a truss-type lattice metamaterial, and its elastic properties are affected by the material properties and geometric characteristics of the Kelvin structure. The cells of the Kelvin structure can form an entire macroscopic material by array operation, and the elastic properties of the macroscopic material are determined by the smallest material volume element (representative volume unit RVE). In the description of the present invention, "elastic properties" and "elastic constants" refer to the elastic properties and elastic constants of the representative volume unit when constituting the macroscopic material. Figure 1 As shown in the figure, the smallest cell has 24 vertices, forming a tetradecahedron with 6 quadrilaterals and 8 hexagons, and 36 edges. When all 36 edges are of equal length, an isometric Kelvin structure is formed, and all vertices are located on the 6 faces of the cube; according to the array arrangement of the lattice metamaterial, only a total of 12 vertices in 3 periodic directions need to be determined to determine the Kelvin structure, and the positions of any 11 vertices can be represented by the remaining vertices as reference vertices, that is, there are 11 independent vertex positions; taking independent vertex No. 1 as the reference vertex as an example, the spatial positions of independent vertices No. 2-12 can be represented by the reference space coordinate vector P, satisfying P=[x 2 -x 1 y 2 -y 1 z 2 -z 1 … x 12 -x 1 y 12 -y 1 z 12 -z 1 ] 1×33 When the position of the independent vertex relative to the reference vertex remains unchanged, the movement of the reference vertex in space is equivalent to the overall movement of the structure in space, which will not affect the elastic performance of the structure; changing the position of the independent vertex will cause the elastic performance of the Kelvin structure to change, that is, the elastic constant matrix C changes.

[0056] Among them, a set of initial sample configurations are generated based on the reference space coordinate vector P of the equidistant Kelvin structure, specifically:

[0057] The space occupied by a single equidistant Kelvin structure is taken as the representative volume unit (RVE), and the cube model boundary of the representative volume unit is limited to the range of ±1 / 6a, i.e., ±0.5mm, along the x, y, and z directions of the coordinate axis. Within the movable range of the independent vertices of the equidistant Kelvin structure, a set of spatial displacement vectors for all independent vertices is randomly generated, and the i-th spatial displacement vector W is set to i After being applied to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained. i , satisfying X i=P+W i After traversing and processing all spatial displacement vectors, a set of initial sample configurations is obtained. It should be noted that the elements of the spatial displacement vector have a one-to-one correspondence with the elements of the reference spatial coordinate vector P. In order to avoid embedding due to periodic array arrangement when the vertex moves, the absolute value of each element in the movement range of the independent vertex in space (i.e., the spatial displacement vector) needs to be limited.

[0058] The initial training data set is constructed based on this group of initial sample configurations, specifically:

[0059] The elastic constant matrix C corresponding to each initial sample configuration is obtained by simulation and calculation using the finite element method. After traversing and processing each initial sample configuration in the group of initial sample configurations, the elastic constant matrix C corresponding to all initial sample configurations is obtained, thereby obtaining the original training data set. After data enhancement is performed on the original training data set using the geometric rotation enhancement method, a data enhancement data set is obtained. The initial training data set is composed of the original training data set and the data enhancement data set. Specifically, the finite element method is used in ABAQUS software for simulation and realization. The unit adopts the tetrahedral solid unit C3D10, and the grid size is about 0.02a. After the finite element method simulation and calculation, each obtained sample configuration X and the corresponding elastic constant matrix C are added to the original training data set D1. The sample configuration X in the original training data set D1 is rotated 90 degrees along the y-axis and z-axis respectively with its midpoint as the rotation center to obtain the y-axis enhanced configuration X' y and the corresponding elastic constant matrix C y And the z-axis enhanced configuration X' z and the corresponding elastic constant matrix C z , and then added to the corresponding y-axis enhanced data set D2 and z-axis enhanced data set D3. The initial training data set is composed of the original training data set D1, the y-axis enhanced data set D2 and the z-axis enhanced data set D3. In the description of the present invention, the simulation and calculation of the "finite element method" refer to the simulation and calculation under the three-dimensional periodic boundary conditions.

[0060] The specific process of data enhancement is as follows:

[0061] Take the given sample configuration X as an example, take its midpoint as the rotation center, rotate 90 degrees clockwise along the positive direction of the z axis, and the resulting new structure is recorded as X' z =R z (X); New sample configuration X' z It represents the same configuration as the given sample configuration X, except that its posture in space has changed. The new sample configuration X' z The stress-strain relationship in the x direction is equal to the stress-strain relationship in the y direction in the given sample configuration X; similarly, the new sample configuration X' zThe stress-strain relations in other directions in the given sample configuration X are all equal, and the new sample configuration X' z The elastic constant matrix is ​​denoted as C z , C z =S z (C), where S z ( ) represents a coordinate rotation transformation function; the present invention can expand the data set by simply rotating the data set 90 degrees along the y-axis and the z-axis without performing finite element calculations, thereby greatly saving computing resources and computing time.

[0062] S2: Taking the representative elastic constant component of each group of elastic constant components as the prediction value, using the current training data set to train a neural network-based machine learning model under different initial conditions, and obtaining several basic prediction functions corresponding to the representative elastic constant component; after traversing and processing all representative elastic constant components, obtaining several basic prediction functions corresponding to each representative elastic constant component;

[0063] S2 is specifically:

[0064] S2.1: According to the physical meaning of the elastic constant components, the elastic constant components in the elastic constant matrix C are divided into 6 groups, and one component is selected from each group of elastic constant components as a representative elastic constant component. It should be noted that, Figure 2 As shown in (a), the elastic constant matrix has a total of 36 elastic constant components. According to its symmetry, it can be reduced to 21 independent components; Figure 2 As shown in (b), according to the physical meaning of the elastic constant components, they can be divided into six groups. Specifically, the first group: the relationship between the normal strain in the i direction and the normal stress in the i direction, such as the relationship between the normal strain in the x direction and the normal stress in the x direction C 11 , the relationship between the normal strain in the y direction and the normal stress in the y direction C 22 , the relationship between the normal strain in the z direction and the normal stress in the z direction C 33 ; The second group: the relationship between the normal strain in the i direction and the normal stress in the j direction (i ≠ j), such as the relationship between the normal strain in the x direction and the normal stress in the y direction C 12 , the relationship between the normal strain in the x direction and the normal stress in the z direction C 13 , the relationship between the normal strain in the y direction and the normal stress in the z direction C 23 ; The third group: the relationship between the shear strain corresponding to the i direction and the shear stress corresponding to the i direction, such as the relationship between the shear strain along the z direction and the shear stress along the z direction on the plane perpendicular to the y direction C 44 , the relationship between the shear strain along the x direction and the shear stress along the x direction on the plane perpendicular to the z direction C 55 , the relationship between the shear strain along the y direction and the shear stress along the y direction on the plane perpendicular to the x direction C66 ; The fourth group: the relationship between the shear strain corresponding to the i direction and the shear stress corresponding to the j direction, such as the relationship between the shear strain along the x direction on the plane perpendicular to the z direction and the shear stress along the z direction on the plane perpendicular to the y direction C 45 , the relationship between the shear strain along the y direction on the plane perpendicular to the x direction and the shear stress along the z direction on the plane perpendicular to the y direction C 46 , the relationship between the shear strain along the y direction on the plane perpendicular to the x direction and the shear stress along the x direction on the plane perpendicular to the z direction C 56 ; The fifth group: the relationship between the shear strain corresponding to the i direction and the normal stress corresponding to the i direction, such as the relationship between the shear strain along the z direction and the normal stress along the x direction on the plane perpendicular to the y direction C 14 , the relationship between the shear strain in the x direction and the normal stress in the y direction on the plane perpendicular to the z direction C 25 , the relationship between the shear strain in the y direction and the normal stress in the z direction on the plane perpendicular to the x direction C 36 ; The sixth group: the relationship between the shear strain corresponding to the i direction and the normal stress corresponding to the j direction, such as the relationship between the shear strain along the x direction and the normal stress in the x direction on a plane perpendicular to the z direction C 15 , the relationship between the shear strain along the y direction and the normal stress in the x direction on the plane perpendicular to the x direction C 16 , the relationship between the shear strain along the y direction and the normal stress in the y direction on the plane perpendicular to the x direction C 26 , the relationship between the shear strain along the z direction and the normal stress in the y direction on the plane perpendicular to the y direction C 24 , the relationship between the shear strain along the z direction and the normal stress in the z direction on the plane perpendicular to the y direction C 34 , the relationship between the shear strain along the x direction and the normal stress in the z direction on the plane perpendicular to the z direction C 35 .

[0065] S2.2: Take the representative elastic constant component of each group of elastic constant components as the predicted value, use the current training data set to train the neural network-based machine learning model under different initial conditions (the initial condition is the random seed in the neural network), and obtain several basic prediction functions corresponding to the representative elastic constant components of the group of elastic constant components; the basic prediction function is used to predict the value of the corresponding representative elastic constant component when the Kelvin structure has different structural characteristics. Select the relationship between the normal strain in the x direction and the normal stress in the x direction C 11 As an example of the first representative elastic constant component, the relationship between the normal strain in the x direction and the normal stress in the x direction C is calculated using different neural network random seeds. 11 After 20 trainings, 20 11 The prediction function N 11(X). In the training process of the machine learning model, the input layer is the spatial coordinate information of 11 independent vertices, and the output layer is the predicted elastic constant component information, that is, the input layer is 33 units, the output layer is 1 unit, and there are several fully connected hidden layers and hidden units in the middle, such as Figure 3 As shown in the figure, the activation function uses Leaky ReLU, the optimization algorithm is Adam algorithm, and the number of training steps is 1000.

[0066] S2.3: Taking the representative elastic constant components of other groups of elastic constant components as prediction values, repeat S2.2 to obtain several basic prediction functions corresponding to the representative elastic constant components of other groups of elastic constant components.

[0067] S3: updating the training data set, and combining the updated training data set, training a number of basic prediction functions corresponding to each representative elastic constant component for multiple times, and finally determining the optimal basic prediction function corresponding to each representative elastic constant component;

[0068] S3 is specifically:

[0069] S3.1: Randomly generate a set of 80,000 spatial displacement vectors for all independent vertices within the movable range of the independent vertices of the equidistant Kelvin structure, and transform the i-th spatial displacement vector W i 'After applying to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained i ', satisfying X i =P+W i ', after traversing and processing all spatial displacement vectors, a set of new sample configurations are obtained;

[0070] S3.2: For each sample configuration in the current group of new sample configurations, use several basic prediction functions corresponding to each representative elastic constant component to predict the representative elastic constant component corresponding to each sample configuration respectively, and then use several basic prediction functions corresponding to the remaining representative elastic constant components to traverse and predict other representative elastic constant components corresponding to the current sample configuration, and determine its matching degree according to the predicted representative elastic constant components of the current sample configuration; traverse and process other sample configurations in the current group of new sample configurations to determine the matching degree of other sample configurations; construct a new supplementary data set based on sample configurations with poor matching degree; when the number of sample configurations in the new supplementary data set reaches 20,000, execute the next step.

[0071] In S3.2, the matching degree of the sample configuration is the variance of each representative elastic constant component predicted. When all variances are less than or equal to the preset variance, the matching degree of the sample configuration is good, otherwise the matching degree of the sample configuration is not good; after traversing and judging the matching degree of all sample configurations, the preset variance is calculated and updated. In this embodiment, the initial value of the preset variance is set to 5.5%. The updated preset variance is the preset variance before the update minus 0.5%.

[0072] S3.3: adding the new supplementary data set to the existing training data set, using the new training data set to train several basic prediction functions corresponding to each representative elastic constant component and update the corresponding basic prediction functions;

[0073] In S3.3, a new supplementary data set is constructed based on the sample configurations with poor matching, specifically:

[0074] The elastic constant matrix C corresponding to each sample configuration with poor matching is obtained by finite element method simulation calculation. After traversing and processing all sample configurations with poor matching, the elastic constant matrix C corresponding to all sample configurations with poor matching is obtained, thereby obtaining the first data set. After data enhancement of the first data set using the geometric rotation enhancement method, the second data set is obtained. The first data set and the second data set form a new supplementary data set and are added to the existing training data set.

[0075] S3.4: Repeat S3.1- S3.3 several times to complete the construction of a new training data set and the training of the basic prediction function, obtain several final basic prediction functions corresponding to each representative elastic constant component, and select the corresponding optimal basic prediction function from the several final basic prediction functions corresponding to the representative elastic constant component. In this embodiment, when the preset variance is less than 1%, the construction of a new training data set and the training of the basic prediction function are completed. For each elastic constant component, the goodness of fit R 2 Select an optimal basic prediction function, goodness of fit R 2 The closer it is to 1, the better the fitting effect of the prediction function. The performance of the optimal basic prediction function corresponding to the six representative elastic constant components in this embodiment on the test set is as follows Figure 4 As shown, Figure 4 (a) is the first representative elastic constant component C 11 'The schematic diagram of the prediction effect, Figure 4 (b) is the second representative elastic constant component C 44 'The schematic diagram of the prediction effect, Figure 4 (c) is the third representative elastic constant component C 12 'The schematic diagram of the prediction effect, Figure 4 (d) is the fourth representative elastic constant component C14 'The schematic diagram of the prediction effect, Figure 4 (e) is the fifth representative elastic constant component C 16 'The schematic diagram of the prediction effect, Figure 4 (f) is the sixth representative elastic constant component C 45 'Schematic diagram of the prediction effect.

[0076] S4: Construct a prediction network model based on the optimal basic prediction function corresponding to each representative elastic constant component, and use the prediction network model to iteratively optimize the sample configuration X' corresponding to the target elastic constant matrix to obtain the optimal sample configuration, and complete the design of the lattice metamaterial based on the optimal sample configuration.

[0077] In S4, a prediction network model is constructed according to the optimal basic prediction function corresponding to each representative elastic constant component, specifically:

[0078] For the other elastic constant components except the representative elastic constant component in each group of elastic constant components, a rotation transformation function between the representative elastic constant component and each elastic constant component is added before the optimal basic prediction function corresponding to the current representative elastic constant component, and the basic prediction function of the elastic constant component is composed of the rotation transformation function corresponding to each elastic constant component and the optimal basic prediction function corresponding to the representative elastic constant component, that is, a rotation enhancement method based on a neural network, traverses and processes the remaining elastic constant components of the current group of elastic constant components, thereby obtaining the basic prediction functions corresponding to all elastic constant components in the current group of elastic constant components; then traverses and processes all groups of elastic constant components to obtain the basic prediction functions corresponding to all elastic constant components in different groups of elastic constant components, and the basic prediction functions corresponding to all elastic constant components are set in parallel to form a prediction network model. The present invention proposes a rotation enhancement method based on a neural network, which extends the basic prediction function for the representative elastic constant component to a prediction that can be applied to the entire group of elastic constant components, and only needs to use the conversion relationship of spatial rotation, without the need for additional neural network training.

[0079] The relationship between the normal strain in the x direction and the normal stress in the x direction in the first set of elastic constant components is C 11 As an example of representative elastic constants, when the sample configuration is X, the basic prediction function N is obtained by training. 11 (X) Relationship between normal strain in x direction and normal stress in x direction C 11 The predicted value C 11 '= N 11 (X); The new sample configuration obtained by rotating the sample configuration X 90 degrees clockwise along the positive direction of the z axis with its midpoint as the rotation center is recorded as X' z =R z (X), new sample configuration X' zIt represents the same configuration as the sample configuration X, but the posture in space has changed. The stress-strain relationship in the y direction in the sample configuration X is the same as the new sample configuration X' z The stress-strain relationship in the x-direction is equal, that is:

[0080] N 22 (X) = N 11 (X' z ) = N 11 (R z (X)

[0081] The other components can be expressed in a corresponding way; therefore, only 6 machine learning models based on neural networks need to be trained, and then by calculating the new relative elastic constant components after changing the structural posture, the prediction of all 21 elastic constant components can be achieved. The prediction network model of the Kelvin structure from "structure" to "C" can be expressed as C'= N(X); this method effectively reduces the number of neural networks that need to be trained and greatly increases the training efficiency.

[0082] In S4, the sample configuration X' corresponding to the target elastic constant matrix is ​​iteratively optimized using the prediction network model to obtain the optimal sample configuration, specifically:

[0083] Based on the target elastic constant matrix C target , construct the objective function f(N(X'), C target ), N(X') is the prediction network model, and the optimization algorithm is used to optimize the sample configuration X' at the local minimum and take it as the optimal sample configuration.

[0084] The objective function in this embodiment satisfies the following formula:

[0085] f(N(X'), C target )=[1 / 21Σ 6 j=i Σ 6 i=1 (N(X')- C target ) 2 ] 0.5

[0086] The optimization algorithm is the conjugate gradient method with bounded constraints, and its process is as follows Figure 5 shown.

[0087] 50 structures are randomly generated and the elastic constants of these 50 structures are calculated. These 50 elastic constants are used as design targets. Through the inverse design method, for each target elastic constant matrix C target, and a corresponding optimal solution X' is obtained. For each solution X' obtained by reverse design, two elastic constant matrices can be calculated. One is the elastic constant matrix C used in the optimization algorithm and predicted by the prediction network model. NN ; The other is the finite element method calculation result C corresponding to the actual structure FE . The target elastic constant matrix C target Respectively with the two elastic constant matrices C NN and C FE By comparison, the elastic constant matrix C predicted by the prediction network model NN R of each component 2 Value Figure 6 As shown in (a), the finite element method calculation result C FE R of each component 2 Value Figure 6 as shown in (b).

[0088] The elastic constant matrix of bovine femur obtained by theoretical calculation is used as the target elastic constant matrix C target ,like Figure 7 The elastic modulus of the material is selected to be E=31GPa, Poisson's ratio v=0.3, and the elastic constant matrix obtained by reverse design according to the method of the present invention is as follows: Figure 7 (b) and the target elastic constant matrix C target In comparison, the maximum absolute error is 0.02GPa, which is a relatively high precision result.

[0089] Finally, it should be noted that the above embodiments and explanations are only used to illustrate the technical solution of the present invention rather than to limit it. Those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope disclosed in the technical solution of the present invention, which should be included in the scope of protection of the claims of the present invention.

Claims

1. A method for designing lattice metamaterials based on Kelvin structure, characterized in that: The steps include: S1: Determine the cell size corresponding to a single equidistant Kelvin structure, thereby determining its reference space coordinate vector P; then generate a set of initial sample configurations based on the reference space coordinate vector P of the equidistant Kelvin structure, and construct an initial training data set based on the set of initial sample configurations; S2: Taking the representative elastic constant component of each group of elastic constant components as the prediction value, using the current training data set to train a neural network-based machine learning model under different initial conditions, and obtaining several basic prediction functions corresponding to the representative elastic constant component; after traversing and processing all representative elastic constant components, obtaining several basic prediction functions corresponding to each representative elastic constant component; S3: updating the training data set, and combining the updated training data set, training a number of basic prediction functions corresponding to each representative elastic constant component for multiple times, and finally determining the optimal basic prediction function corresponding to each representative elastic constant component; S4: Construct a prediction network model based on the optimal basic prediction function corresponding to each representative elastic constant component, use the prediction network model to iteratively optimize the sample configuration X' corresponding to the target elastic constant matrix, obtain the optimal sample configuration, and complete the design of the lattice metamaterial based on the optimal sample configuration; In S1, an initial training data set is constructed based on the group of initial sample configurations, specifically: The elastic constant matrix C corresponding to each initial sample configuration is obtained by finite element method simulation calculation. After traversing and processing each initial sample configuration in the group of initial sample configurations, the elastic constant matrix C corresponding to all initial sample configurations is obtained, thereby obtaining the original training data set. After data enhancement of the original training data set using the geometric rotation enhancement method, a data enhanced data set is obtained. The initial training data set is composed of the original training data set and the data enhanced data set.

2. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: In S1, a set of initial sample configurations is generated based on the reference space coordinate vector P of the equidistant Kelvin structure, specifically: Within the movable range of the independent vertices of the equidistant Kelvin structure, a set of spatial displacement vectors for all independent vertices is randomly generated, and the i-th spatial displacement vector W i After being applied to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained. i , satisfying X i =P+W i , after traversing and processing all spatial displacement vectors, a set of initial sample configurations are obtained.

3. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: The S2 is specifically: S2.1: According to the physical meaning of the elastic constant components, the elastic constant components in the elastic constant matrix C are divided into several groups, and one component is selected from each group of elastic constant components as a representative elastic constant component; S2.2: Taking the representative elastic constant component of each group of elastic constant components as the prediction value, using the current training data set to train a neural network-based machine learning model under different initial conditions, and obtaining several basic prediction functions corresponding to the representative elastic constant component of the group of elastic constant components; S2.3: Taking the representative elastic constant components of other groups of elastic constant components as prediction values, repeat S2.2 to obtain several basic prediction functions corresponding to the representative elastic constant components of other groups of elastic constant components.

4. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: The S3 is specifically: S3.1: Within the movable range of the independent vertices of the equidistant Kelvin structure, a set of spatial displacement vectors for all independent vertices is randomly generated, and the i-th spatial displacement vector W i 'After applying to the reference space coordinate vector P of the equidistant Kelvin structure, the corresponding sample configuration X is obtained i ', satisfying X i =P+W i ', after traversing and processing all spatial displacement vectors, a set of new sample configurations are obtained; S3.2: For each sample configuration in the current group of new sample configurations, use several basic prediction functions corresponding to each representative elastic constant component to predict the representative elastic constant component corresponding to each sample configuration, and then use several basic prediction functions corresponding to the remaining representative elastic constant components to traverse and predict other representative elastic constant components corresponding to the current sample configuration, and determine its matching degree according to the predicted representative elastic constant components of the current sample configuration; traverse and process other sample configurations in the current group of new sample configurations to determine the matching degree of other sample configurations; construct a new supplementary data set according to the sample configurations with poor matching degree; S3.3: adding the new supplementary data set to the existing training data set, using the new training data set to train several basic prediction functions corresponding to each representative elastic constant component and update the corresponding basic prediction functions; S3.4: Repeat S3.1- S3.3 several times to complete the construction of a new training data set and the training of the basic prediction function, obtain several final basic prediction functions corresponding to each representative elastic constant component, and select the corresponding optimal basic prediction function from the several final basic prediction functions corresponding to the representative elastic constant component.

5. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: In S3.2, the matching degree of the sample configuration is the variance of the predicted representative elastic constant components. When the variances of all representative elastic constant components are less than or equal to the preset variance, the matching degree of the sample configuration is good, otherwise the matching degree of the sample configuration is not good. After traversing and judging the matching degrees of all sample configurations, the preset variance is calculated and updated.

6. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: In S3.3, a new supplementary data set is constructed based on the sample configurations with poor matching, specifically: The elastic constant matrix C corresponding to each sample configuration with a poor matching degree is obtained by simulation calculation using the finite element method. After traversing and processing all sample configurations with a poor matching degree, the elastic constant matrix C corresponding to all sample configurations with a poor matching degree is obtained, thereby obtaining the first data set. After data enhancement of the first data set using the geometric rotation enhancement method, the second data set is obtained, and the first data set and the second data set form a new supplementary data set.

7. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: In S4, a prediction network model is constructed according to the optimal basic prediction function corresponding to each representative elastic constant component, specifically: For the elastic constant components other than the representative elastic constant component in each group of elastic constant components, a rotation transformation function between the representative elastic constant component and each elastic constant component is added before the optimal basic prediction function corresponding to the current representative elastic constant component, and the basic prediction function of the elastic constant component is composed of the rotation transformation function corresponding to each elastic constant component and the optimal basic prediction function corresponding to the representative elastic constant component. The remaining elastic constant components of the current group of elastic constant components are traversed to obtain the basic prediction functions corresponding to all elastic constant components in the current group of elastic constant components; then all groups of elastic constant components are traversed to obtain the basic prediction functions corresponding to all elastic constant components in different groups of elastic constant components, and the basic prediction functions corresponding to all elastic constant components are set in parallel to form a prediction network model.

8. The method for designing a lattice metamaterial based on a Kelvin structure according to claim 1, characterized in that: In S4, the sample configuration X' corresponding to the target elastic constant matrix is ​​iteratively optimized using the prediction network model to obtain the optimal sample configuration, which is specifically: Based on the target elastic constant matrix C target , construct the objective function f(N(X'), C target ), N(X') is the prediction network model, and the optimization algorithm is used to optimize the sample configuration X' at the local minimum and take it as the optimal sample configuration.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for designing a lattice metamaterial based on a Kelvin structure as described in any one of claims 1 to 8 are implemented.

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